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

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

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

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

Quantum States of light. We talked about Fock, or number, states. For these states, the expectation value of the electric field is 0, but the variance depends on n.

Coherent states. These states are produced by a laser (maybe) and classical currents (an antenna). Coherent states are a specific superposition of number states, where the probability distribution is Poisson-ian in the number state basis. Coherent states are also characterized by a single parameter that is a complex number. The expectation value of the field is finite, and shows classical-like behavior. That means that the electric field strength oscillates in time. What is not classical about coherent states is the extra quantum "fuzz" on the electric field, although the size of the fuzz as a fraction of the electric field strength shrinks as the expectation value of n grows.

We talked about the correlation function g(2) as something that distinguishes Fock from coherent states. More on this next time!

Cheers,

Brian