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Journal of Physics A Mathematical and Theoretical

Comment on ‘Gazeau–Klauder cat states’

Rimvydas Aleksiejūnas

Published May 20, 2015• 1 citation
Publisher

Abstract

Gazeau–Klauder cat states for a nonlinear Kerr oscillator has been investigated by Dajka and Łuczka (2012 J. Phys. A: Math. Theor. 45 244006 ). We show that their derivation of a geometric phase for cat states contains an error, and the corrected time dependence of the geometric phase exhibits step-like behavior characteristic to quantum geometric phases.

DOI
10.1088/1751-8113/48/23/238001

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We reply to the comment by Aleksiejunas on our article Dajka J and Łuczka J 2012 J. Phys. A: Math. Theor. 45 244006 . We point that the mistake mentioned in the comment is trivial and rather technical and does not influence main physical content of our work.

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Gazeau–Klauder cat states for a nonlinear Kerr oscillator has been investigated by Dajka and Łuczka (2012 J. Phys. A: Math. Theor. 45 244006 ). We show that their derivation of a geometric phase for cat states contains an error, and the corrected time dependence of the geometric phase exhibits step-like behavior characteristic to quantum geometric phases.
Generalization of single-mode Schrödinger cat states is proposed, and their construction in terms of superposition of Gazeau–Klauder coherent states is presented. A comparative analysis of selected properties of this novel states for a nonlinear Kerr oscillator and the ‘traditional’ Schrödinger cats is given with emphasis on the photon statistics and the properties of non-cyclic geometric phase. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.