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AIP conference proceedings

The Photo-Carnot Cycle: The Preparation Energy for Atomic Coherence

Muhammad Suhail Zubairy

Published Jan 1, 2002• 9 citations
Publisher

Abstract

We consider a Carnot cycle engine in which the working medium is a photon gas inside a cavity with perfectly reflecting walls. The thermal baths responsible for supplying heat to the radiation field is a stream of three‐level atoms. The phase of the atomic coherence provides a new and interesting control parameter. Here we discuss the questions pertaining to the preparation energy of atomic coherence with an explicit calculation of the associated entropy change.

DOI
10.1063/1.1523787

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We consider a Carnot cycle engine in which the working medium is a photon gas inside a cavity with perfectly reflecting walls. The thermal baths responsible for supplying heat to the radiation field is a stream of three‐level atoms. The phase of the atomic coherence provides a new and interesting control parameter. Here we discuss the questions pertaining to the preparation energy of atomic coherence with an explicit calculation of the associated entropy change.
We present here a quantum Carnot engine in which the atoms in the heat bath are given a small bit of quantum coherence. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which we operate and the heat bath is essentially thermal. However, the phase phi, associated with 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 deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.
We investigate scaling of work and efficiency of a photonic Carnot engine with a number of quantum coherent resources. Specifically, we consider a generalization of the "phaseonium fuel" for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], to the case of N+1 level atoms with N coherent lower levels. We take into account atomic relaxation and dephasing as well as the cavity loss and derive a coarse-grained master equation to evaluate the work and efficiency analytically. Analytical results are verified by microscopic numerical examination of the thermalization dynamics. We find that efficiency and work scale quadratically with the number of quantum coherent levels. Quantum coherence boost to the specific energy (work output per unit mass of the resource) is a profound fundamental difference of quantum fuel from classical resources. We consider typical modern resonator set ups and conclude that multilevel phaseonium fuel can be utilized to overcome the decoherence in available systems. Preparation of the atomic coherences and the associated cost of coherence are analyzed and the engine operation within the bounds of the second law is verified. Our results bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.
In a previous note (1) we argue that the entropy for a pure quantum bound state is given by S=Sx+Sp where Sx = -k{ Integral dx Wn(x)Wn(x)ln(WnWn) + Integral dp an(p)an(p) ln(an an) }. It was shown that for any energy level pure bound state for the case of a particle in a box with an infinite potential or for an oscillator S does not depend on the parameters L (length of box) or k (spring constant) or m (mass). Thus a quantum adiabatic change of the parameter leaving the particle in the same quantum state leads to no change in entropy. In (2) a two level quantum Carnot cycle is considered for a particle in a box with an infinite potential. Energy levels n=0 and n=1 are considered.. The wavefunction is a(1)W1(x) + a(2)W2(x). Shannon’s entropy is used namely S=-k Sum over n an(an) ln{|an an|} ((1)) and an expression is found linking an*an to L and T (temperature) for a particle in a box with infinite potential walls. A Carnot cycle with two isotherms and two adiabatic dS=0 parts is considered. No consideration is given to the internal entropy of a bound state eigenstate. In this note we try to show how the overall entropy changes if the internal bound energy eigenfuntion entropy ((1)) is considered and also show how an*an(T,L) changes. We find that a1*a1 changes as do the overall values of Q (heat) and W(work) for the Carnot cycle, but that the efficiency does not.
We consider a photo-Carnot engine that consists of a single-mode radiation field in an optical cavity. One the heat reservoirs is made of a beam of thermally entangled pairs of two-level atoms that interact resonantly with the cavity. We express the thermodynamic efficiency of the engine in terms of the quantum discord of the atomic pair and find that it can exceed its classical value. Our results show that useful work can be extracted from quantum correlations, indicating that the latter are a valuable resource in quantum thermodynamics.
A master equation for a single mode radiation field interacting with a coherently prepared beam of atoms is derived. The atomic quantum coherence is built up via interaction with an external microwave field. We discuss various applications of the derived master equation, including lasing without population inversion and the possibility of exceeding the Carnot efficiency of a quantum heat engine fueled by a beam of phase coherent atoms. The main motivation for this paper is to settle subtle technical issues involving the derivation of the master equation.