Quantum Optics with Quantum Dots

Here at the CQT, Alexia Auffèves from the Institut Néel is talking about “Revisiting cavity quantum electrodynamics with quantum dots and semiconducting cavities (when decoherence becomes a resource)”.

She did her graduate work doing experimental work on Rydberg atoms — that is, atoms in highly excited states, which can be much larger than normal atoms. But then — according to her collaborator Marcelo Santos, who introduced her — she “went over to the dark side” and became a theorist. She now works at a quantum optics group at Institut Néel in Grenoble, France.

This group does a lot of quantum optics with quantum dots. If you’ve never heard about quantum optics or quantum dots, I’ve got to tell you about them: they’re really quite cool! So, the next section will be vastly less sophisticated than Auffèves’ actual talk. Experts can hold their noses and skip straight to the section after that.

An elementary digression

Quantum optics is the branch of optics where we take into account the fact that light obeys the rules of quantum theory. So, light energy comes in discrete packets, called “photons”. You shouldn’t visualize a photon as a tiny pellet: light comes in waves, which can be very smeared out, but the strength of any particular wave comes in discrete amounts: no photons, one photon, two photons, etc. To really understand photons, you need to learn a theory called quantum electrodynamics, or QED for short.

A quantum dot is a very tiny piece of semiconductor, often stuck onto a semiconductor made of some different material. Here are a bunch of quantum dots made by an outfit called Essential Research:



 

What’s a semiconductor? It’s a material in which electrons and holes like to run around. Any matter made of atoms has a lot of electrons in it, of course. But a semiconductor can have some extra electrons, not attached to any atom, which roam around freely. It can also have some missing electrons, and these so-called holes can also roam around freely, just as if they were particles.

Now, let quantum optics meet semiconductor! If you hit a semiconductor with photon, you can create an electron-hole pair: an extra electron here, and a missing one there. If you think about it, this is just a fancy way of talking about knocking an electron off one of the atoms! But it’s a useful way of thinking.

Imagine, for example, a line of kids each holding one apple in each hand. You knock an apple out of one kid’s hand and another kid catches it. Now you’ve got a “hole” in your line of apples, but also a kid with an extra apple further down the line. As the kids try to correct your disturbance by passing their apples around, you will see the extra apple move along, and also perhaps see the hole move along, until they meet and — poof! — annihilate each other.

To strain your powers of visualization: just like a photon, an electron or hole is not really a little pellet. Quantum mechanics applies, so every particle is a wave.

To add to the fun, electrons and holes often attract each other and sort of orbit each other before they annihilate. An electron-hole pair engaged in such a dance is called an exciton — and intriguingly, an exciton can itself roam around like a particle!

But in a quantum dot, it cannot. A quantum dot is too small for an exciton to “roam around”: it can only sit, trapped there, vibrating.

Next, let quantum optics meet quantum dot! If a quantum dot absorbs a photon, an exciton may form. Conversely, when the exciton decays — the electron and hole annihilating each other — the quantum dot may emit a photon.

Put this setup in a very, very tiny box with an open door — a “cavity” — and you can do all sorts of fun things.

Back to business

The quantum optics group at the Institut Néel does both experimental and theoretical work. Four members of this group have come to visit the CQT. There are three main topics studied by this group:

• Cavity QED with quantum dots and optical semiconducting cavities. There are interesting similarities and differences between quantum dots and isolated atoms.

• One-dimensional solid-state atoms. This kind of system can operate at “giant optical nonlinearity”, and it can be stimulated with single photons.

• “Broad” atomic ensembles coupled to cavities, and their potential for solid-state quantum memories.

She will only talk about the first!

The simplest sort of cavity QED involves a 2-level system — for example, an atom that can hop between two energy levels — coupled to the electromagnetic field in a cavity.

But instead of an atom, Alexia Auffèves will consider a quantum dot made of one semiconducting material sitting on some other semiconducting material. An electron-hole pair created in the dot wants to stay in the dot, since it has less energy there. Like an atom, a quantum dot may be approximated by a 2-level system. But now the two “levels” are the state with nothing there, and the state with an electron-hole pair. The electron-hole pair has an energy of about 1 eV more than the state with nothing there.

Next, let’s put our quantum dot in a cavity. We want an ultrasmall cavity that has a high Q factor. Remember: when you’ve got a damped harmonic oscillator, a high Q factor means not much damping, so you get a tall, sharp resonance. For a cavity to have a high Q factor, we need light bouncing around inside to leak out slowly. That way, the cavity emits photons at quite sharply defined frequencies.

There are various ways to make tiny cavities with a Q factor from 1000 to 100,000. But the trick is getting a quantum dot to sit in the right place in the cavity!

Now, a quantum dot acts differently than an isolated atom: after all, it’s attached to a hunk of semiconductor. So, our quantum dot interacts with electrons and holes and phonons in this stuff. This causes a lowering of its Q factor, hence a broadening of its spectral lines. But we can adjust how this works, so the dot acts like a 2-level system with a tunable environment.

This lets us probe a new regime for cavity QED! The theorists’ game: replace a 2-level atom by a quantum dot, and see what happens to standard cavity QED results.

For example, look at spontaneous emission by a quantum dot in a cavity.

For an atom in a cavity, the atomic spectral lines are usually much narrower than the cavity resonance modes. Then the atom emits light at essentially its natural frequencies, with a strength affected by the cavity resonance modes.

But with quantum dots, we can make the quantum dot spectral lines much wider than the cavity resonance modes! Then the dot seems to emit white light, as far as the cavity is concerned. But, the dot emits more photons at the cavity frequency: this is called “cavity feeding”. People have been working on understanding this since 2007.

I think I’ll stop here, though this is where the real meat of Auffèves’ talk actually starts! You can get a bit more of a sense of it from her abstract:

Abstract: Thanks to technological progresses in the field of solid-state physics, a wide range of quantum optics experiments previously restricted to atomic physics, can now be implemented using quantum dots (QDs) and semi-conducting cavities. Still, a QD is far from being an isolated two-level atom. As a matter of fact, solid state emitters are intrinsically coupled to the matrix they are embedded in, leading to decoherence processes that unavoidably broaden any transition between the discrete states of these artificial atoms. At the same time, very high quality factors and ultra small modal volumes are achieved for state of the art cavities. These new conditions open an unexplored regime for cavity quantum electrodynamics (CQED) so far, where the emitter’s linewidth can be of the same order of magnitude, or even broader than the cavity mode one. In this kind of exotic regime, unusual phenomena can be observed. In particular, we have shown [1] that photons spontaneously emitted by a QD coupled to a detuned cavity can efficiently by emitted at the cavity frequency, even if the detuning is large; whereas if the QD is continously pumped, decoherence can induce lasing [2]. These effects clearly show that decoherence, far from being a drawback, is a fundamental resource in solid-state cavity quantum electrodynamics, offering appealing perspectives in the context of advanced nano-photonic devices.

And for more details, read the references:

• [1] Alexia Auffèves, Jean-Michel Gérard, and Jean-Philippe Poizat, Pure emitter’s dephasing: a resource for advanced single photon sources PRA 79, 053838 (2009).

• [2] A. Auffèves, D. Gerace, J. M. Gérard, M. Franca Santos, L. C. Andreani, and J. P. Poizat, Controlling the dynamics of a coupled atom-cavity system by pure dephasing: basics and applications in nanophotonics, PRB 81, 245419 (2010).

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