Random Quantum Optics Question

Consdier a coherent photon state |alpha> interacting with a two-level system.  Now, in the large photon limit, we ought to be able to recover the semi-classical interaction: i.e. a classical EM field interacting with a two-level system.  Conceptually, this should be the case.  Has anyone shown this?  From what I can tell, the interaction with a coherent state gives rise to Rabi flopping that decays, and has revivals.

Light traveling faster than light

There has been a small splash in the past couple days about a couple Germans who have purportedly violated special relativity (see here, and here). So what’s going on here? Is this another superluminal propagation of light in a region with strong anomalous dispersion? For starters, here’s another article with a bit more detail, as well as a comment from Aephraim Steinberg (a quantum opticist at University of Toronto). Additionally, here’s the paper on the ArXiv: arXiv:0708.0681v1.

Well, what they’ve done is worked with Frustrated Total Internal Reflection (FTIR). First of all, total internal reflection is when all the light is reflected at the interface. This only happens when moving from a denser optical material to a more rarefied material. Past a certain angle, all the light is reflected. You’ve seen this if you look up while underwater. Typically, you can see the sky above you, only in a small disc. Outside that, all you see is the water. This is the same principle by which fiber optics works—the light is confined in a small glass rod.

Now, here’s a slightly weird part. Even though all the light is reflected, there is a small portion of it that hangs out at the interface, and extends into the rarer material. This portion is called the evanescent wave. Now, it turns out if another dense material is placed close enough to this evanescent wave, the light can actually be transmitted to the second material. This is very similar to Quantum Tunneling, where a particle can be transmitted through a potential barrier. This process is called frustrated total internal reflection.

Back to the paper and experiment. They conducted a FTIR experiment with microwaves, and measured the arrival times of both the reflected and transmitted signals. They claim that the signals arrived at the same time. This means that since the transmitted signal travels a longer distance, it must be moving faster than the speed of light. The paper is slightly dubious, as there is no data present in the paper.

The crux of the matter is the tunneling time. Now, the notion of time is slightly problematic in quantum mechanics—there is no ‘time’ operator to give us the arrival time of particles. In fact there has been much research on this. If I had decided I wanted to be a theorist, I probably would have been working with Herbert Winful on the theory of this.

The two questions are: Is there superluminal propagation in tunneling? How do we interpret what is going on?

Now we’re getting somewhere interesting. In their paper, they have an interesting take on this. They identify the evanescent wave with virtual photons:

All three properties - the violation of the Einstein energy
relation, the zero time spreading, and the non observability of
evanescent modes - can be explained by identifying evanescent
modes with virtual photons as predicted by several authors, see
for instance references 6, 7, 8, 9, 10. The corresponding Feynman
diagram is sketched in Fig. 2. Tunneling and evanescent modes
are properly described by quantum mechanics.

That is, a photon that doesn’t really exist, but can have an effect on the system. Virtual particles are abound in particle physics, where we typically detect the decay products of a virtual particle. Does this interpretation hold water? Perhaps. The theorist in me wishes for there to be a thorough, rigorous QED calculation showing this.

Steinberg offers a different interpretation:

Steinberg explains Nimtz and Stahlhofen’s observations by way of analogy with a 20-car bullet train departing Chicago for New York. The stopwatch starts when the centre of the train leaves the station, but the train leaves cars behind at each stop. So when the train arrives in New York, now comprising only two cars, its centre has moved ahead, although the train itself hasn’t exceeded its reported speed.

That is, given a pulse of light, the back end of it is eaten up, giving the impression that the center of the pulse has moved faster. I’m not sure if this holds water in this particular case. Perhaps when dealing with superluminal propagation in an region of anomalous dispersion, sure. But for evanescent waves, I don’t know.

Winful has another explanation of this effect (a long paper on this is available in the New Journal of Physics). From PRL 90, 023901 (2003), the final paragraph is:

In conclusion, we have shown that the apparent superluminal
tunneling of pulses is a quasistatic phenomenon
in which the output envelope adiabatically follows the
input. The incident peak does not actually propagate to
the exit which means that the notion of a transit time is
meaningless. The input field merely modulates the amplitude
of a standing wave created through the interference
between forward and backward waves. When properly
interpreted in this context, no superluminal transport is
seen

So what does this mean? It’s sort of like saying that the input merely increases and decreases the level of an existing wave inside the barrier. The pulse that comes out is not the pulse that goes in.

Suffice to say, I don’t think that this issue will be resolved any time in the near future.

Double the fun.

Last Friday I was attempting to squeeze more power out of the Raman BBO, and proceeded to lose all the power.  So I spent this past weekend fixing it.  Fun.  But I managed to accomplish what I had set out to do.  All is well and good.

Or so I thought.  Turns out, when I turned on the Microwaves for the EO (phase modulator), the power dropped significantly.  Apparently, the free-spectral-range of the cavity wasn’t matched to the microwave sidebands, and hence weren’t building up.

Some explanation:

To double the frequency of our laser light (change color from infrared to blue, or blue to ultraviolet), we shine the light into a cavity with the nonlinear crystal (this crystal changes the color).  A cavity basically is a set of mirrors aligned such that the light makes a complete circuit and ends up exactly where it started, heading in the same direction, and building up inside the cavity.

For an optical cavity, there are a discrete set of colors that will build up in the cavity.  The spacing between these adjacent colors is called the free-spectral-range.  So here’s the problem I had:  without the phase modulator on, I only had one color in the cavity, and it built up just fine.  Got a decent amount of power out of it.  Turning on the phase modulator creates additional colors of the light.  And these different colors were not in the set of colors that build up in the cavity. 

So, basically, I had to re-align the cavity such that these additional colors build up.  And that is why I’m posting this at 3am. 

Stupid mistakes

I’ve been quite non-existent the past couple weeks.  Undoubtedly because of two things.  (1)  I have no internet at home.  The person whose wifi I’ve been using must have left for the summer.  Hence, I have no signal at home.  With three months left in Michigan(!), I don’t care.  It’s obvious that I’ve become a product of the ‘information age.’  What did I do before the internet?  Ah yes.  Read.    (2)  Because I only have a couple months left, I’ve been working ridiculous hours, hoping to finish this experiment before leaving.  12+ hours for the past few weeks is not fun.  (sometimes, it’s 15 or 16 hours).  Additionally, Dan—the senior grad student on my project—just defended his thesis, and will be leaving the lab shortly.  That means I’ll be in charge of this project, and I don’t know what I’m doing.

And things are not peachy in the lab.  We have a new student on my project, and I have to explain everything all over again.  We have very little power in our Raman laser, and Yisa just chipped the BBO crystal today (which is extremely expensive).  He’s too cavalier with optics.  But I figured out why I was only getting ~90% qubit detection fidelity—apparently some idiot turned off the RF generator for the doppler cooling beam.  Thus, we weren’t cooling the ions.  Alas, the initialization beam got mis-aligned.  The fun never ends. 

The night of the red moon

Don’t know if many of you knew, but there was a total lunar eclipse tonight. Unfortunately, it was quite overcast here in Michigan, so I couldn’t see it. This picture is evidence that it was one of the “best in years”.

The reason for the deep-red color of the moon is due to the scattering of light in the atmosphere. Since the moon is deep inside the earth’s shadow (in the umbra), there is no ballistic illumination of the moon. All the light that hits the moon is scattered light from the atmosphere of the earth. However, the air molecules act as Rayleigh scatterers, hence scattering the shorter wavelengths of light stronger—blue scatters more than red. Since all the other colors have been scattered more strongly, the red is left on the moon.

I see the light at the end of the tunnel

And there’s a needle there:

Photonic qubits: Schrödinger six-pack

I took a look today at Nature Physics, a relatively new physics journal from the makers of Nature. The latest issue has an article about the entanglement of six photons in both a ‘GHZ’ state and a ‘cluster’ state.

The Greenberger–Horne–Zeilinger (GHZ) state is an entangled state in which (for this experiment) all six photons are in a superposition of all being horizontally polarized and all vertically polarized. In computer lingo, that is all zero (000000) and all one (111111) at the same time. This state is entangled, as the state of each individual photon is correllated with the others. The six-qubit ‘Cluster state’ is quite a different beast. Basically, it is another entangled state of the six photon system. The entanglement properties of these states are quite different, and can be represented as points on a graph. Each qubit is a point/node, and the entanglement is like a line connecting the points.

Six-Qubit GHZ state:

Six Qubit Cluster State:

Of course, when I think of a Schrödinger six-pack, I think of Bob the Angry Flower.

Thermal Radiation & Photon Gasses

One thing that has always puzzled me is thermal radiation. This is electromagnetic radiation from an object simply because it is warm. I never understood why a warm body emits light (NB: I use “light” and “electromagnetic radiation” interchangeably).

In quantum mechanics, we are taught that light is emitted with a sharply defined color—given by the energy difference between levels. I guess it could make sense that if, naively, hot bodies consisted of atoms in motion and that there were a continuum of motional states, then there could be a continuous energy spectrum.

But this means that the atoms would be losing energy to emit thermal radiation, thus cooling it. Hence it seems like all bodies would then be at zero temperature and all the energy in the universe would be in light.

Here’s the insight I recently found:
Remember that there is a vacuum electromagnetic field, containing an infinite number of modes. Each mode has a certain number of photons. Here’s the kicker: the vacuum field is in thermal contact with the hot body! That is, the electromagnetic field is in thermal equilibrium with the hot body! Therefore, since the body has a nonzero temperature, then there must be a nonzero photon distribution in all the modes. This distribution is exactly the distribution of thermal radiation.

Thermal Radiation & Photon Gasses

One thing that has always puzzled me is thermal radiation. This is electromagnetic radiation from an object simply because it is warm. I never understood why a warm body emits light (NB: I use “light” and “electromagnetic radiation” interchangeably).

In quantum mechanics, we are taught that light is emitted with a sharply defined color—given by the energy difference between levels. I guess it could make sense that if, naively, hot bodies consisted of atoms in motion and that there were a continuum of motional states, then there could be a continuous energy spectrum.

But this means that the atoms would be losing energy to emit thermal radiation, thus cooling it. Hence it seems like all bodies would then be at zero temperature and all the energy in the universe would be in light.

Here’s the insight I recently found:
Remember that there is a vacuum electromagnetic field, containing an infinite number of modes. Each mode has a certain number of photons. Here’s the kicker: the vacuum field is in thermal contact with the hot body! That is, the electromagnetic field is in thermal equilibrium with the hot body! Therefore, since the body has a nonzero temperature, then there must be a nonzero photon distribution in all the modes. This distribution is exactly the distribution of thermal radiation.