Using quantum erasure to exorcise Maxwell's demon: II. Analysis

doi:10.1016/j.physe.2005.05.052

Physica E: Low-dimensional Systems and Nanostructures

Volume 29, Issues 1–2, October 2005, Pages 40-46

https://doi.org/10.1016/j.physe.2005.05.052 Get rights and content

Abstract

We present an analysis of the single atom negentropy quantum heat engine to determine the fundamental limits of its operation. The engine has an internal reservoir of negentropy which allows one to extract work from a single thermal reservoir. The process is attended by constantly increasing entropy and does not violate the second law of thermodynamics.

Introduction

Thermodynamics [1], that is usually treated within the framework of classical mechanics, has recently been revisited within the context of quantum optics and interesting and novel features have been predicted in the operation of quantum heat engines (QHEs) [2], [3]. In particular, the recent advances in quantum optics such as cavity QED [4], the maser [5], and LWI [6], have been employed to show that it is indeed possible to improve the efficiency of classical heat engines. For example, as has been shown recently in Refs. [7], [8], a classical Otto-cycle heat engine can be improved by adding a laser system that is able to extract coherent laser energy from thermally excited atoms.

Also a quantum Carnot engine has been analyzed in which the atoms in the heat bath are given a small bit of quantum coherence [9], [10]. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which the engine operates, and the heat bath is essentially thermal. However, the phase of the atomic coherence provides a new control parameter that can be varied to increase the temperature of the radiation field and to extract work from a single heat bath.

The present work is an outgrowth of Ref. [11] where it is shown that the internal “spin” states of an atom can be cooled to absolute zero via a state selective Maser scheme, see also Ref. [12]. This process has been employed in the design of a QHE based on cycling a single atom through a micromaser cavity [5] many times [2].

In classical heat engines, useful work is produced by drawing energy from a high-temperature source and depositing entropy in a low-temperature entropy sink. Specifically a working fluid, such as steam, draws energy from a boiler, does work on a piston and deposits entropy in the cooling water. In the QHE presented in Ref. [13], the atomic spin states play the role of the working fluid, a blackbody Hohlraum is the energy source and the atomic spins drive a maser field producing useful work. However there is no lower temperature entropy sink in such a QHE. Instead, the atomic center of mass (COM) degrees of freedom are used to provide a source of negentropy [13], [14], [15] which allows the QHE to operate for a finite number of cycles. There is however a constantly increasing entropy in the engine operation such that there is no violation of the the second law.

Negentropy QHE consists of Hohlraum to heat atomic internal degrees of freedom and intelligent Maxwell demon realized via Stern–Gerlach apparatus (SGA) which separated hot and cold atoms. The relation of the single-atom heat engines to the Maxwell demon [19] concept is presented in Ref. [14], and the details of the different implementations can be found in [15]. The separation of hot and cold atoms is responsible for the running of the heat engine. It has been shown that a laser can be viewed as a heat engine [16].

The goal of the present paper is to perform an analysis to determine the fundamental restrictions and limitations of the negentropy QHE using internal degrees of freedom. We describe in details the general process of producing atomic beam pulse for the QHE and find out limitations on how many cycles it is able to perform.

Section snippets

Preparation of a single atom wave packet

The schematic of negentropy QHE is shown in Fig. 1. The atoms are initially stored in some material (see Fig. 1(B)). The binding energy of the atoms $U_{0}$ is low enough that the thermal radiation cannot effectively excite them. Note here that the process of creating a wave packet has similar physics with atom laser [20].

The atoms interact with the laser pulse to create an atomic pulse. The Hamiltonian of the atom is given by $H = H_{0} + U (z) + V (z, t)$ where $H_{0}$ is the Hamiltonian of atoms; $U (z)$ is bounding

How many cycles can the single atom wave packet make?

As discussed in Refs. [2], [13], [14], [15], the single atom wave packet while moving in a closed path doubles its width during each cycle (see Fig. 1). There are also other sources of wave packet spreading: due to dispersion in free space via uncertainty in velocity of the atom $δ v ≃ h / ML$ , and due to interaction with thermal radiation in Hohlraum. However we note that the effect of atomic recoil given by $δ ε = \frac{(ℏ ω)^{2}}{2 {Mc}^{2}} = \frac{(kT)^{2}}{2 {Mc}^{2}}$ is negligible for reasonable temperatures because of mass of atoms.

After

Conclusion

In conclusion, we have presented an analysis of the single atom negentropy quantum heat engine to determine fundamental limits of its operation. The engine has an internal reservoir of negentropy which allows us to extract work from one thermal reservoir. The process is attended by constantly increasing entropy and does not violate the second law of thermodynamics.

The similarities and differences of the QHE and the Maxwell demon problem are interesting. In particular, our QHE has much in common

Acknowledgements

The authors wish to thank helpful and stimulating interactions with E. Fry, K. Kapale, A. Matsko, G. Sussmann, and H. Walther and we are also gratefully acknowledged the support from the Office of Naval Research (Grants No. N00014-03-1-0639 and No. N00014-04-1-0336), the Air Force Office of Scientific Research (Grant No. F49620-01-1-0566), the Defense Advanced Research Projects Agency-QuIST, the Texas A&M University Telecommunication and Information Task Force (TITF) Initiative and the Robert

References (19)

F. Sears, Thermodynamics, Reading, MA, Addison-Wesley,...
M.O. Scully
Phys. Rev. Lett.
(2001)
M.O. Scully
Phys. Rev. Lett.
(2002)
For a cavity QED review see, S. Haroche, D. Kleppener, Phys. Today 42...
D. Meschede, H. Walther G. Müller, Phys. Rev. Lett. 54 (1995)...S. Haroche J. M. Raimond, Atom. Mol. Phys., 20 (1985)...D. Bates and B. Bederson (Academic Press, New York 1985), p. 350; “The first theory for the micromaser is given by P....
O. Kocharovskaya, Phys. Rep. 219 (1992) 175; S. E. Harris, Phys. Today (1997)...M. O. Scully, M. S. Zubairy, Quantum Optics, Cambridge University Press, Cambridge, UK,...
Y.V. Rostovtsev et al.
Phys. Rev. A
(2003)
A. Hill, Y.V. Rostovtsev, M.O. Scully, J. Mod. Opt. 51 (2004)...A. Hill, Y.V. Rostovtsev, M.O. Scully, CO2-laser-Coupled Quantum Heat Engine, in...
M.O. Scully et al.
Science
(2003)

There are more references available in the full text version of this article.

Cited by (13)

Using quantum erasure to exorcize Maxwell's demon: III. Implementation
2005, Physica E: Low-Dimensional Systems and Nanostructures
We present a negentropy quantum heat engine [M.O. Scully, Phys. Rev. Lett. 87 (2001) 220601] which uses a Stern–Gerlach apparatus as a quantum sorter and a pair of Raman pulses in order to adiabatically transfer population from one hyperfine ground sublevel to another. Work is produced in a microwave cavity by exploiting the energy of an atom's internal degrees of freedom. Such a scheme may be possible to implement under realistic experimental conditions.
Using quantum erasure to exorcize Maxwell's demon: I. Concepts and context
2005, Physica E: Low-Dimensional Systems and Nanostructures
Szilard [L. Szilard, Zeitschrift für Physik, 53 (1929) 840] made a decisive step toward solving the Maxwell demon problem by introducing and analyzing the single atom heat engine. Bennett [Sci. Am. 255 (1987) 107] completed the solution by pointing out that there must be an entropy, $Δ S = k \ln 2$ , generated as the result of information erased on each cycle. Nevertheless, others have disagreed. For example, philosophers such as Popper “have found the literature surrounding Maxwell's demon deeply problematic.”
We propose and analyze a new kind of single atom quantum heat engine which allows us to resolve the Maxwell demon paradox simply, and without invoking the notions of information or entropy. The energy source of the present quantum engine [Scully, Phys. Rev. Lett. 87 (2001) 22601] is a Stern–Gerlach apparatus acting as a demonesque heat sorter. An isothermal compressor acts as the entropy sink. In order to complete a thermodynamic cycle, an energy of $Δ W = kT \ln 2$ must be expended. This energy is essentially a “reset” or “eraser” energy. Thus Bennett's entropy $Δ S = Δ W / T$ emerges as a simple consequence of the quantum thermodynamics of our heat engine. It would seem that quantum mechanics contains the kernel of information entropy at its very core. That is the concept of information erasure as it appears in quantum mechanics [Scully and Drühl, Phys. Rev. A 25 (1982) 2208] and the present quantum heat engine have a deep common origin.
Quantum relative entropy of tagging and thermodynamics
2020, Entropy
Entropy distribution in a quantum informational circuit of tunable Szilard Engines
2019, Entropy
Quantum information remote carnot engines and voltage transformers
2019, Entropy
Enhanced energy distribution for quantum information heat engines
2016, Entropy

View all citing articles on Scopus

View full text