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Physical Review Letters

Quantum Szilard Engine with Attractively Interacting Bosons

J. Bengtsson, M. Nilsson Tengstrand, A. Wacker, Peter Samuelsson, Masahito Ueda, Heiner Linke, S. M. Reimann

Published Mar 9, 2018• 60 citations
Publisher

Abstract

We show that a quantum Szilard engine containing many bosons with attractive interactions enhances the conversion between information and work. Using an ab initio approach to the full quantum-mechanical many-body problem, we find that the average work output increases significantly for a larger number of bosons. The highest overshoot occurs at a finite temperature, demonstrating how thermal and quantum effects conspire to enhance the conversion between information and work. The predicted effects occur over a broad range of interaction strengths and temperatures.

DOI
10.1103/physrevlett.120.100601

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Journal of the Korean Physical Society•Oct 1, 2012•16 citations
We show that a quantum Szilard engine containing many bosons with attractive interactions enhances the conversion between information and work. Using an ab initio approach to the full quantum-mechanical many-body problem, we find that the average work output increases significantly for a larger number of bosons. The highest overshoot occurs at a finite temperature, demonstrating how thermal and quantum effects conspire to enhance the conversion between information and work. The predicted effects occur over a broad range of interaction strengths and temperatures.
In a classic thought experiment, Szilard suggested a heat engine where a single particle, for example an atom or a molecule, is confined in a container coupled to a single heat bath. The container can be separated into two parts by a moveable wall acting as a piston. In a single cycle of the engine, work can be extracted from the information on which side of the piston the particle resides. The work output is consistent with Landauers principle that the erasure of one bit of information costs the entropy kB ln 2, exemplifying the fundamental relation between work, heat and information. Here we apply the concept of the Szilard engine to a fully interacting quantum many-body system. We find that a working medium of a number of bosons (larger or equal two) with attractive interactions is clearly superior to other previously discussed setups. In sharp contrast to the classical case, we find that the average work output increases with the particle number. The highest overshoot occurs for a small but finite temperature, showing an intricate interplay between thermal and quantum effects. We anticipate that our finding will shed new light on the role of information in controlling thermodynamic fluctuations in the deep quantum regime, which are strongly influenced by quantum correlations in interacting systems.
It was recently found that the information-to-work conversion in a quantum Szilard engine can be increased by using a working medium of bosons with attractive interactions. In the original scheme, the work output depends on the insertion and removal position of an impenetrable barrier that acts like a piston, separating the chambers of the engine. Here, we show that the barrier removal process can be made fully reversible, resulting in a full information-to-work conversion if we also allow for the interaction strength to change during the cycle. Hence, it becomes possible to reach the maximum work output per cycle dictated by the second law of thermodynamics. These findings can be experimentally verified, for instance, with ultracold atoms as a working medium, where a change of interaction strength can be controlled by Feshbach resonances.
In this thesis, different aspects of the quantum Szilard engine are studied using the configuration interaction method. The engine is modelled as a one-dimensional infinite well. The effects of a contact-interaction are examined and it is found that attractive contact-interactions can improve the work output at certain temperatures of an engine that has bosons as a working medium. The role of impurities in the engine is investigated and found to have a large impact on the low-temperature behaviour of the engine. Dynamics of a single-particle engine are considered in order to identify finite-speed effects in the engine's cycle.
The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically study the basic physical properties of both fermion and boson SQSZEs in a low-temperature approximation. We give the analytic formulation of the total work. For the fermion SQSZE, the work might be absorbed from the environment, and the change rate of the work with temperature exhibits periodicity and even-odd oscillation, which is a generalization of a spinless QSZE. It is interesting that the average absorbed work oscillates regularly and periodically in a large-number limit, which implies that the average absorbed work in a fermion SQSZE is neither an intensive quantity nor an extensive quantity. The phase diagrams of both fermion and boson SQSZEs give the SQSZE doing positive or negative work in the parameter space of the temperature and the particle number of the system, but they have different behaviors because the spin degrees of the fermion and the boson play different roles in their configuration states and corresponding statistical properties. The critical temperature of phase transition depends sensitively on the particle number. By using Landauer's erasure principle, we give the erasure work in a thermodynamic cycle, and we define an efficiency (we refer to it as information-work efficiency) to measure the engine's ability of utilizing information to extract work. We also give the conditions under which the maximum extracted work and highest information-work efficiencies for fermion and boson SQSZEs can be achieved.
The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information. We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process. We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.
We investigate Szilard’s information heat engine in the deep quantum regime. If the ground state is non-degenerate, the work extracted from the engine divided by temperature, ~S , vanishes as the temperature approaches zero, where the third law of thermodynamics manifests itself in information science. The degenerate ground state induced by the symmetry or by accident gives rise to non-zero ~S at zero temperature. Based upon these two rules, namely the third law and the degenerate ground state, we can understand the low-temperature behavior of the quantum Szilard engine in various physical situations such as an engine consisting of either bosons or fermions either with or without interactions.