April 23, 2005
Final project references
Hey Class,
Only a few of you have sent me a reference list for your final projects. Everyone should do this soon! I've posted what I've got on the final project section of the website.
Brian
Posted by Brian at 08:30 PM | Comments (0)
April 19, 2005
Class review — 4/19
Hey Class,
Recall that Onur, Andrea, Man-Hong, and Xu Wang are giving talks on Thursday. I will provide snacks :) Also remember to put in a vote (via email) to me if you want an extra, bonus class on atomic collisions (and quantum mechanical scattering theory).
Today we talked about:
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Resonance fluorescence!
If we drive an atom with a strong laser field close to resonance, we see funky things:
The Mollow triplet - sidebands appear in the fluorescence spectrum.
Funny features in the correlation function g(2). Not only do we observe anti-bunching, but wiggles in g(2).
The dressed-state picture is useful for understanding the spectrum of the emitted light. In that picture, we have new states that are combination of the ground and excited atomic states and photon states with different occupation numbers. Spontaneous decay between the dressed states at different frequencies are possible because all of the dressed states have excited state and ground state character.
A radiative cascade picture is useful for understanding what's going on with g(2). In that picture, decay occurs between the bare states with the same photon number in the field (technically, this only makes sense for an atom in a cavity, where decay represents light that leaves the cavity). After a photon is emitted, you have to wait for Rabi oscillations to re-excite the atom. What you see in g(2) depends on when you look relative to the Rabi oscillation pi-time, and how fast the Rabi rate is compared with the spontaneous decay rate.
Cheers,
Brian
Posted by Brian at 06:54 PM | Comments (0)
April 16, 2005
Lecture notes up, etc.
Hey Class,
The lecture notes on laser cooling are available, and I've posted some reading material on resonance fluorescence if you're interested (see the class notes for 4/19).
Cheers,
Brian
Posted by Brian at 04:28 PM | Comments (0)
April 15, 2005
Class Revew — 4/14
Class,
Make sure that you read this entire entry -- there is information on the talks you will be giving!
For your talks, plan on 13 minutes plus 5 minutes for questions. Do not plan on using the board -- instead, use Powerpoint or transparencies. I can provide you with transparencies of various kinds. I can also supply a laptop for use during your talk. Let me know in advance if you will be using Powerpoint.
I need to clean up the lecture notes on Sysiphus cooling before I post them. There will be no pre-flight for Monday, but I will post reading material on resonance fluorescence for those of you who are interested.
Yesterday in class we talked about:
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The Doppler limit, which is the limiting temperature (about 150 microK) for simple Doppler cooling. It comes from the competition between Doppler cooling and recoil heating.
So-called Sysiphus cooling (or polarization gradient cooling, or sub-Doppler cooling, or...). This is a tricky cooling process which relies on optical pumping among hyperfine ground states as an atom moves through the optical potentials produced by overlapping laser beams. Sysiphus cooling can produce a very large force for low-velocity atoms, which lets us cool to lower temperatures (few-10 microK)
Magneto-optic traps (MOTs). MOTs are the workhorses of atomic physics -- they let us trap and cool billions of atoms from a room temperature vapor. A MOT is an optical molasses with an added quadrupole magnetic field. The magnetic field adds a position dependence to the optical force using the Zeeman effect. The overall trap is characterized by a spring-constant and a damping rate.
Cheers,
Brian
Posted by Brian at 10:20 AM | Comments (0)
April 14, 2005
Final project talks coming soon!
Hey Class,
Only one of you has signed up to give her final project talk. These talks will start next week (Thursday) and will take up the last 4 class periods!
Each of you needs to sign up for a date (4/21,4/26,4/28, or 5/3) to give your talk. Send me an email -- first come first served. If you do not send me an email (by 5 pm today) then I will randomly assign you to a date.
I will give more details about the talk in class today. We will finish up laser cooling, then do resonance fluorescence, and then you guys are basically teaching the rest of the class.
Also remember that the final project is due by 5/13. I will not and cannot be flexible on that date.
Brian
Posted by Brian at 09:13 AM | Comments (0)
Note from Man-Hong on "Energy-time Uncertainty relation"
Hey Everyone,
Man-Hong sends this comment our way:
I accidentially found a comment by Seth Lloyd, in his nature article "Ultimate physical limits to computation". It is said that
"In particular, the correct interpretation of the time-energy Heisenberg uncertainty principle [DE Dt >= hbar] is not that it takes time Dt to measure energy to an accuracy DE (a fallacy that was put to rest by Aharonov and Bohm) but rather that that a quantum state with spread in energy DE takes time at least [Dt = pi hbar / 2 DE] to evolve to an orthogonal (and hence distinguishable) state."
Brian
Posted by Brian at 08:45 AM | Comments (0)
April 12, 2005
Class review — 4/12
Hey Class,
Don't forget that there is a pre-flight for Thursday. Don't do it at the last minute!
Today we talked about:
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Some issues brought up in the last class.
The spectrum of scattered light is equal to the driving light
The spectrum of spontaneous emission (what comes out of an atom if we start in an an excited state) is a Lorentzian with a width set by Gamma.
The fact that I dislike my old picture for why saturation occurs. I think it's just an effect related to damping in a two-level system.
A puzzle (based on the micromaser) related to quantum measurement.
Laser cooling. We saw how Doppler cooling works by creating velocity-dependent, or friction-like, force.
We also calculated the cooling rate for Doppler cooling, and we could see how it cannot work well for atoms with large initial velocities (something above a few-10 m/sec).
We talked about recoil heating, which occurs for any atom that is scattering light. The so-called "recoil limit" is around a few micro-Kelvin.
More next time!
Brian
Posted by Brian at 07:08 PM | Comments (0)
April 11, 2005
Error in lecture notes
Hey Class,
Shizhong found an error in my lecture notes on a quantum atom interacting with the quantum EM field. My definition of the saturation intensity was off by a factor of the wavelength. I'll update the online lecture notes right away!
Brian
Posted by Brian at 02:58 PM | Comments (0)
April 09, 2005
Pre-flights ready for class on 4/12
Hey everyone,
The pre-flights (and some reading material) are ready for class on Tuesday.
Brian
Posted by Brian at 12:54 PM | Comments (0)
April 08, 2005
Class review — 4/7
Hey Class,
Remember that problem 2 is due on Tuesday.
There will be reading material for next class and pre-flights up by tomorrow afternoon.
A few questions came up in class; the answers follow. First: the scattered light for a single, two-level atom in free-space is always exactly at the frequency of the driving field (the spectrum is a delta-function). Second: one should not employ an intermediate state when arguing this (like I did, when I said that the atom was in the excited state). Hmmm... it seems as if there were more questions. Comment on this blog entry if you can think of them! I still haven't figured out what's going on with the entropy of the universe.
Yesterday we spoke about:
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We learned about Mollow's transformation, which tells us that an EM field in a coherent state interacting with an atom is equivalent to a classical field plus the quantum vacuum interacting with the atom.
We talked about "scattering" and the Optical Bloch Equations (OBEs). Thi is just a density matrix description of light scattering (laser incident on an atom and a detector measuring scattered light). We define the fluorescence rate as the decay rate times the excited state population. The fluorescence rate has a Lorentzian dependence on detuning, and saturates at high driving intensities (there are many ways of understanding that).
We saw spontaneous Raman scattering in the context of quantum jumps.
We ended with a summary of what we know about light and atoms now, and the different pictures that we have.
Cheers,
Brian
Posted by Brian at 10:27 AM | Comments (0)
April 01, 2005
Class Review — 3/31
Hey Class,
Remember: Homework 2, problem 1 is due 4/7 and problem 2 is due 4/11.
And: Class is cancelled on 4/5.
Lecture notes will be up on the website today or tomorrow. There will be no pre-flight for next class.
Yesterday in class we learned about:
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A quick answer to what happens inside of a simple laser (single-mode, gain medium has three levels). The number of photons in the laser mode increases dramatically at a "threshold" pumping rate. Well above that threshold, the number of photons in the mode is described by a Poisson distribution that has a larger variance than a coherent state.
The Jaynes-Cummings Hamiltonian. This Hamiltonian describes the interaction of an atom with a single mode of the quantum EM field. The J-C Hamiltonian has two terms, emission + |e> -> |g> and absorption + |g> -> |e>, which results in a Rabi rate that depends on the number of photons in the mode. We saw how micromaser experiments are a realization of the J-C Hamiltonian, and how one can observe "vacuum Rabi oscillations." Note that the J-C Hamiltonian does not describe atoms in free space.
Spontaneous emission, as described by the Wigner-Weisskopf theory (which is not pertubation theory). The W-W solution is a solution to Schrodinger's equation (quantum EM field + quantum atom), in the limit that our quantization volume gets very large. An atom in the excited state decays exponentially to the ground state with a rate that depends on the dipole matrix element squared.
Cheers,
Brian
Posted by Brian at 12:23 PM | Comments (0)