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Physics Today

An inexpensive crystal makes a fine quantum time machine

Johanna L. Miller

Published Nov 1, 2019• 0 citations
Publisher

Abstract

To understand the intricacies of thermodynamics in the quantum regime, it helps to be able to turn back the clock.
DOI
10.1063/pt.3.4335

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•Oct 1, 2016•0 citations
Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.
Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping devices. Owing to the level of complexity in the clock structure and its energy consumption, such devices show trade-offs whose characterization remains an open challenge. Indeed, even conceptual designs for thermodynamically efficient quantum clocks are not yet well understood. In condensed matter theory, time crystals were found as an exciting new phase of matter featuring oscillations in (pseudo) equilibrium with first experimental observations appearing recently. This naturally prompts the question: Can time crystals be used as quantum clocks, and what is their performance from a thermodynamic perspective? We answer this question and find that quantum time crystals are indeed genuine quantum clocks with a performance enhanced by the spontaneous breaking of time-translation symmetry.
Thermodynamics is one of the core disciplines of physics, and despite its long history it is still a very active area of research. Particularly in the regime of non-equilibrium processes and at small scales many open questions remain. In this thesis we critically study the role that autonomous machines play in the emerging field of quantum thermodynamics. We show that autonomous machines generally comprise several interacting subsystems that can take on various roles. In Part I we look at the issue of external control. Any non-autonomous machine by definition requires some external agent to interact with the machine. This agent is generally assumed to be classical and to not suffer any back-actions from the machine. If all the involved systems are of microscopic size this approximation is no longer valid and we have to include all the control mechanisms within a unified quantum framework. We show that in order to avoid external control and operate autonomously, a machine that is to extract work from another system requires an inbuilt quantum clock. Being itself a finite-size quantum system, such a clock will inevitably experience back-actions and develop correlations with the other systems, which lead to its degradation as a time keeping device. We show that this degradation can be counteracted by a judicious choice of quantum measurements. These measurements not only allow us to stabilise the clock, but also magnify thermodynamic properties such as work from the quantum scale, where their definition can be ambiguous, to the well understood classical scale. In Part II we consider the scenario of an autonomous quantum machine interacting with a thermal environment, for which we are experimentally restricted to only observe a subset of all the possible environment interactions, while the remaining ones are hidden from direct observation. Using a modification of the notion of quantum jump trajectories we show that the visible interactions in many cases still allow us to make some inferences about the hidden interactions. We introduce a new quantity, the coarse-grained hidden entropy, which quantifies the entropy production in the hidden subsystem conditioned on our observations of the visible part. The total entropy production consisting of the sum of visible and coarse-grained hidden entropy is shown to satisfy an integral fluctuations theorem. Depending on the information flow between the subsystems, the hidden entropy can assume negative values in which case the hidden systems acts as a Maxwell's demon. This behaviour is also captured by a modified second law like inequality which gives a refinement of the conventional second law for autonomous quantum machines with continuous information flows between the machine's subsystems.