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Australian Journal of Physics

An Atom-optical Maxwell Demon

Gerard J Milburn

Published Feb 10, 1998• 4 citations
Publisher

Abstract

The separation, by an optical standing wave, of a beam of two-level atoms prepared in a thermal mixture of ground and excited states, is considered as an example of a Maxwell demon. By including the momentum exchanged with the cavity, it is shown how no violation of the second law is possible. A classical and quantum analysis is given which illustrates this principle in some detail.

DOI
10.1071/p97021

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The separation, by an optical standing wave, of a beam of two-level atoms prepared in a thermal mixture of ground and excited states, is considered as an example of a Maxwell demon. By including the momentum exchanged with the cavity, it is shown how no violation of the second law is possible. A classical and quantum analysis is given which illustrates this principle in some detail.
Maxwell's Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to "exorcise" the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell's Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer's thesis, are not general. In this paper we demonstrate that Maxwell's Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of "macrostates", thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of “Maxwell’s Demon”, a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell’s challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The more recent proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through a neglected feature of quantum theory, namely the Heisenberg Uncertainty Principle, which also decisively serves to defeat the Demon.
We propose an optical Maxwell demon which efficiently captures, concentrates, and damps the kinetic motion of sodium atoms in a gas cell. A bath of radiation tuned just below resonance can prove to be a very viscous medium for atoms. We propose to use this effect to produce and concentrate very slow atoms in a vapor cell. Our bath of radiation consists of three orthogonally intersecting pairs of counterpropagating laser beams. Each beam is tuned about half of the natural linewidth below the resonance transition frequency. (Because of the hyperfine splitting of the Na ground state, two separate frequencies are used.) Atoms which enter the intersection region with velocities less than ~15 m/s (for 1-cm diam beams) are quickly damped to ~0.5 m/s. Thereafter, the velocity is randomized in a characteristic time of ~10 μs. The atoms will then execute diffusive motion in this photon bath, escaping only after many seconds. Since the effusion time for atoms to enter the intersecting beam demon is much shorter than the diffusion time out of it, the demon acts to collect and concentrate the slow atoms into a cold, dense, central gas superposed on the hot, rarified, background gas.
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of ``Maxwell's Demon'', a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell's challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through neglected features of quantum theory. In particular, an application of the Heisenberg Uncertainty Principle is shown to decisively defeat the Demon, as well as to serve as justification for Landauer's Principle, albeit in terms distinct from the usual computational formulation.
In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.