Wednesday, December 31, 2008

How did my 2008 go ?

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:,,,,,,
There is no question that the following website was highly clicked on:
The visits to the following web pages was also made at high frequency:
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 !

Monday, December 29, 2008

The coldest transistor ever !

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.


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.

Saturday, December 20, 2008

What is Interference?

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 !

Tuesday, December 9, 2008

Inversion of ammonia molecule

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.

Tuesday, December 2, 2008

What is Schrodinger's Cat?

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.



Here is a nice youtube video:

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

Saturday, November 29, 2008

What good do blogs do to the Physicists?

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, which says 'Blogs add a new dimension to physics'.

Friday, November 28, 2008

Without Quantum Mechanics, ...?

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):

Wednesday, November 26, 2008

Blogs on PHYSICS !

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.

Tuesday, November 25, 2008

Quantum Tunneling - No Classical Analogue !

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:

Sunday, November 23, 2008

What is the Quantum Theory of Radiation?

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?

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 !

Thursday, November 20, 2008

What is SPIN?

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 !

Sunday, November 16, 2008

When You're a KET !

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:

Thursday, November 6, 2008

Milky Way to Quarks : Powers of TEN

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.

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

Sunday, November 2, 2008

Heisenberg Uncertainty Principle !

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:

Thursday, October 30, 2008

Some Quanta/Packets of Matter/Energy

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.

Note: This was first written by me in THE NPS GOOGLE GROUP in May 06, 2008.

Tuesday, October 28, 2008

What is Quantum Mechanics?

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

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 !