Monthly Archives: October 2013

How to cool your (quantum) beer

Everybody has a fridge. Maybe not an Eskimo, but I have heard that Eskimos actually use fridges to make sure that their foodstuffs are not always completely frozen. I have never personally met an Eskimo to verify this, but anyway everybody has a fridge, and everybody enjoys a nice cold beverage every now and then. Including physicists.

Now, as physicists are wont to do, they start to think: What if you have a quantum beer?

Suppose said beer is a qubit. This is the smallest possible beer since a qubit only has 2 discrete energy states. What is the smallest self contained refrigerator that, in principle, can be constructed?

This was a question that was tackled by Linden et. al. (See link). Their answer: a single atom that can occupy at least 3 discrete energy states. Or alternatively, if you construct your fridge out of qubits, then the answer is 2 qubits which collectively occupy a grand total of 4 possible energy states.

How does it work? Well, technicalities aside, it really is pretty simple. Consider the case where the fridge is made out of 2 qubits. Suppose when a qubit is occupying its lowest energy (ground) state, we label the state 0 and say the qubit is in the state 0. If the qubit is occupying its excited state (the only other energy level), then we say it is in state 1.If you have 3 qubits, then we can describe them compactly in the following way: 000 means all 3 qubits are in the lowest energy state, 001 means only the 3rd qubit is excited, and so on.

All you then need to do is to arrange an interaction between the qubits (or in physics nomenclature, introduce an interacting Hamiltonian) which transfers a 3 qubit state from an energy configuration of 101 to 010. If your quantum beer is the first qubit, then if you start at state 1, you will end in state 0. This means basically that the qubit becomes less energetic and therefore cooler. The problem is that such an interaction between 101<–>010 typically go both ways, which causes the state of your beer to go from 1->0 (cooling) and from 0->1 (heating) with equal measure, messing up the cooling process. This is where a little bit of ingenuity becomes necessary. By putting part of the fridge at a different (higher) temperature, and tweaking the energy levels of the qubits appropriately, you can make the beer and fridge system more likely to find itself in the 101 configuration than the 010 configuration. This means that your beer is more likely to go from 1->0 than from 0->1, and wala! you have a 2 qubit fridge and a nice chill qubit beer.

And that’s pretty cool.

 

 

If you leave no trace it’s like it never happened…

Everyone has heard about the perfect murder. If you leave no trace, there is nothing that can lead anyone to you. However, if you did something (either bad or good) but no one was watching, is it like you never did it?

Now, think for a moment – is there really no trace? Well, of course YOU know that you DID it, so the trace is inside your head! This information seems safe, but in principle there might exist a sci-fi machinery capable of getting this information from inside your brain, or simply a pair of gentlemen in black suits playing amateur dentists can get it out of you using less sophisticated methods…

However, if you suffered from amnesia, brain damage, or some other unpleasant accident, this information seems to be permanently lost. In this case the question “did it really happened?” seems to be unanswerable.

Recently I rediscovered a paper [PRL 103, 080401 (2009)]  (clearly the original event where I first read the paper did exist even if I had forgotten it) that addresses the above question. In particular, it is suggested that events in which entropy is decreasing might actually happen in our universe, but they necessarily leave no trace. Therefore, one cannot observe them and hence we conclude from observable data that entropy can never decrease. Since the job of a physicist is to study things that we do observe, it seems that these strange events are beyond the scope of physics…

Conway’s game of life

One of the cooler things I discovered recently was that when you google search “Conway’s game of life” google automatically begins to play the game of life in the background of the search results page. It is rather mesmerizing,

The game of life is played on a grid of little squares; squares have two configurations “alive” and “dead” which are usually represented by using two different colours. A single game consists of a initial seed or starting configuration and a set of rules which govern how the grid updates:

(1) Any live cell will remain alive if it has 2 or 3 live neighbors; otherwise it will die.

(2) Any dead cell with 3 live neighbors will become alive.

The rules are roughly motivated by physical considerations; if the population density is too low or too high then individual members of a colony will die before reproducing. However three alive cells may reproduce to create a extra adjacent live cell.

The game is extremely popular because the seemingly overly simple rules can generate extremely complicated patterns. Recently it was demonstrated that certain initial conditions of the game of life can give rise to emergent behavior in the sense that we can aggregate large sections of the grid (consisting of multiple cells) and treat this section as an individual “macroscopic cell” which behaves non-trivially. There are no simple set of rules for how these macroscopic cells behave; all update

rules continue to apply to the small indivisible cells which constitute them. Nevertheless it is possible to  initialize the game of life so that the macroscopic squares effectively appear to evolve according to conditions (1) and (2). There is quite a spellbinding example of this available here. Check it out as it is unbelievable at first sight.

Distinguishing identical twins

Can you tell apart identical twins easily? Identical twins are quite close to each other so it is hard to figure out who it is at a glimpse. Each twin, however, lives his/her own life, like classical particles having its own trajectory. We can consider the twin paradox in special relativity as an example, assuming that we cannot distinguish identical twins before sending one of them to space. After sending one of twins to space in a high-speed rocket, we can distinguish one twin on the earth from the other twin coming back to the earth, due to gravitational time dilation. In the same sense, we can also distinguish classical particles because they are also in macroscopic dimensions controlled by deterministic mechanics. Now the question is whether we can distinguish quantum particles too? The answer is in one of our papers, http://arxiv.org/abs/1212.5338v3 .