Lab Visit Report: Cavity QED

While Kate was off being all lawyerly at her NAAG workshop, I spent my time visiting my old group at NIST, and some colleagues at the University of Maryland. This wasn't just a matter of feeling like I ought to do something work-like while she was workshopping-- I genuinely enjoy touring other people's labs, and hearing about the cool things they're working on.

I figure that, having spent a day and a half talking about hot new physics experiments, I may as well mine them for blog fodder. I've managed to scrounge up papers related to a lot of the experiments in question on the arXiv, but the arXiv isn't as widely used in my subfield as in high-energy physics, so there were a few things I haven't found. One of them was a cavity QED experiment that Luis Orozco is working on at Maryland, and I'll start with that.

"Cavity Quantum Electro-Dynamics" deals with the interaction between atoms and light that's confined in a cavity consisting of two mirrors facing one another. In this sort of system, a single photon can bounce back and forth thousands of timesbefore escaping, which leads to some dramatic changes in the interaction between atoms and the field. With the advent of laser cooling techniques, it's possible to pass atoms through a cavity very slowly, which makes all sorts of interesting things possible.

One clever trick Luis talked about was a method for knowing when they've produced an atom in a particular superposition state. The set-up looks basically like this:


They have a cavity consisting of two mirrors about 2mm apart, and they use a slow atoms source to drop atoms into the cavity roughly one at a time (on average, there's one atom in the cavity at all times). They shine a laser into the cavity that's vertically polarized, and tuned to be resonant with the atoms. On the far side of the cavity, they put a polarizing beamsplitter, and two detectors.

The beamsplitter is arranged so that vertically polarized light passing through the cavity goes straight through the beamsplitter onto one detector. The other detector would pick up any horizontally polarized light that comes out, but in the absence of an interaction between the atoms and the light, there is no horizontal light.

When an atoms absorbs one of the vertically polarized photons, though, it gets excited to a higher energy state. The polarization is critically important, though-- the atoms they use (rubidium) have multiple sub-levels with different angular momentum projections (given the quantum number "m"), and when they absorb vertically polarized light, they get excited to the upper state without changing m, so if they start in the m=0 sublevel of the lower state, they end up in the m=0 sublevel of the upper state. This is shown on the right of the diagram above.

From there, one of two things can happen. Either the atom can re-emit a vertically polarized photon, and return to the m=0 state, or it can emit a circularly polarized photon, and change the m-state:


The vertical case is uninteresting, but something cool happens when the atom emits a circular photon. There are two possibilities here: either it can emit a right-hand-circular photon, and drop down to m=-1, or it can emit a left-hand-circular photon, and drop down to m=+1. Either of those photons has a 50% chance of being reflected at the beamsplitter, and detected by the second detector.

So if the second detector records the arrival of a photon, they know that an atom has emitted a circularly polarized photon, and changed its m-state. But, they don't know which circular polarization was emitted-- either is equally likely-- so the state is indeterminate. The atom is not in m=-1 or m=+1, but a superposition of the two.

So, when they see a photon at the detector for horizontal polarization, they know that not only has the atom in the cavity at that instant absorbed a photon, but it's ended up in a superposition of two states. This won't necessarily happen every time, but when it does, they know that they're dealing with a second state.

Now, imagine doing this a second time. The vertically polarized photon from their laser excites both parts of the superposition in the same way, so they go from a superposition of m=-1 and m=+1 in the lower state to a superposition of m=+/-1 in the upper state. This can also decay in one of two ways, either emitting a boring vertical photon and going back to the start, or emitting a circular photon, and going back to m=0.

But if the atom emits a circular photon and returns to m=0, there are two possible paths it could've taken to make that loop. And any time you have two possible paths for a quantum system, you expect to see interference between those two paths. Atoms in m=+1 and m=-1 can evolve very slightly differently, and if the two different paths are in phase, the probability of returning to m=0 is high, while if the paths are out of phase, the probability is zero.

That's exactly what they see. By varying the conditions of the experiment, they can look at different versions of the two paths, and they see these "quantum beats" in the probability of returning to m=0 and emitting a second circularly polarized photon.

There are a number of additional tricks they can pull with this to produce states in which the state of the atoms is entangled with the state of a photon, and other quantum information topics. All of them rely on this basic trick, though, using the polarization of the emitted photons to inform them when the atom has made a transition into a superposition state.

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I looked up the wikipedia article for circular polarization but it's not in the context of an experiment so it doesn't make a whole lot of sense to me. Is the emission of vertically vs. circularly polarized photons simply a probability? What about the circularly polarized photon makes the quantum number change?

Circularly polarized photons carry one unit of angular momentum (+/- 1, really), and thus absorbing or emitting one causes a change in the angular momentum state of the atom. I believe (and I'm sure I'll be corrected if I'm wrong) that this is a classical effect-- if you treat light as just an oscillating electric and magnetic field, you still find that circular polarization has angular momentum associated with it. You can (very loosely) think of it as having to do with the rotating direction of the electric field.

The emission of circular vs. linear light is just a matter of probabilities. When the atom is in an excited state, it can decay into one of several lower-energy states, and which state it goes into is wholly random (for spontaneous decay, at least). The states aren't all equally likely-- the exact probability of decaying into a particular state depends on the angular momentum of the states involved, and is something you spend hours calculating in grad school quantum classes-- but it's ultimately probabilistic.

I'm trying to think if there's a way to break the coherence between the two states with a different analyzer. If one were to drop a quarter-wave plate in front of the beamcube, then the RCP and LCP light would be linearized and end up on different detectors. The vertical polarization, however, would end up on either detector with equal probability. This would seem to create a coherence between one of the two |m|=1 states and the m=0 state. This just replaces one coherence with another. Is there a way that I don't see to determine unambiguously the polarization of a given emitted photon, and thus make the system behave classically?

Your post about "What Kind of Blogging Brings the Most Traffic" reminds me that I had two questions to this very interesting post:

What breaks the degeneracy between the m = +1 and m= -1 states? Do they need a magnetic field? And then, I am a bit puzzled what are the different paths in this experiment and how the interference pattern shows up. That's not a spatial interference pattern, as in the double slit experiment? Does one have to look at the numbers of "double clicks" at the horizontal detector as a function of the delay between the clicks?

Best, Stefan

What breaks the degeneracy between the m = +1 and m= -1 states? Do they need a magnetic field?

They apply a small magnetic field-- I believe it's perpendicular to the mirrors-- to set the quantization axis and break the degeneracy between the magnetic sublevels.

And then, I am a bit puzzled what are the different paths in this experiment and how the interference pattern shows up. That's not a spatial interference pattern, as in the double slit experiment? Does one have to look at the numbers of "double clicks" at the horizontal detector as a function of the delay between the clicks?

I believe that's it.
It's an interference between different transition paths, so I believe it shows up as an oscillation in the transition probability.

The essential physics is the same is in "quantum beat" experiments, such as Hellmuth et. al. PRA 35, 2532 (1987).