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Physical Review A

Phase diffusion and continuous quantum measurements in the micromaser

Christian Wagner, R. J. Brecha, Axel Schenzle, HERBERT WALTHER

Published Nov 1, 1992• 27 citations
Publisher

Abstract

We propose a method to investigate the phase dynamics of the radiation field of a micromaser in steady-state operation. The phase-diffusion information is deduced from the population statistics of the atoms leaving a classical coherent field placed after the micromaser cavity. By using the classical coherent field, one gains an additional degree of freedom which allows one to probe the polarization component of the atomic dipole which is directly correlated to the cavity-field amplitude. As an illustration we present the results of a computer experiment, modeling the complete dynamics of the proposed experiment.

DOI
10.1103/physreva.46.r5350

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We propose a method to investigate the phase dynamics of the radiation field of a micromaser in steady-state operation. The phase-diffusion information is deduced from the population statistics of the atoms leaving a classical coherent field placed after the micromaser cavity. By using the classical coherent field, one gains an additional degree of freedom which allows one to probe the polarization component of the atomic dipole which is directly correlated to the cavity-field amplitude. As an illustration we present the results of a computer experiment, modeling the complete dynamics of the proposed experiment.
We discuss a scheme to relate the phase diffusion dynamics of the micromaser field to the measured atomic population statistics. This can allow us to measure the linewidth of the micromaser spectrum and to solve a relevant decoherence problem in cavity quantum electrodynamics. The main steps are (i) a suitable preparation of the cavity field state to generate coherences, (ii) the transfer of information on the dynamics of field coherences to probe atoms by the action of an external resonant coherent field and (iii) the derivation of the phase diffusion rate, hence the micromaser linewidth, from the measured population statistics of the probe atoms. The method can be applied even in the presence of trapping states, where peculiar linewidth oscillations are expected for increasing pump rate, due to the quantum nature of the micromaser field.
We propose a realistic scheme for measuring the micromaser linewidth by monitoring the phase diffusion dynamics of the cavity field. Our strategy consists of exciting an initial coherent state with the same photon number distribution as the micromaser steady-state field, singling out a purely diffusive process in the system dynamics. After the injection of a counterfield, measurements of the population statistics of a probe atom allow us to derive the micromaser linewidth in all ranges of the relevant parameters, establishing experimentally the distinctive features of the micromaser spectrum due to the discreteness of the electromagnetic field.
We show how our recently proposed scheme for the measurement of the micromaser linewidth, which relates the phase diffusion dynamics of the cavity field to the population statistics of probe atoms, can be applied in the presence of trapping states, where the phase diffusion approximation does not strictly hold. This should allow the observation of the peculiar linewidth oscillations versus atomic pumping which are expected in this regime, and whose origin lies in the quantum nature of the cavity field.
In this paper we show how different measurement schemes for a micromaser system may be used to investigate different aspects of the maser dynamics. The features which are investigated include a measurement of the phase diffusion in steady-state, transient states with several orders of coherence, and an interesting connection to questions of the Einstein-Podolsky-Rosen paradox. In addition, it is shown rigorously that different measurement schemes acting only on the atomic part of the system after the cavity have no influence on the ensemble properties of the cavity field.
We suggest an iterative, maximum-likelihood–based, method to reconstruct the photon number distribution of the steady-state cavity field of a micromaser starting from the statistics of the atoms leaving the cavity after the interaction. The scheme is based on measuring the atomic populations of probe atoms for different interaction times and works effectively using a small number of atoms and a limited sampling of the interaction times. The method has been tested by numerically simulated experiments showing that it may be reliably used in any micromaser regime, leading to high-fidelity reconstructions for single-peaked distributions as well as for double-peaked ones and for trapping states.
We describe the dynamics of a micromaser pumped by atoms in superposition states and driven by a resonant coherent field. By a quantum jump approach to the master equation solution, we show how the coherences excited in the cavity mode affect the nonclassical steady-state behaviour of the system, in a way that depends on the relative phase between the polarized atoms and the driving field. Both the mean photon number and the phase of the cavity field can be controlled via the atomic transit time and pump rate, or the driving field intensity. The predicted coherence and phase competition effects can show up in the statistics of the populations of outgoing atoms.