Simple to understand Quantum Dot information?

[kalel]

I'm looking to learn a bit more about quantum dots (currently reading up on Wikipedia), yet I've noticed that Wikipedia can sometimes expect you to have relevant knowledge in the field to understand given information.

Is there any source that provides easy to understand information for laymen?

[T3sl4co1l]

The simplest to understand -- if you know atoms and solids -- is that a quantum dot is intermediate between the cases.

Whereas an atom has few energy levels (and hence a sparse emission/absorption spectrum, since the energy levels are transitioned by pure energy -- photons, light), and whereas a solid has a quasi-continuous band of energy levels (meaning, practically speaking, any wavelength in the band will be absorbed; emissions however are a more complicated matter*), quantum dots have more energy levels than atoms, but still discrete, not so many as to have an effectively-solid block of levels.

*For example, LEDs emit light corresponding to the band gap (give or take a fairly small error spread, 5 or 10%).  This is characteristic of direct bandgap semiconductors, while indirect bandgap semiconductors (like silicon) emit no light at all**.

**Actually you can make silicon emit light.  You can add quantum dots (ha!) as a phosphor, or you can avalanche it (which causes the weak emission of green-yellow light).  The latter is the mechanism through which Bob Widlar infamously posed the riddle: how can you generate a negative voltage from a 2N3055, simply by applying voltage or current to the remaining terminals?  (You avalanche the E-B junction, and the B-C junction acts like a photodiode, generating a paltry -- but nonzero -- negative bias.)

The number of energy levels, and their spacing, is determined by the number of atoms interacting together.  Equivalently, it depends on the geometry; so a qdot that's oddly shaped (rod shaped, say) will have different responses in different directions (which is perceptible, because photons can be polarized one way or another, and thus will only excite one axis or another).

The classic chemistry experiment is growing colloidal crystals of cadmium selenide (or related semiconductor), where the particle size is controlled by the concentration of reactants and temperature, and the fluorescence (light emission resulting from UV stimulation) color therefore as well.

The application to quantum computing is natural; anywhere there is a set of discrete states that are reasonably well separated in energy levels, and which can be potentially long-lived, is useful.  The energy separation has to be much greater than the thermal energy at the operating temperature, so that random motion of the particles and surroundings does not upset the state***.  Lifetime of a state depends on what forces cause it to relax to the ground state; in traditional semiconductors, an electron above the bandgap can transition below by getting trapped on a dopant or defect site, where it's much more likely to recombine.  Qdots are nice because they are small crystals, which can potentially be completely free of defects.  Alternately, a defect site can itself be used, as long as it's well separated from other defects.

***Or cause entanglements with the existing state; whatever the case, the effect is, time and heat mixes and scrambles the computer's state, and the information diffuses out into the surroundings, being diluted by meaningless ambient noise.  Perhaps analogous to how your brain feels groggy, forgetful and incapable of concentration (coherent operation) when you're running a fever (high temperature!).

Maybe this, too, is not nearly basic enough; "state" and "bands" and "energy levels" can be hard to pin down as well.  Let me know.

Tim

[kalel]

Thanks for taking the time to write such a thorough explanation! I have read it a few times (for now), and I would not dare to to claim that I have completely understood it, on the other hand it does give me something to think about.

One thing I wanted to ask was about this case of "entanglement with the existing state", and what would cause it. However, it might be contained in your answer already (as you stated the random motion of particles and surroundings), and it might become clear on a subsequent read after some rest.

[T3sl4co1l]

The trick with quantum interactions is you can work them as interactions of single pairs of particles.  You can map out the entire [possible] history of interactions of all particles in a system.  This gets you a sequence of interactions, where the system of particles moves from one state to another, each state transition (the finest possible division between states, anyway) being a single interaction.

For significant quantum behavior to manifest, the number of interactions between states needs to be small enough that the change is perceptible.  If a very small [average] change occurs, that is distributed over practically all particles in the system (as is normal for macroscopic objects consisting of unthinkable numbers of particles, all vibrating with significant energy), the increment between states is essentially continuous -- and hence we model it as actually continuous (in statistical mechanics, thermodynamics and so on).

This, to me, is the most useful interpretation of QM: the information-theoretic interpretation.

The state transition diagram is just Feynman diagrams (from QED+), expanded to cover the whole system.

Of course, mapping the whole thing is unknowable, which is why QM exists: we can't reconstruct a total diagram (except in contrived situations*), but we can -- very accurately, I might add -- measure and calculate the probabilities of certain transitions to occur.

*This is what particle physicists do: smash particles together, then sift through the debris.  The debris might be high energy electrons, gamma rays, protons, etc.  Familiar every day stuff (if a bit "hotter" than usual).  The paths of these particles are traced back to the collision, and the sequence of more exotic, high energy particles within the collision are solved based on selection rules that apply to those particles.

What we call "particles" are not physical in the same sense as, say, dust particles are to us; rather, they are literally the states of the respective quantum fields, and tracing this path through space-time, is in fact the state transition diagram.

It is still of course very difficult to solve, with a lot of luck involved, even with very powerful detectors.  Combine that with some interactions having very low probabilities in the first place, and that explains why the LHC had to sift through years of data to prove the existence of the Higgs boson.

Anyway, what this does for semiconductors is, if you follow the path of a free (conducting) electron, you'd see a huge (~infinite) number of interactions with the substrate -- a solid is full of electrons (and some nuclei hiding in there), which gives rise to the somewhat odd behavior of an electron in a solid in the first place (like the effective mass being very different from the (free in vacuum) electron mass).  Filtering those out, you'd see the behavior which is distinctive of semiconductors: the interactions which result in the electron losing energy are relatively low probability, so the electron can propagate or wander some distance before recombining.  And these interactions are catalyzed (more probable) around defects and stuff.

Tim