Thermodynamic control by frequent quantum measurements (original) (raw)

Non-Markovian control of qubit thermodynamics by frequent quantum measurements

Physica E-low-dimensional Systems & Nanostructures, 2010

We explore the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems (TLS), alias qubits, in contact with a thermal bath. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control of heating, cooling and statepurification (entropy reduction) of qubits, much sooner than their thermal equilibration time.

Role of correlations in the thermalization of quantum systems

New Journal of Physics, 2012

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite-dimensional environment. By exploiting the concept of time-averaged states, we introduce a completely positive map which allows us to describe in a quantitative way the dependence of the equilibrium state on the initial condition. Our results show that the thermalization of quantum systems is favored if the dynamics induces small system-environment correlations, as well as small changes in the environment, as measured by the trace distance.

Thermalization in Nature and on a Quantum Computer

2011

In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.

Equilibration by quantum observation

New Journal of Physics, 2010

We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.

Perspective on quantum thermodynamics

2016

Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems,made up ofmicroscopic particles, in terms of a small number ofmacroscopic quantities, such aswork and entropy. As systems get ever smaller, fluctuations of these quantities become increasingly relevant, prompting the development of stochastic thermodynamics. Recently we have seen a surge of interest in exploring the quantum regime, where the origin offluctuations is quantum rather than thermal.Many questions, such as the role of entanglement and the emergence of thermalisation, lie wide open. Answering these questionsmay lead to the development of quantumheat engines and refrigerators, as well as to vitally needed simple descriptions of quantummany-body systems.

The second laws of quantum thermodynamics

Proceedings of the National Academy of Sciences of the United States of America, 2015

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparen...

Information-theoretic equilibrium and observable thermalization

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light. To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. However, despite the fact that the theory is more than 100 years old, we are still discussing its foundations and its regime of applicability. The ordinary way in which thermal equilibrium properties are obtained, in statistical mechanics, is through a complete characterisation of the thermal form of the state of the system. One way of deriving such form is by using Jaynes principle 1-4 , which is the constrained maximisation of von Neumann entropy S vN = − Trρ logρ. Jaynes showed that the unique state that maximises S vN (compatibly with the prior information that we have on the system) is our best guess about the state of the system at the equilibrium. The outcomes of such procedure are the so-called Gibbs ensembles. In the following we argue that such a notion of thermal equilibrium, de facto is not experimentally testable because it gives predictions about all possible observables of the system, even the ones which we are not able to measure. To overcome this issue, we propose a weaker notion of thermal equilibrium, specific for a given observable. The issue is particularly relevant for the so-called "Pure states statistical mechanics" 5-19 , which aims to understand how and in which sense thermal equilibrium properties emerge in a closed quantum system, under the assumption that the dynamic is unitary. In the last fifteen years we witnessed a revival of interest in these questions , mainly due to remarkable progresses in the experimental investigation of isolated quantum systems 20-25. The high degree of manipulability and isolation from the environment that we are able to reach nowadays makes possible to experimentally investigate such questions and to probe the theoretical predictions. The starting point of Jaynes' derivation of statistical mechanics is that S vN is a way of estimating the uncertainty that we have about which pure state the system inhabits. Unfortunately we know from quantum information theory that it does not address all kind of ignorance we have about the system. Indeed, it is not the entropy of an observable (though the state is observable); its conceptual meaning is not tied to something that we can measure. This issue is intimately related with the way we acquire information about a system, i.e. via measurements. The process of measuring an observable on a quantum system allows to probe only the diagonal part of the density matrix λ ρ λ i i , when this is written in the observable eigenbasis λ { } i. For such a reason, from the experimental point of view, it is not possible to assess whether a many-body quantum system is at thermal equilibrium (e.g. Gibbs state ρ G): the number of observables needed to probe all the density matrix elements is too big. In any experimentally reasonable situation we have access only to a few (sometimes just one or two) observables. It is 1 tomic ann aser sicss arennon aaoratorr niiersitt of OOforr arrs oaa OOforr O1 333. Centre for uantum eccnooooiess ationaa niiersitt of innaporee 1177433 innapore. 3 Department of Physics, National niiersitt of innapore cience Driie 3 1171 innapore. 4 Center for Quantum Information, Institute for Interiscippinar Information ciences sinua niiersit 1000844 eiiin ina. * These authors contributed eeua to tis wor. orresponence an reeuests for materias souu e aressee to .. emai: faio.ana pppsics.oo.ac.uuu receiiee: 13 Octooer 016 acceptee: 31 anuarr 017 Puuuissee: 07 arcc 017 OPEN

Approach to thermal equilibrium of macroscopic quantum systems

2010

We consider an isolated, macroscopic quantum system. Let H be a microcanonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace H eq of H such that dim H eq / dim H is close to 1. We say that a system with state vector ψ ∈ H is in thermal equilibrium if ψ is "close" to H eq . We show that for "typical" Hamiltonians with given eigenvalues, all initial state vectors ψ 0 evolve in such a way that ψ t is in thermal equilibrium for most times t. This result is closely related to von Neumann's quantum ergodic theorem of 1929.

Stochastic thermodynamics of a finite quantum system coupled to a heat bath

2021

We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.