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Journal of Physics A Mathematical and General

Properties of nonclassical maximum-entropy states

Istok P. Mendaš, Marko Djordjević, M Markovic

Published Feb 1, 2000• 0 citations
Publisher

Abstract

The density matrix in the position and momentum representation, the position-momentum uncertainty product, the Wigner and Q functions, and thermal properties of the family of the nonclassical maximum-entropy states of a single harmonic oscillator are determined. Any such state, having the mean number of quanta n , has the uncertainty product x p = (2 n +1)( /2), and this product attains its minimum value for the temperature parameter 0. Generically, the Wigner function has alternating sign so that the underlying maximum-entropy state is truly nonclassical. The von Neumann entropy and the heat capacity, expressed via the temperature parameter , coincide with the corresponding quantities for the thermal state. The properties discussed here are of interest for the description and analysis of the vibrational motion of a trapped ion in a harmonic-oscillator potential since the equilibrium states which result under certain conditions are the maximum-entropy states.

DOI
10.1088/0305-4470/33/5/308

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We investigate specific maximum-entropy states of a single harmonic-oscillator mode that arise when only number states (Fock states) differing by a multiple of a certain integer kkk (k> 1)(k>~1)(k> 1) are allowed to be occupied. For k=2k=2k=2 the number-probability distribution of the even-number maximum-entropy state has a close resemblance to that of a squeezed-vacuum state. These maximum-entropy states can be obtained as the stationary solutions of a master equation which takes into account kkk-quantum absorption as well as kkk-quantum emission processes only. The steady-state solution of this master equation depends on the initial conditions. For the vibrational motion of a trapped ion such nonclassical maximum-entropy states could be produced with the help of the recently proposed method of laser-assisted quantum reservoir engineering.
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