Quantum World

Quantum phase slip

2012-01-05T12:51:00.000-08:00

A superfluid shows several strange behaviors which are absent in a classical fluid. One such phenomenon that can be observed in superfluids is the nucleation of quantized vortices. Consider the flow of a superfluid through a narrow channel. A vortex may nucleate in the fluid near its one edge due to thermal or quantum fluctuations, and it may roll across the channel. When this happens, the superfluid loses its phase and hence the velocity because the vortex carries energy with it and finally it dissipates as thermal energy. The loss in phase in such an event is 2pi. Such an event is called a quantum phase slip event or a velocity slip event. A quantum phase slip event can be utilized to detect rotation by using a toroidal supefluid in a superfliud gyroscope.

Happy New Year 2012 !

2011-12-29T18:20:00.001-08:00

Happy New Year 2012 !

Eigenstates, eigenvectors, and eigenvalues

2011-12-27T08:35:00.000-08:00

The eigenstates of a system are its characteristic states, the eigenvectors are the characteristic vectors describing the states, and the eigenvalues are the characteristic values representing the states of the system. For example, if we consider a one dimensional quantum harmonic oscillator, its ground state is one of its eigenstates which is represented by the eigenvector |g> and the eigenvalue is (one-half *hbar*omega), where (omega) is the frequency of the oscillator. The other eigenstates of the oscillator are the excited states |e> with the increase of energy by (hbar*omega) while climbing up from the ground state.

Quantum World

2011-12-26T07:03:00.000-08:00

'The World of Small' has been given a new title 'Quantum World' to make its purpose obvious to the readers !

Happy reading !

Condensed Matter via Atomic Physics

2011-10-16T08:43:00.000-07:00

Condensed matter systems are complicated systems because they are ensemble of atoms and molecules held tight by inter-atomic and inter-molecular forces. The forces arise as a result of various interactions - interactions between electrons in neighboring atoms, dipole interactions, overlap of the wave functions, etc. A condensed matter system may also have defects and dislocations of various kinds. Therefore, studying the properties of condensed matter systems like a chunk of gold or a cup of water is not an easy subject.

Because of the discovery of new ideas and a rapid development of technology, there are a lot of new methods developed to study condensed matter systems. One such way is simulating condensed matter using an optical lattice. An optical lattice is a 'light crystal' formed by interfering laser light waves traveling in opposite directions. A pair of counter-propagating laser light waves form a standing wave - a wave with intensity maxima and minima at regular spatial intervals. This is a one dimensional optical lattice. Two orthogonal pairs of lasers form a sheet of optical lattice - a two dimensional structure. If three pairs of counter-propagating lasers along X-, Y- , and Z- directions interfere each other, they form a structure which is called a three dimensional optical lattice.

An optical lattice can be controlled as you wish, by varying the wavelength of the component lasers. What is an optical lattice good for? An optical lattice is a clean system - free of defects. It is tunable, controllable and easily manipulated as desired and required. An optical lattice can simulate a condensed matter system. How? In an optical lattice, there are arrays of regularly spaced sites of low potential which can be filled with atom(s). One can fill with similar or dissimilar atoms in the sites. Therefore, the optical lattice with atoms sitting in the potential minima simulates condensed matter systems.

A condensed matter system as it stands is 'GOD-MADE', and so it can not be manipulated easily. For example, you can not change the lattice constant or the coupling strength in a block of silver. Therefore, a system which may represent widely distributed condensed matter systems - ranging from a water molecule to the complex structure like a human brain is extremely important to understand the properties of the condensed matter, and ultimately the Universe !

Note: This posting is in progress. Your comments are highly appreciated !

Happy Deepawali 2068 !

2011-10-15T07:46:00.000-07:00

We wish you all a very HAPPY

DEEPAWALI of 2068 !

BOSE-EINSTEIN CONDENSATE vs EXAM

2011-09-29T10:50:00.000-07:00

Read for fun !

A Bose-Einstein condensate(BEC) is like an Exam ! It seems funny, but please keep on reading, I'll prove it. A BEC is created out of atoms or molecules at low temperatures so that all atoms in an ensemble reach the ground state of the potential or a trap. A commonly used trap is a Magneto-Optical Trap (MOT). This is like an exam room with physical walls, exam questions, proctors, professors, and the career in a long term. They bind the test-takers in the exam room tightly.

The most energetic atoms leave an MOT quickly, the same way as a smart test-taker does. The low energy atoms go towards the lower and lower state of the trap and they are bound to form a BEC. Similarly, a less smart test-taker remains in the exam room for the whole time assigned to the exam or even more if the proctors or professors allow to do so ! If the trap is stronger or tighter, the atoms are more firmly trapped than in a weaker trap and the coherence is also maintained for a longer time. Analogously, if the questions in the exam are tougher, it makes a test-taker to remain in the exam room for a longer time; but if the questions are easier, the test takers escape right away ! A good exam will help making a good career of a test taker; it is a similar situation to a good BEC, which can be used for various purposes ranging from the study of its properties to the applications in inertial navigation systems and precision measurements. Oh, most importantly, all atoms in a BEC are in the same quantum state like all the test takers in an exam room; all of them are solving the problems the same way, with a goal of succeeding in the test; they are supposedly in the same state of their minds!

I hope I convinced you that a BOSE-EINSTEIN CONDENSATE is NOT different from an EXAM !

Spin-1/2 system is bizarre object !

2011-07-24T10:10:00.000-07:00

Consider a spin-1/2 particle. Rotate it about an axis by a 2 pi angle. You are not getting it back into the same state but with sign flipped. If you rotate it further by another 2 pi angle, you will see the particle in the original state. This is a bizarre object, which is beyond our intuition !

If you ask physicists, why is this? The answer is simple : it is an SU(2) physics, not an SO(3) ! If you want to visualize it, please look at Feynman's description of the rotation of a coffee cup in the following links:

(1) WIKI: http://en.wikipedia.org/wiki/Orientation_entanglement

(2) DEMO: http://www.youtube.com/watch?v=Rzt_byhgujg

Your views on this matter are highly welcome !

Happy New Year !

2011-04-09T05:49:00.001-07:00

HAPPY NEW YEAR 2068 B.S. !

Happy New Year 2011

2010-12-23T08:41:00.000-08:00

HAPPY NEW YEAR 2011 !

Quantum Biology

2010-12-16T06:01:00.000-08:00

If there is something very complex and mysterious in nature, that should be the creation of 'life' from 'non-living' atoms and molecules. How is life created out of these atoms and molecules? Keeping the identity from generation to generation with slight modifications in each generation is a real mystery. No two individuals are exactly identical ! 'Thinking ability' or 'intelligence' is a superior quality that humans have; how does this work? Will classical thoughts and laws be enough to solve this mystery or should quantum physics come into play to address this problem ? Erwin Schrodinger, a pioneer of Quantum Physics wrote 'What is life?' in the 1930s and has expressed his thoughts about this in this book. What is BEYOND there than what we think about life?

Let's consider the living beings around us. There are lives of all kinds in nature and they are going this way from millions of years in the past. What forms of life were there in the start of life? It might be an assembly of some materials in a little microscopic pouch which showed some signs - movement, being two or more from the single existing one in the course of time, absorbing some water or air, etc, etc. At first what stimulated the formation of this pouch out of the those non-living atoms? There is another mystery there of atoms and its constituents but for now lets assume that the atoms were already there for some reason. Why did that pouch need to proliferate? Why did it start moving?

Note: This posting is in progress.

Happy Dasain and Tihar 2067 !

2010-10-08T06:05:00.000-07:00

We wish you, your family, and your near and dear ones a very happy Dasain and Tihar of 2067 !

BEC and spontaneous symmetry breaking

2010-09-09T17:52:00.000-07:00

When we consider a non interacting or a weakly interacting dilute thermal gas containing in a vessel, there is a symmetry in the system. That means for an atom, there is not a preferred direction, all directions look the same and it has a random phase. Once the gas is cooled to some low temperature in a trap, it enters in a new phase called a condensate, in which all atoms lie in the same quantum state and have the same macroscopic quantum phase, which is a completely different situation in comparison to the thermal gas. Therefore, the phenomenon of Bose-Einstein condensation is a spontaneous symmetry breaking !

Note: This posting is in progress !

Optically synthesized magnetic field

2010-07-21T18:29:00.000-07:00

When charged particles move in a magnetic field, gauge potentials arise and the effective Hamiltonian has a term containing the vector potential, A. Neutral atoms can also behave like charged particles if the container in rotated in a trapping magnetic fields. But recently, an optically synthesized magnetic field has been created where the neutral atoms experience an effective gauge potential without any rotation, similar to the case of charged particles in an electromagnetic field.

Please look at the following reference for details:

(1) http://www.nature.com/nature/journal/v462/n7273/full/nature08609.html

(2) http://prl.aps.org/abstract/PRL/v102/i13/e130401

Note: This post is in progress.

30th CNLS Annual conference at SANTA FE, NM

2010-07-11T11:23:00.000-07:00

The 30th CNLS Annual Conference, http://cnls.lanl.gov/ultralow/, was organized on 'COMPLEXITY and DISORDER at ULTRA-LOW TEMPERATURES' in La Fonda Hotel, Santa Fe, NM from June 21-25, 2010. A lot of strange and impossible-looking things happen at ultra-low temperatures, including the phenomenon of Bose-Einstein Condensation (BEC). There were a lot of nice oral and poster presentations in the program by the physicists from all around the world. I also presented a poster in the program.

DAMOP2010 at Houston, Texas

2010-07-11T10:40:00.000-07:00

DAMOP2010, http://damop2010.rice.edu/, was organized in Hyatt Regency Hotel, Houston, Texas from May 25-29, 2010. There were a lot of interesting presentations - oral and poster both, several exciting activities, including some activities to celebrate the 50th anniversary of the invention of LASER. In fact, the discovery of LASER has drastically changed the science and technology and the world as a whole. The LASER has found its applications in diverse fields. In fact, one can rarely find a field of science and technology where there is no presence/use of a LASER in one form or another. Atomic, molecular and optical physics is one of the major fields which has gotten a tremendous advantage from the discovery of LASER. In fact, the first observation of a BOSE-Einstein Condensate (BEC) became possible in 1995, after about 70 years of its prediction by Einstein, because of the development of the technique of cooling atoms using a laser.

There were thousands of atomic, molecular and optical physicists, including several Nobel Laureates in the fields.

I also presented by current research in the meeting http://meetings.aps.org/Meeting/DAMOP10/Event/126565.

Third Annual Greater Boston Area Quantum Matter Meeting

2010-04-13T18:07:00.000-07:00

The Third Annual Greater Boston Area Quantum Matter Meeting took place on Saturday, April 3, 2010 at the University of Massachusetts Boston, Campus Center, 3rd floor, 100 William T. Morrissey Blvd., Boston. There were four invited talks and more than 30 contributed talks. Here is a link for more information:

http://cmt.harvard.edu/bahbar/

Here is a group photo taken on the conference site:

http://www.physics.umb.edu/news.htm

Happy New Year 2067 !

2010-04-13T18:01:00.000-07:00

Happy Nepali New Year 2067 !

How does a Cs-fountain clock work?

2010-02-24T08:19:00.000-08:00

A clock is a timekeeping device. In the past, people used the shadow of a building, the position of some fixed stars, the sun, the moon and some other heavenly bodies to keep track of time. As the human civilization progressed, they developed some devices like a water clock and a sand clock to know time. In the early seventeenth century, Galileo discovered that a swinging pendulum can be used as a time keeping device. Inspired by this discovery, Christian Huygens invented a pendulum clock in the mid seventeenth century. These clocks can still be seen used in several places. In the mid twentieth century, it was discovered that atoms can be used to keep time. The 1955 Cesium Atomic Clock with a Cesium beam tube developed at the National Physical Laboratory, UK, kept time to a second in 300 years. To increase the accuracy of the clocks, the interrogation time had to be increased. This could be done by decreasing the speed of the atomic beam or by increasing the length of the the tube. But the problem with the increasing the length of the tube was that the atoms would form a sag in travelling through the tube due to gravitational potential. A new idea was developed where the tube could be rotated so that it would be in a vertical position and the atomic beam could be projected vertically upward. This new configuration along with the development of the laser cooling techniques developed in early nineties made the modern, highly accurate Cesium fountain clocks possible. The modern Cesium clocks developed at NIST, Boulder, Colorado, USA would neither gain nor lose a second in more than 60 million years.

Note: This posting is in progress.

2010-01-02T12:01:00.000-08:00

HAPPY NEW YEAR 2010 !

Physics Journals

2009-12-04T06:12:00.001-08:00

The following links contain a number of physics and astrophysics journals published all around the world:

(1) http://www.slac.stanford.edu/spires/coden/list.shtml

(2) http://www-library.desy.de/eljnl.html#physics

(3) http://www.ifpan.edu.pl/journal.html

(4) http://journals.aip.org/

Bosons or Fermions?

2009-08-15T17:23:00.000-07:00

A class of particles which have an integer spin are called bosons. Example - photon, etc. Any number of bosons can go to the same quantum state. Thus they are friendly to each other ! They obey Bose-Einstein statistics. The wave function associated with bosons is symmetric.

A class of particles which have a half- integer spin are called fermions. Example - proton, neutron, electron, etc. Unlike bosons, only two fermions (at maximum) can go to the same quantum state, as dictated by the Pauli Exclusion Principle. They obey Fermi-Dirac statistics. The wave function associated with fermions is anti-symmetric.

An atom can also be classified as a composite boson or a composite fermion. To find whether an atom is a composite boson or a composite fermion, you need to look at the net spin of the atom due to its constituent particles that make it. For example, consider the simplest of the atoms - Hydrogen. Hydrogen has a proton and an electron. A proton is a half-integer particle and so is an electron. Therefore, the net spin of a normal hydrogen atom is one, which is an integer. Therefore, hydrogen is a composite boson. If we consider a helium-4 atom, there are two protons, two neutrons and two electrons. Each of these particles has a half integer spin. Therefore, the net spin of a normal helium atom is an integer. Hence, helium is a composite boson. What's about lithium-7 ? A lithium-7 atom has three protons, four neutrons and three electrons. Therefore, the net spin of a lithium-7 atom is an integer and hence it is a composite boson. On the other hand, by the same way of reasoning, lithium-6 is a composite fermion.

In general, an atom can be classified as a composite boson or a composite fermion on the basis of the total number of constituent particles contained in it. If the total number of constituent particles is even it is a composite boson where as if the total number of constituent particles is odd, it is a composite fermion !

Gordon Research Conferences - 2009 (Atomic Physics)

2009-07-06T14:20:00.001-07:00

The gordon research conferences take place on a number of frontiers in research areas every years and the conference in the same area is organized every two years. They were started by Professor Neil E. Gordon in 1930s. Therefore, these confernces carry a long hostory with them. The GRC-2009 in Atomic Physics was organised from June 28-July 03 at Tilton Shcool, Tilton, New Hampshire.

More than 150 participants incuding twenty plus speakers were present in the conference. The speakers were the top researchers in the field from around the world. About a 100 posters were presented on current researches in two sessions. Most of the talks and posters were from the experimentalists on the subject but there were some atomic physics theorists too to give talks and present posters. The talks were on variety of disciplines of Atomic physics - Bose and Fermi gases, atomic reactions in ultra cold environments, formation of qubits using atomic ions, etc. A day started with breakfast at 7:30 A.M. and ended with a social from 10:00 P.M. - 12:00(midnight) or so. I was so surprised to see that the frontier research scientists work all the time no matter whether they are in a meeting hall or in a dining table or in a social or wherever they are !

There were a lot of indoor and outdoor extra activities too in the free time like hiking, rafting and kayaking. Unfortunately, because of the weather, we could not do outdoor activities. Most of the week was spent on campus, attending the conferences, presenting poster, chatting, working on computers and eating and drinking.

I can not stop myself writing on the quality and quantity of foods in the conference. It was the place where you could eat anything of your choice and any amount you would want. It was really great. The conference staffs in the kitchen and everywhere were so friendly and helpful. We spent a very good time in overall in the GRC-2009 in Atomic Physics at Tilton School !

Second Annual Greater Boston Area Quantum Matter Meeting

2009-05-11T05:49:00.000-07:00

The Second Annual Greater Boston Area Quantum Matter Meeting took place in Metcalf Science Center, Physics Department, Boston University, on Saturday, May 9, 2009. The topics of presentation were mainly on quantum systems: strongly correlated systems, atomic and optical systems, and mesoscopics. There were four invited talks, each of about 30 minutes duration and more than thirty contributed talks, each of 4-5 minutes. The schedule is available here. This program was a continuation of the First Annual Greater Boston Area Quantum Matter Meeting, which took place in Jefferson Building, Physics department, on Saturday, May 10, 2008. The link of this meeting can be found in here.

Happy New Year 2066 !

2009-04-08T10:30:00.001-07:00

I wish you all a Happy and Prosperous Nepali New Year B.S. 2066 !

How is the information extracted from cold atom interferometers?

2009-03-31T13:00:00.000-07:00

The cold atoms (thermal atoms) or a BEC sitting at the bottom of a magnetic trap is split by a laser standing wave and the wave packets are allowed to evolve in time. At the end of the interferometric cycle, the wave-packets are recombined by a recombining pulse (identical to the splitting pulse). The trap is switched off and the wave packets are allowed to expand. Then the imaging of the wave packets is done by using laser light. One of the techniques is the absorption imaging technique. In this method, a resonant light is shone on the wave packets and the images obtained from this are fitted with some suitable known models. The useful information is then extracted by interpreting the fitting parameters.

Note: This post is in progress !

BEC in a triple well potential

2009-02-26T16:44:00.000-08:00

This is a review of a paper by Rab et. al.

Consider a triple well potential with the wells 'L' , 'M' and 'R' for the left, middle and right wells respectively. A BEC sitting in the 'L' well can be transported to the 'R' well so that no atoms are left in the 'M' well. The researchers call this process as macroscopic matter-wave Transport Without Transit (TWT) and this can be done by Stimulated Raman Adiabatic Passage(STIRAP). In STIRAP, is a technique to transfer population between two atomic states - 1 and 3 via an intermediate excited state 2. The atomic population is adiabatically transferred from the state 1 to state 3 by coupling the states 1 to 2 and and 2 to 3 using electromagnetic pulses. The population transfer is achieved via a superposition of the states 1 and 3 with the occupation of the state 2 strongly suppressed. That's why is is called the TWT.

Note: This post is in progress.

Collapse of a wave function !

2009-02-24T12:40:00.001-08:00

What happens when light passes though a single slit? What happens when light passes through a double slit? What happens when a beam of electrons passes through a single slit? a double slit? What happens when the electron beam hitting a double slit is observed? The following YOUTUBE video by Dr. Quantum answers most of these questions.

What is a BOSE Einstein Condensate ?

2009-02-20T14:00:00.001-08:00

A Bose Einstein Condensate (BEC) is a special phase of matter when a dilute bosonic gas is cooled to a temperature below the critical temperature (Tc). The critical temperature is in the range of some micro Kelvins to nano Kelvins. The Bose Einstein Condensation was predicted by Albert Einstein in 1924 by applying the Bose Statistics to massive particles - atoms. Satyendra Nath Bose , an Indian physicist, developed a statistics for the photons (light particles), which are massless.

Because of the lack of cooling technology, the world had to wait for the next 70 years to realize a BEC in a laboratory. In 1995, a BEC was realized in JILA by cooling down a dilute atomic gas of Rubidium-87 to a temperature of about 170 nano Kelvins. In the same year, BECs were observed in MIT by cooling down a dilute atomic gas of Sodium-23 and in Rice University by cooling down a dilute atomic gas of Lithium-7. Three physicists- Carl Wieman, Eric Cornell and Wolfgang Ketterle were awarded the 2001 Nobel Prize in Physics for this great achievement.

A BEC is made by cooling a dilute gas in the following sequence. A dilute atomic gas obtained from oven is cooled down by Helium to its temperature which is about 4 Kelvin. Then it is loaded in a trap called a Magneto-Optical-Trap (MOT), where the atoms are trapped and cooled by six polarized lasers directed orthogonally towards the center of the trap. Lasers cool the atoms to a lower temperature but not to the critical temperature. Beyond that the trapped gas is cooled by evaporative cooling, where the cooling is done by varying the frequency of the radio-frequency waves.

A nice analogy to evaporative cooling is the cooling of the coffee in a coffee mug. The most energetic coffee molecules close to the surface of the coffee in a coffee mug escape from the surface taking some energy and so the rest of the coffee in the mug will have less energy. As a result of which the coffee in the mug cools down. Similar is the case of evaporative cooling where the most energetic gas atoms from the trap escape taking the energy away, cooling down the remaining atoms. Finally, when the critical temperature is reached, all the atoms in the trap come to occupy the ground state, forming a blob of matter. This is neither solid, liquid, nor a gas. It is a condensate and is called a Bose-Einstein Condensate (BEC).

A BEC is a very nice mesoscopic quantum system and so is a nice candidate to test the laws of quantum mechanics and perform atom interferometric experiments.

Daniel Kleppner, an MIT professor, gives a really illuminating picture of the Bose-Einstein condensate in the following YOUTUBE video.

Ramsey-Borde Atom Interferometer

2009-02-05T12:29:00.000-08:00

A Ramsey-Borde interferometer is a matter wave interferometer which uses a beam of cold atoms/molecules as a matter wave and four traveling waves as beam-splitters. The matter wave is split at first by a laser traveling wave into two wave packets of which 50% of the atoms/molecules remain in the ground state and the other 50% go to the excited state by absorbing a photon from the laser. After a certain time interval, the second laser wave is used to split the two wave packets again. Then two subsequent splittings are made by two waves traveling in an opposite directions to the direction of the previous waves.

Note: This posting is in progress.

Bragg diffraction of atoms by light standing wave

2009-01-30T15:50:00.000-08:00

When a monochromatic electromagnetic wave incidents at some angle on a crystal lattice, it is reflected by the crystal lattice planes and a maximum intensity can be observed if the path difference of the reflected waves from the adjacent planes is an integral multiple of the wavelength of the wave. This phenomenon is called Bragg diffraction, after William Henry Bragg and his son William Lawrence Bragg, who were jointly awarded the 1915 Physics Nobel Prize for their services in the analysis of crystal structure by means of X-rays. Interestingly enough, diffraction can be observed when an atomic beam is directed through a light standing wave. A laser standing wave can be produced by reflecting a laser beam between two mirrors. When a beam of atom is passed through the standing wave, an atom absorbs a photon from a beam of laser and it does stimulated emission of a photon of the same momentum into the next beam, imparting a net momentum to the atom which is two times the momentum of a single photon. This is similar to the Bragg diffraction of electromagnetic waves as the laser standing wave is analogous to the crystal lattice planes.

Note: This posting is on progress.

What is the Poisson's Spot?

2009-01-29T13:04:00.001-08:00

When a small opaque circular disc is placed in front of a point source of light, it casts a shadow on the screen placed behind it. But, the most amazing observation will be that there will be a bright spot at the center of the geometrical shadow. This spot is called the Poisson's Spot, after the famous physicist Simeon Denis Poisson. Poisson in the early nineteenth century, mathematically derived from the diffraction theory that there should be a bright spot at the center of the geometrical shadow of the disc, which he disliked as it was against an intuition. But when his mathematical results were experimentally verified, he became a strong follower of the wave theory of light.

The formation of the Poisson's spot can be explained using the Huygens' Theory. When light from a point source hits a circular disc, each point on the circumference of the disc acts as a secondary source of light. Since the waves from the points at circumference reach the center of the geometrical shadow in phase, they interfere constructively. As a result of this, the intensity there is a maximum which gives rise to the Poisson's Spot.

Noise-supressed large area atom interferometers

2009-01-22T15:37:00.000-08:00

A paper-review

Atom interferometers can use just cold atoms or a BEC. The difference is that a BEC is a coherent source of cold atoms like a LASER unlike a beam of cold atoms which is at temperatures much above the BEC temperature. The researchers all around the world are working to realize more sensitive and more efficient atom interferometers by using either of these sources. One reason for that is - an atom interferometer is much more sensitive than an optical interferometer in the sense that the signal-to-noise ratio of an atom interferometer is greater than 10^11, compared to an optical interferometer of comparable area and the particle flux. Therefore, atom interferometers can prove to be more effective in precision measurements.
Atom interferometers are of trapped-atom-type or free-space-type. Recently, Herrmann et. al. have shown that a pair of simultaneous conjugate Ramsey-Borde atom interferometers can be operated at large momentum transfer to cold atoms from the optical pulses to supress the vibrational noise and to enhance the enclosed space-time area by a factor of 2500 of the area of the existing atom interferometers. They have used this interferometer to measure the fine structure constant more precisely.
A cold atom beam of Cs-133 shot vertically upward in a space of about a meter high is split by using a pi/2 laser pulse. It is split again after an interval of time by using another pi/2 pulse and two simultaneous interferometers are formed by using further two consecutive pi/2 pulses before they are finally recombined. Each atom can be given a momentum as large as that of the momenta of twenty optical photons (20*hbar*k). The total phase gained by the atoms during the interferometric cycle time has three contributions - the phase due to recoil velocity of the atoms, the phase due to free-evolution of the wave packet between the beam splitters and the phase due to the interaction of the wave packet with beam-splitting pulses. By operating both interferometers simultaneously, the phase due to free evolution and the effects of noise/vibrations can be subtracted off, leaving the contributions of the recoil velocity and the splitting pulses only. This is how the simultaneous conjugate Ramsey-Borde atom interferometers can be operated to get a large area without losing contrast.

What and why is normalization of wave function?

2009-01-21T12:27:00.000-08:00

Quantum mechanics treats moving matter as a wave, called a 'matter wave'. A matter wave is always assigned a wave function, usually called a 'psi'. The wave function is usually complex and composed of two parts - an amplitude and a phase. The square of the modulus of the wave function gives the probability density of finding the particle somewhere in space. If this quantity is integrated around the whole space, it gives the probability of finding the particle in that space. Since the particle should exist somewhere in space, this probability should be a maximum. To fulfill this requirement, the wave function is normalized in such a way that the total probability in the whole space of our consideration is 1 (maximum). The fixing of the coefficient of the wave function by requiring to fulfill the above condition is called normalization. Therefore, to get a normalized wave function - (1) Write a suitable wave function with some coefficient to represent the quantum system of your consideration. (2) Integrate the modulus square of the wave function over the whole space of your consideration and get the value of the coefficient in terms of some known quantities. (3) Plug the coefficient back into the wave function, which now is a normalized wave function. It is more convenient to work with a normalized wave function than with a non-normalized one !

Matter waves and wave packet

2009-01-16T13:57:00.000-08:00

Moving matter behaves like a wave in quantum mechanics. The wavelength associated with a matter wave can be obtained by dividing the Planck's constant (6.63*10^-34 Js) by its momentum. This wavelength is called the de Broglie wavelength and the matter waves are called the de Broglie waves after the pioneer on matter waves, Louis de Broglie, who was awarded the 1929 Physics Nobel Prize for his discovery of the wave nature of electrons. Since for a massive particle moving with some velocity, the momentum of the particle is large and since this quantity divides the Planck's constant which itself is very small, the de Broglie wavelength is very small and hence we can't visualize the wave nature of the moving matter in day-to-day observation. For example, if a ball of 1kg is rolling on a ground with a speed of 1 m/s, the de Broglie wavelength of the ball is just 6.63*10^-34 m, which is too small to realize as a wave but if we consider atomic and subatomic particles moving at some speed, the wavelength is large enough to visualize the wave nature of matter, at least, doing some precise experiments. For example, the electron microscopes work on the principle that a de Broglie wave is associated with the moving electrons. In atom interferometers, the moving atoms are considered to be waves. In fact, in the modern quantum world, there are a number of devices where matter waves are used.
A wave packet is the unit of a matter wave which carries matter and energy in its direction of propagation at the speed of the wave. It is a small region around a matter particle where there is a very high probability of finding the particle. These wavepackets show properties like that of optical waves ,e.g., diffraction, interference, etc. The following YouTube videos depict how matter waves look like !

God does not play dice with the universe !

2009-01-13T15:47:00.000-08:00

No one can say for sure which face is turned up when a dice is rolled in a game of dice. One can say something like - the chance of getting a 6 in a single roll of a dice is 1/6 and so on. Quantum physics also deals with the probability of occurrence of some event or existence of something rather than the certainty of it. In most of the cases, we find the probability of occurrence of any quantum mechanical event or the uncertainty that exists in its measurement. Heisenberg, Born and other quantum physicists were in favor of the probabilistic nature of the atomic and subatomic phenomena which Einstein did not like. In his disagreements of such 'may be' kind of thing, Einstein said that - 'God does not play dice with the universe'.
But the winner were the quantum physicists in the sense that the probabilistic nature of quantum physics was shown experimentally and a new discipline was established !
You can also visit HERE and HERE !

What is Gross-Pitaevskii Equation?

2009-01-12T14:44:00.000-08:00

A non-degenerate system can be explained by the Schrodinger equation, which is a linear second order differential equation: ( i hbar del/ del t ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi. But for a degenerate quantum gas like a Bose-Einstein Condensate(BEC), there is a non-linearity caused by the atom-atom interactions, which needs to be explained by a non-linear second order differential equation of the form: ( i hbar del/ del t ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi + NU|psi|^2 psi. This equation was first derived by Gross and Pitaevskii independently and is called the Gross-Pitaevskii equation. The last term in the equation is the nonlinear term introduced by the atom-atom interactions.

What is Schrodinger's Equation ?

2009-01-11T13:25:00.000-08:00

In quantum mechanics, the Schrodinger equation plays the same role as the Newton's second law does in classical mechanics. The Schrodinger equation was such a breakthrough made in the history of mankind which revolutionized the world of physics. The total energy of a particle is obtained by adding its kinetic energy to its potential energy. This is called the Hamiltonian of the particle. A simple way to get the most respected equation which was written by Erwin Schrodinger in the first quarter of the 20th century is to replace the energies by operators. The total energy is replaced by ( i hbar del/ del t ), the kinetic energy is replaced by ( hbar^2/(2m) * laplacian^2) and the potential energy is replaced by the potential energy operator, V. Then, we get the time dependent schrodinger equation, which can be operated to a wave function psi as :
( i hbar del/ del t ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi
This equation is the backbone of quantum mechanics. If we consider a free particle, the potential energy of the particle is zero. Then this equation explains how a free particle evolves with time. The solution to this equation under a suitable potential always gives the time evolution of a quantum system under that potential. If we replace ( i hbar del/ del t ), by the energy operator E, the above equation takes a form:
( E ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi
This is time-independent (stationary) Scrodinger equation. The solution to this equation gives the stationary state of a system depending upon the nature of the potential. For example, if we take the potential to be parabolic, V = (1/2)m (omega)^2 (x)^2, in the time-independent schrodinger equation, we will get the stationary states of this potential, which is popularly known as the stationary states of a harmonic oscillator.

What are GOOD QUANTUM NUMBERS?

2009-01-11T12:43:00.000-08:00

In classical mechanics, we can assign any number of variables to specify the state of a system. For example, for a free particle, its position, momentum, etc,. can be known and can be assigned simultaneously to specify the state of the free particle. But the story of quantum mechanics is different. If the position of a particle at some instant is correctly known, its momentum will be highly/maximally uncertain. This means, we can't assign both the position and momentum to specify the quantum mechanical state of the particle simultaneously. In this sense, the quantities (observables) which can be assigned simultaneously to a quantum system at any time to specify its state at that time are called the good quantum mumbers of the system. A set of good quantum numbers is also called a complete set of commuting observables (C.S.C.O.). These coordiantes commute each other, which means that their measurements can be made simultaneously.

Is light a wave or a particle?

2009-01-09T15:05:00.000-08:00

Sir Isaac Newton gave a theory of light- called the corpuscular theory of light. As soon as the light particles reach some material mediums like glass, water, etc., the particles are attracted by a force (F = ma) and the particles will be accelerated in the medium, resulting into an increase of speed. This means that light should travel faster in material medium than in a vacuum. But this theory failed when Olaf Roemer, Armand Fizeau, Leon Foucault and other experimentalists measured the speed of light, the result of which showed that the speed of light in a material medium be less than that in a vacuum. To comply with the experimental observations, the wave theory of light was proposed at about the end of the 18th century by Christiaan Huygens. A deeply-rooted concept is difficult to change at once. The world had to wait about a hundred years to accept that light was a wave until when Thomas Young first demonstrated the interference of light in his famous double-slit experiment in 1801. 'Light is a wave' was now established. It remained like that until the end of the 19th century. One of the three groundbreaking papers of Albert Einstein in 1905 was on the photoelectric effect. The phenomenon of photoelectric effect couldn't be explained if light behaved like a wave. Therefore, he proposed the particle theory of light. Light consisted of 'quanta' (packets) of energy-which he called 'photons.' His theory explained the phenomenon of the photoelectric effect without any discrepancy, proving that light shows a particle-like nature. Although the fame of Einstein spread all over the world by his work on the Theory of Relativity, he was awarded the Nobel Prize of Physics in 1921 for his discovery of the law of the photoelectric effect.
Thus, light shows a dual nature - wave like nature in the phenomena of reflection, refraction, diffraction, interfernece and polarization but particle-like nature in the phenomenon of the photoelectric effect.

Can ALICE be of BOB?

2009-01-04T15:29:00.000-08:00

BOB and ALICE make a short talk over phone. Bob is desperate to get Alice and the same goes with Alice, too. But they have heard that there is Heisenberg Uncertainty Principle (?), which may be a problem(?) for their union.

HERE is their telephone conversation:

BOB : OH ALICE, YOU'RE THE ONE FOR ME !
ALICE : BUT BOB - IN A QUANTUM WORLD, HOW CAN WE BE SURE ?

Can ALICE be of BOB?

How did my 2008 go ?

2008-12-31T07:21:00.000-08:00

Everyday Life

The everyday life was usual as in the past. Some of the chores were to help my daughter with her homework, to organize and participate in a get together periodically like MO:MO parties, Dashain and Tihar celebrations, etc. Most of the time was spent in internet - improving personal website, visiting the facebook and writing blogs. Other day-to-day activities were checking e-mails and reading all kinds of news papers that are published all around the world !! There was not a single day that passed without clicking on the following websites:
http://arxiv.org/,
http://prola.aps.org/,
http://kantipuronline.com/,
http://mysansar.com/,
http://sajha.com/sajha/html/index.cfm,
http://news.bbc.co.uk/,
http://www.cnn.com/
There is no question that the following website was highly clicked on:
http://www.google.com/.
The visits to the following web pages was also made at high frequency:
http://groups.google.com/group/nps_nepal?pli=1
http://physicsworld.com/cws/home.
Thus walking to the office after morning tea/coffee, spending the morning at university, coming back to home for lunch, going back to the university and spending the rest of the day until dinner becomes ready and come back to home and chat with friends and family - was a pendulum-like life of the year 2008. Oh, we also visited the Niagara Falls and the 1000 islands in the month of August.

Research and Academia

I was continuing my research work on the BEC-based atom interferometry, under a distant supervision of my adviser as he was in sabbatical for about a year and half in University of Colorado, Boulder. He came back to the University in January 2008. Therefore, I started learning more research skills under his direct supervision right from the beginning of the Spring semester. I participated in the 2008 March Meeting of the American Physical Society (APS) in New Orleans, Louisiana. I presented my research work on Single and double reflection atom Michelson interferometers in a weakly confining magnetic trap in that meeting. After my return from New Orleans, we had a campus wide poster presentation at WPI, which WPI celebrates annually as the Graduate Research Achievement Day (GRAD). I made a poster presentation there on Theoretical Analysis of single and double reflection atom interferometers in a weakly- confining magnetic trap. I was more than happy when the first research paper was published in Physical Review A in April, 2008 ! I was awarded the Graduate Research Government(GSG) Conference funding award by the GSG at WPI. I gave a presentation on Theoretical analysis of a free-oscillation atom interferometer in a weakly confining magnetic trap at Harvard University in May, 2008. I was awarded the Graduate Research Assistantship (GRA) for the summer of 2008. I also got an opportunity of teaching a summer course on Waves and Oscillations at WPI. I got an award of Graduate Teaching Assistantship (GTA) for the year 2008-2009 in August. I learnt research skills in theoretical atomic physics in this year more than ever in the past. Thus, I enjoyed 2008 with teaching, research and normal everyday work !

The coldest transistor ever !

2008-12-29T16:20:00.000-08:00

This is a brief review of the paper published in Physical Review A.

An electronic transistor is a three-terminal, solid-state device, used to amplify a signal in electronic circuits. The three terminals are called - an emitter (E), a base(B) and a collector(C). Can we make a transistor out of a Bose-Einstein Condensate (BEC)? The answer is - YES ! A transistor can be designed by using a BEC in an asymmetric triple-well potential. Let's consider a triple-well potential with wells labeled - Left(L), Middle(M) and Right(R). The left well, L, has a lot of cold atoms in the BEC state, so it acts as an emitter (E). If there are no atoms or a very few atoms in the middle well, M, and no atoms in the right well, R, no atoms can tunnel through the middle well to reach the right well, which acts as collector(C). This is because of the mismatch of the chemical potential between the three wells. If the atomic population in M is increased to some value, there will be a large flux of atoms reaching R, tunelling through M. Because when the number of atoms are increased in M, the chemical potential rises due to the nonlinearity caused by atom-atom interactions, making tunnelling possible. Thus, M is analogous to the base of an electronic transistor. Thus by controlling the atomic population in M, the atomic population in R can be controlled/amplified. Hence, this system clearly shows a transistor-like behavior and is the coldest transitor ever as it functions at BEC temperature, which is some micro/nanoKelvins! A BEC transistor may prove to be useful in precision measurements.

HAPPY NEW YEAR 2009 !

2008-12-29T08:59:00.000-08:00

I WISH YOU A HAPPY AND PROSPEROUS NEW YEAR 2009 !

ULTRACOLD ATOM GROUPS AROUND THE WORLD

2008-12-29T08:19:00.000-08:00

There are hundreds of research groups all around the world, working with the ultra cold atoms. Some of them are working with just the cold atoms where as many others are working with the Bose-Einstein Condensates(BECs). Bose-Einstein Condensation (BEC) was predicted by Albert Einstein in the early 1920s, when he applied the BOSE STATISTICS to the massive particles-the atoms. Bose had developed his statistics to study the behavior of light particles, called the photons. Although the phenomenon of BEC was made that early, the world had to wait for about 70 years to realize a Bose-Einstein condensate experimentally. The reason was the lack of the technology to cool a gas to a temperature of some nanoKelvins at which the BEC could be observed. The BEC was realized experimentally in Rubidium-87 gas in JILA, Colorado in 1995. In the same year, it was also realized in Sodium-23 in MIT and in Lithium-7 in Rice University. Now there are several laboratories in the world which prepare a BEC and manipulate it in different ways. One of the potential applications of a BEC is in making sensors like interferometers/gyroscopes.

What is Interference?

2008-12-20T07:16:00.000-08:00

If we observe the flame of a burning candle from the other side of three card boards having holes aligned on a straight line with the the flame, we will be able to see the flame. What happens when we slightly displace one of the three card boards so that all the three holes and the flame are no more in a straight line ? The answer is - we can not see the flame any more. This is a very simple table top experiment to show that light travels in a straight line in a given medium. Sometimes, this is also called the rectilinear propagation of light. But what happens when the medium changes or some special condition arises on the path of light? Reflection, refraction, diffraction, INTERFERENCE or polarization can be observed in such situation.

A ray of light falling on a smooth surface bounces to the previous medium at the glancing angle, which is termed as the reflection of light. If light passes from one medium to the next, its speed changes and takes a new direction at the boundary unless the ray hits normally to the boundary surface, which is called refraction of light. A ray of light passing through a very narrow hole, of the size of the wavelength of light, will spread and a pattern of bright and dark regions are obtained at a fairly large distance (relative to the size of the hole) behind the hole, which is termed as the diffraction of light. If a ray of light hits two narrow holes, very close to each other, the pattern obtained is really interesting-the width of the bright and dark regions are the same and the phenomenon is called the INTERFERENCE of light. When a ray of light passes through some medium like calcite crystal (even through air, water, etc), the light field (particularly electric field) is confined in a plane, and the phenomenon is called polarization.
Let's go beyond this. Are these phenomena specific to light? What's about other waves? The answer is - all light-like waves - called the transverse waves have these properties. There is another category of waves which shows sound-like behavior - called longitudinal waves also show all the above properties except polarization. Whatever I wrote above was known before the advent of QUANTUM MECHANICS.

What's about the matter-waves? Quantum mechanics treats the moving matter as a wave called a matter wave. Matter waves also show all the above properties as the light waves do !

Consider a beam of monochromatic light (light beam with a single frequency) passing through a closely spaced double slits. What do we observe behind the slits? We observe a nice pattern, called interference fringe, on the screen placed at a fairly large distance behind the slits. What happens here is the interference of light. The two slits act as the secondary sources (Huygens' Principle) called the coherent sources and the waves from there reach the screen in phase or out of phase. If the waves from the slits reach a point on the screen in phase, they will reinforce each other, producing a bright fringe/band. This is called a constructive interference. If the waves from the slits reach a point on the screen out of phase, they cancel each other and a dark fringe/band is produced in there. This is called a destructive interference. But let's think about somewhat weird situation that there is a single photon reaching the slits. Do we still see the interference pattern? If so, how do we explain this? The single photon can go through one or the other slit? What does it then interfere with?

Note: This post is on progress !

Inversion of ammonia molecule

2008-12-09T11:30:00.000-08:00

Ammonia molecule has a pyramidal structure with the basal plane as an equilateral triangle defined by the three HYDROGEN atoms and a NITROGEN atom at the apex on the line passing normally through the center of the triangle. This structure can be represented by a symmetric double well potential. The nitrogen atom can come closer to the basal plane. As it comes closer to the basal plane, it experiences a repulsive force due to the hydrogen atoms. Thus there is a potential barrier. The nitrogen atom then passes to the other side by tunneling effect. This can not be explained classically and is a purely a quantum mechanical problem. The frequency at which the nitrogen atoms oscillates back and forth about the basal plane is called the inversion frequency. Here are some references-Ref-1 , Ref-2.

Online Resourrces on Qunatum Mechanics !

2008-12-03T15:57:00.000-08:00

There are tons of online resources for teaching and learning quantum mechanics. Some of the resources I found useful and interesting are the following:
(1) http://farside.ph.utexas.edu/teaching/qmech/lectures/lectures.html
(2) http://farside.ph.utexas.edu/teaching/qm/lectures/index.html
(3) http://phys.educ.ksu.edu/
(4) http://www.oberlin.edu/physics/dstyer/TeachQM/
(5) http://perg.phys.ksu.edu/papers/vqm/HandsOnQM.html
(6) http://arxiv.org/abs/0709.4503v1
(7) http://phet.colorado.edu/simulations/search.php?search_for=Quantum&submition=x%3AWed+Dec+03+2008+19%3A20%3A38+GMT-0500+(Eastern+Standard+Time)
(8) http://bouman.chem.georgetown.edu/atomorbs/qmbasics.html
(9) http://msc.phys.rug.nl/quantummechanics/
(10) http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/mathbas/mathbas.htm
(11) http://web.phys.ksu.edu/vqm/VQMNextGen/qmbasics/index.html

What is Schrodinger's Cat?

2008-12-02T11:33:00.000-08:00

It is well-accepted fact that a quantum particle can exist in a superposition/combination state of two or more possible states. To show this, Erwin Schrodinger proposed a thought experiment in 1935, in which a cat locked in a box along with a radioactive atom and a vial of deadly poison could be somehow both alive and dead at the same time. Schrodinger's argument was that a quantum particle such as an atom can be in more than one different quantum states at the same time but a classical object such as a cat couldn't be in two different states.Thus, a Schrodinger's Cat State is generally understood as a quantum superposition state of two or more possible quantum states of a particle.

References:

(1) http://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat
(2) http://physicsworld.com/cws/article/news/2815
(3) http://physicsworld.com/cws/article/print/525
(4) http://www.sciencemag.org/cgi/content/abstract/272/5265/1131
(5) http://www.nature.com/nature/journal/v438/n7068/abs/nature04251.html
(6) http://www.nist.gov/public_affairs/releases/cat_states.htm

Here is a nice youtube video:

Note: This was first posted on the NPS Google group Web page:

http://groups.google.com/group/nps_nepal/browse_thread/thread/91831b29417f6816/25f85d63eecb4a95?lnk=gst&q=Schrodinger+cat#25f85d63eecb4a95

What good do blogs do to the Physicists?

2008-11-29T16:48:00.000-08:00

Blogging may be regarded as self-publicity. Is it that much or is there something beyond this too? Here is a short-nice-analysis from physicsworld.com, which says 'Blogs add a new dimension to physics'.
http://physicsworld.com/cws/article/print/24088

Without Quantum Mechanics, ...?

2008-11-28T08:52:00.000-08:00

What would happen if there did not exist QUANTUM MECHANICS? Here is an ANSWER (please see the page-4 of the document in the link):http://vmsstreamer1.fnal.gov/VMS_Site_02/Lectures/NOS2002/Presentations/Greytak.pdf

Blogs on PHYSICS !

2008-11-26T08:57:00.000-08:00

I had no idea that there exist so many blogs on academic fields. I Googled this morning and was astonished to find that there exist so many physics-related blogs too ! Please click on the following link to find some of them.

http://www.academicblogs.net/wiki/index.php/Physics

Quantum Tunneling - No Classical Analogue !

2008-11-25T08:30:00.000-08:00

Consider a quantum particle with energy less than the potential energy barrier (that binds the particle) lying in a potential well. Is there any probability of finding the particle outside the well? Classically - NO ! The particle is always trapped by the potential and there is no chance for the particle to come out of the trap. If that is the case, there should be no chance of coming out of the alpha particle from a heavy atomic nucleus as they are bound by a strong potential barrier. George Gamow gave the theory of ALPHA DECAY saying that the alpha particles come out of the nucleus by a Quantum Phenomenon called the Tunneling. Therefore, a quantum mechanical particle trapped by a potential barrier can show up outside the barrier too ! - This is a phenomenon that can be explained ONLY by quantum mechanics !
There are broad range of phenomena of this kind that we can observe in nature everyday ! Here is a nice youtube video to explain this phenomenon:

What is the Quantum Theory of Radiation?

2008-11-23T15:06:00.000-08:00

The advent of the twentieth century brought a lot of exciting discoveries in the world of Physics. The dawn of the breakthroughs was from the quantum theory of radiation by Max Planck in around 1900. A hot body radiates or absorbs energy in the form of packets called quanta; the radiation or absorption is not continuous but in discrete units. Each quantum carries an energy given by the product of a constant h ( the Planck's constant) and f (the frequency of the radiation). The value of h = 6.63x10^-34 J s. Albert Einstein in 1905 wrote a famous paper on the theory of photoelectric effect applying the quantum theory of radiation, which earned him the 1921 Nobel Prize in Physics. In fact, the Quantum theory of radiation is a kind of start of a new physics - Quantum Physics !

What is a wave function?

2008-11-23T08:51:00.000-08:00

A wave function is a mathematical tool to represent a physical system. It is usually denoted by the letter psi. It is usually complex, meaning- it has a real part and an imaginary part. It is usually a function of coordinate and time. If it is only a function of coordinate, the wave function is independent of time. A physical system is completely described quantum mechanically if its amplitude and phase at any time are known. Therefore, a wave function should consist of these two information - an amplitude and the phase. Once a well-defined wave function is assigned to a physical system, a complete information related to the system can be drawn easily. For example, the modulus squared of the wave function gives the probability density - meaning the probability of finding a particle per unit volume. If this quantity is integrated in the overall space, the result will be '1', which means that the particle is somewhere in that space. A wave function is the fundamental tool for a quantum physicists ! NO wave function -NO Qunatum Physics !

Photons+Water molecules = Rainbow

2008-11-21T17:31:00.000-08:00

The quanta of light are called photons and the quanta of matter are the atoms /molecules.When light falls on water molecules, it is scattered and a colorful pattern called the 'RAINBOW' is formed.

That's what is happening here i n NIAGARA FALLS in an early morning of August 2008!

What is SPIN?

2008-11-20T16:50:00.000-08:00

SPIN is a special kind of angular momentum of some fundamental particles like protons, electrons and neutrons which does NOT have a classical analogue. Can we visualize the quantum mechanical spin like the spin of a rotating top in everyday life? NO ! To see this, consider an electron with uniform spherical charge distribution so that it rotates about its axis like the earth. If we calculate the rotating speed of the electron using classical electrodynamics, the speed comes to be equal to several times bigger than the speed of light, which is not possible as we know that no physical entity can have speed greater than the speed of light. Moreover, the spin of a quantum mechanical particle is a half , which is not compatible with the notion of spin in classical mechanics.
Therefore, spin exists in nature; it is always there. It can be measured, but it is different, not like the spin of a spinning top. It is purely quantum mechanical !

When You're a KET !

2008-11-16T07:11:00.000-08:00

Paul Dirac, a famous quantum physicist, introduced in 1930 a unique notation called a 'KET' to represent the state of a quantum system . To define a scalar product, there is another notation, called a 'BRA', so that we can define a scalar product 'BRA-KET', which gives a number. This notation greatly simplified the mathematical development of Quantum Mechanics.

What happens WHEN YOU'RE A KET? Please sing the song When You're a Ket by Prof. Paul Halpern in the following link:

http://www.haverford.edu/physics/songs/Halpern/ket_music.htm

Milky Way to Quarks : Powers of TEN

2008-11-06T18:03:00.000-08:00

If we start from viewing the Milky Way at 10 million light years from the Earth and go down by a factor of 10^-1 ( a tenth), how does the world look like in each step? Here is a very nicely programmed Java applet to answer this question. Please read the caption, while viewing the slides.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

This is a quick view of a VERY BIG to a VERY SMALL world !

Heisenberg Uncertainty Principle !

2008-11-02T08:14:00.000-08:00

In Quantum Mechanics, nothing is certain, but probabilistic. This means that you can just say that the chance of finding a particle in a particular region of space is p% (p<100). p =" 100" p =" 0," style="color: rgb(0, 153, 0);"> Heisenberg Uncertainty Principle. According to this principle, the uncertainties of the conjugate quantities are related by the formula - delta(P)*delta(Q) greater than or equal to h divided by 4*pi, where h = 6.63*10^-34 Js is called the Planck's constant and pi = 3.1416. In this formula, delta(P) is the uncertainty of measurement in the quantity P and delta(Q) is the uncertainty of measurement in the quantity Q. This means if you measure the quantity P more accurately, the measurement of the quantity Q will be less accurate. For example, if we are making the measurements of the position and the momentum of a particle, the more accurately we measure the position, the more inaccurate or uncertain will be the momentum, always giving the product of the two uncertainties greater than or equal to h divided by 4*pi.

The following YOUTUBE video gives a nice explanation of the Heisenberg Uncertainty Principle:

Some Quanta/Packets of Matter/Energy

2008-10-30T11:33:00.000-07:00

An atom was named that way assuming that it was non-divisible into smaller units. But because of the growth of scientific geniuses, techniques and technologies, atoms were found to be divisible into the constituents like protons, neutrons and electrons. Protons and neutrons were also found to be composite particles themselves, formed out of quarks. Still we can consider them as units or quanta of matter/ energy, in fact matter is equaivalent to energy (E = mc^2). Here are some units of matter and energy:
(1) Proton - A constituent of an atomic nucleus with one unit positive (+1e) charge. (2) Electron - A constituent of an atom with one unit negative (-1e) charge. (3) Photon - A quantum of light/energy ( hf , h being planck's constant and f bing the frequency of radiation). (4) Phonon - A quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid (5) Gluon - An elementary particle that causes quarks to interact, and is indirectly responsible for the binding of protons and neutrons together in atomic nuclei. (6) Exciton - A quasiparticle formed by the combination of an electron and a positive hole which is free to move through a nonmetallic crystal as a unit. (7) Plasmon - A quasiparticle resulting from the quantization of plasma oscillations (8) Doppleron - A quantum of energy or momentum emitted or absorbed in the processes regarding the Doppler effect for atoms in the standing light wave. (9) Polaron - A quasiparticle composed of an electron and its accompanying polarization field. (10) Graviton - A postulated quantum that is thought to be the carrier of the gravitational field. (11) Magnon - A quasiparticle carrying a fixed amount of energy and lattice momentum, can be viewed as a quantized spin wave. (12) Tachyon - A hypothetical particle that travels at superluminal speed (>c) , first proposed by Arnold Sommerfeld. (13) Polariton - A quasiparticle resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. (14) Ion - An ion is an atom or molecule which has lost (cation) or gained (anion) one or more valence electrons, giving it a positive or negative electrical charge.

HAPPY TIHAR 2065 B.S. !

2008-10-29T06:52:00.000-07:00

HAPPY TIHAR of the year 2065 B.S.(Bikram Sambat) to ALL the NEPALI PEOPLE and ALL the BLOG READERS !

What is Quantum Mechanics?

2008-10-28T17:24:00.000-07:00

Quantum Mechanics is the science of the small. If we are to consider the interactions between the molecules, atoms and the sub-atomic particles, we need to follow the quantum mechanical procedures. Thus, in a sense, quantum mechanics is a tool to study the behavior of the atomic and subatomic particles. The fundamental equation of Quantum Mechanics is the Schrodinger equation, which is like Newton's second law of motion in Classical Mechanics. We treat matter as a wave or a wave packet and a wave function, commonly denoted by 'psi' is assigned to the matter wave. Under different initial and boundary conditions as specified in the problem, the Schrodinger equation is solved to get the wave function for that particular problem. The more meaningful quantity is the modulus square of the 'psi' function - which gives the probability of finding the particle at any place. There is nothing certain in quantum mechanics, all is what is probabilistic. The probability of finding a particle is high where the square of the 'psi' function is high. The integral of the square of the 'psi' function in overall space is 'one', meaning that the particle must be situated somewhere in the space defined in the problem.

The World Of Small

2008-10-28T08:25:00.000-07:00

I have chosen the topic of my blog 'The World Of Small' to indicate the world reigned by Quantum Mechanics. The advent of the Twentieth Century brought two EXTREME WORLDS- the world of the big -the world explainable by the Einstein's Relativity and a little later -the world of the small- the world governed by Quantum Mechanics. The groundbreaking 1905 paper by Albert Einstein on the Special Theory of Relativity and his 1916 paper on General Relativity are the two seminal papers which lead one towards the world of the big. On the other hand, the great works by Bohr, Schrodinger, Heisenberg and Dirac laid the strong and sound foundation of Quantum Mechanics which lead one to the world of the small. Here I would like to mention that the Quantum theory of radiation- the radiation by a black body is not continuous but in the form of quanta or packets was already given by Max Planck!

I have started this blog as a student who is learning and trying to learn more towards the world of the small but I am equally interested towards the world of the big too, so in this sense I am more interested to see a sound marriage between the BIG and the SMALL (to understand the world better way) - as the one put forward by the great physicist Stephen Hawking - The Quantum Theory of Gravity.

Hey, it's a start !