August 27, 2017

A few weeks back, we had a paper out on the arXiv, which I haven’t had time to write about yet. https://arxiv.org/abs/1707.09211

The topic of the paper is quantum master equations – a somewhat technical subject, but very important for much of the other physics we study, especially small thermal machines, like the ones I have written about here and here.

When we try to describe a thermal machine, we are faced with a problem. The machine necessarily interacts with some thermal reservoirs. These are large, messy systems with many, many particles. In fact, this is true more generally. Any small quantum system interacts with the surrounding environment in some way. We may do our best to isolate it (and experimentalists typically do a good job!), but some weak interaction will always be present. The environment is big and complicated, and it is extremely cumbersome, if not impossible, to describe in detail what is going on with all the individual particles there. It would make our lives miserable if we had to try…

This is where quantum master equations come in. Instead of describing the environment in detail, one can account for the average effect it has on the system. The noiseless behaviour that an isolated system would follow is modified to include noise introduced by the environment. There are various techniques for doing so. The quantum master equation approach is one of the most important and wide spread.

They gives us a powerful computational tool, and we rely on them a lot we try to understand what is going on, for example in quantum thermal machines. They have been around for more than half a century, but there are still aspects which are not completely understood. Since it accounts for the effects of a large, complicated environment, which is not explicitly described, deriving a master equation always involves some approximations. And it can sometimes be unclear when these approximations are reliable.

In our paper, we address one such ambiguity which is particularly relevant for studying small quantum thermal machines, or more generally, energy transport in a small quantum system (this might be relevant e.g. in photosynthesis, where light energy is transported through molecules).

Imagine that the quantum system consists of two particles. Imagine that each particle is in contact with a separate environment, and that the particles also interact with each other. Now one could derive a quantum master equation for the system in two different ways. One could either first account for the noise introduced by the environments on each particle separately, and then account for the interaction between them. Or one could first account for the interaction between the particles, and then find the noise induced by the environments on this composite system. This leads to two different master equations, often referred to as ‘local’ and ‘global’, because in the former case, noise acts locally on each particle, while in the latter it acts on both particles in a collective manner.

There has been quite a bit of discussion in the community on whether the local or global approach is appropriate for describing certain thermal machines, and even results showing that employing a master equation in the wrong regime can lead to violation of fundamental physical principles such as the second law of thermodynamics. In our paper, we compare the two approaches against an exactly solvable model (that is, where the environment can be treated in detail) and study rigorously when one or the other approach holds. We find what could be intuitively expected: When the interaction between the system particles is weak, the local approach is valid and the global fails. On the other hand, when the inter-system interaction is strong, the two particles should be treated as single system, and the global approach is the valid one. For intermediate couplings, both approaches approximate the true evolution well.

This is reassuring, and provides a solid foundation for our (and others’) studies of small quantum thermal machines and other open quantum systems.

Published paper: https://iopscience.iop.org/article/10.1088/1367-2630/aa964f

August 7, 2017

Today we have a new paper out on the arXiv in which we describe a quantum thermal machine which generates maximal entanglement in any dimension. https://arxiv.org/abs/1708.01428

Thermal machines do a lot of useful tasks for us. Power plants turn heat into electricity. Refrigerators keep our beers cold. Steam locomotives pull trains (OK, maybe they mostly don’t any more – but a steam engine is the archetypical picture of a thermal machine). In general they are machines which move heat around, or transform it. Often by connecting different points of the machine to different temperatures and exploiting the heat flow between them.

Classical thermal machines are big. Think about power plants – and even a fridge is about the size of a person. At these scales, we don’t need to worry about quantum physics to understand what is going on. But what happens if make such a machine smaller and smaller, to the point where quantum effects become important? Say we take a locomotive and scale it down, down, down, until the boiler and gears and so on consist of just a few atoms? Of course, it won’t really be a locomotive any more – but maybe we can learn something interesting?

Indeed, we can. And the machine can still be useful.

In recent years, physicists (such as Paul Skrzypczyk and Marcus Huber) have learned a lot about thermodynamics on the quantum scale by studying such tiny thermal machines. Looking at how fundamental concepts from classical thermodynamics, such as the 2nd law or Carnot efficiency, behave in the quantum regime, we gain new insights into the differences between the classical and quantum worlds.

In the spirit of invention of steam engines (like at the time of the industrial revolution), we can also think about whether there are new tasks that such quantum thermal machines could do.

Entanglement is an essential quantum phenomena. Objects which are entangled behave as if they are a single entity even when separated and manipulated independently. This enables new, powerful applications such as quantum computing and quantum metrology, and is at the heart of the foundations of quantum physics. So creating and studying entanglement is very interesting from both fundamental and applied points of view. Might a thermal machine be used to generate entanglement then?

Entanglement is generally very fragile, and thermal noise tends to wash it out quickly. In fact, a lot of effort in quantum physics experiments goes into keeping the systems cold and isolated, so as to be able to observe the genuinely quantum effects. So it is not at all obvious that using a thermal machine for entanglement generation would work. However, it turns out that connecting with noisy environments can indeed help to create and keep entanglement stable, in certain systems.

This was already realised and studied by other researchers. Then, a couple of years ago, we described a minimal thermal machine generating entanglement (as I wrote about here). That setup was nice because it was really the simplest quantum thermal machine imaginable, using just two quantum bits and two different temperatures, and it turned out this was already sufficient to see entanglement.

However, the amount of entanglement which that machine could generate was rather limited. In our new paper, we present a new quantum thermal machine – not much more complicated – which generates maximal entanglement. And it does this, not only for two quantum bits, but also for two quantum trits, and in fact for two quantum systems of any dimension (which we prove analytically thanks to the hard work of Armin Tavakoli). The new machine again uses just two different temperatures and two quantum systems of some given dimension. One system is connected to a cold bath, one to a hot bath, and they interact with each other. When heat flows from hot to cold through the two systems, they become entangled.

So indeed, a quantum thermal machine can be useful. And maybe in the future we might see quantum computers, or sensitive quantum sensors, based on thermally generated entanglement.

Published paper: https://quantum-journal.org/papers/q-2018-06-13-73/