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Physical Review A

Comment on “Collective effects and trapping states by a quantum-trajectory treatment of micromaser dynamics”

David B. Johnson, William C. Schieve

Published Feb 25, 2003• 2 citations
Publisher

Abstract

A quantum trajectory analysis of the steady-state photon statistics of a micromaser by Casagrande and collaborators [F. Casagrande et al., Phys. Rev. A 60, 1582 (1999)] shows a significant suppression of the trapping behavior due to the inclusion of two-atom events. We use numerical integration in our investigation and obtain results that disagree with their analysis and show less suppression of the trapping behavior. A comparison with two extreme cases places our results between the two extremes and gives us confidence that our calculations are correct. The results of Casagrande and collaborators do not satisfy this condition.

DOI
10.1103/physreva.67.027801

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Reply to “Comment on ‘Collective effects and trapping states by a quantum-trajectory treatment of micromaser dynamics’ ”

Federico Casagrande, F. Castelli, ALFREDO LULLI

In the preceding Comment [Phys. Rev. A 67, 027801 (2003)] Johnson and Schieve raise doubts on the validity of a result obtained in our treatment of collective atomic effects in micromaser dynamics [Phys. Rev. A 60, 1582 (1999)]. We fully confirm the validity of our results, showing that the conclusions derived from their analysis are not relevant.

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Physical Review A•Mar 2, 2000•2 citations
A quantum trajectory analysis of the steady-state photon statistics of a micromaser by Casagrande and collaborators [F. Casagrande et al., Phys. Rev. A 60, 1582 (1999)] shows a significant suppression of the trapping behavior due to the inclusion of two-atom events. We use numerical integration in our investigation and obtain results that disagree with their analysis and show less suppression of the trapping behavior. A comparison with two extreme cases places our results between the two extremes and gives us confidence that our calculations are correct. The results of Casagrande and collaborators do not satisfy this condition.
By applying a quantum-trajectory approach to a master equation for the cavity mode density operator, we investigate the dynamics and the trapping states of a micromaser or microlaser including the effects of cavity temperature, two-atom events, atomic velocity spread, and partial excitation of the atomic beam. In the description of two-atom collective effects we allow for the nonsimultaneous arrival of atoms in the cavity, generalizing to a mean number of atoms ${N}_{\mathrm{at}}\ensuremath{\approx}1,$ a recent treatment [M. I. Kolobov and F. Haake, Phys. Rev. A 55, 3033 (1997)]. We show that, in trapping regions, our treatment of two-atom events can give strikingly different effects with respect to the approximation of simultaneous arrival of atom pairs; e.g., detrapping instead of trapping, different times of approach to the steady state, and different photonstatistics. Also, we simulate micromaser dynamics with parameter values corresponding to the recent experimental observation of the trapping effect by Walther and collaborators [H. Weidinger et al., Technical Digest of the European Quantum Electronics Conference '98 (IEEE, Piscataway, NJ, 1998)].
Both approximate and exact methods exist to determine the density matrix of the field inside an incoherently driven micromaser, but as of yet only a steady-state Fokker-Planck solution has been found for the micromaser with injected atomic phase [Phys. Rev. A 34, 2032 (1986)]. Since Fokker-Planck solutions have been shown not to represent the effect of trapping states on the cavity field adequately, other solutions must be sought. In this paper, we present both a highly accurate approximate analytical solution and a more computationally complex numerical solution based on the exact methods of Lu [Phys. Rev. A 47, 1347 (1993)], both of which demonstrate symmetry breaking in the phase. Since the spectra of the injected phase micromaser will be the same as that of the incoherently pumped case, we present numerical comparisons of our two solutions via the phase variance.