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Journal of Physics B Atomic Molecular and Optical Physics

Micromaser cavity field spectrum by atomic beam measurements

James D. Cresser

Published Jul 24, 2006• 2 citations
Publisher

Abstract

It is shown that complete information on the micromaser cavity field correlation function and hence the spectrum for the cavity field at absolute zero is encoded on the atomic beam exiting from the cavity. A possible means of measuring the atomic beam correlation function is discussed.
DOI
10.1088/0953-4075/39/15/s19

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It is shown that the autocorrelation function of the current produced through the ionization of ground-state atoms emerging from a micromaser cavity can be expressed, apart from a shot-noise contribution, in terms of a two-time correlation function of cavity-field variables. Numerical comparisons between this latter correlation function and the intensity correlation function of the cavity field show that the two are closely related and, in fact, in the limit of a zero-temperature cavity-field reservoir, become identical. A proof of this last result is presented.
The field in the micromaser cavity, the atoms which both pump and probe the micromaser, and the detectors that determine the outgoing states of the atoms are treated as a single system in order to derive a nonlinear master equation for the field in the micromaser cavity which takes the effect of undetected atoms into account. Analytic solutions for this master equation are found for both phase-insensitive and phase-sensitive detection. These solutions can be used to explicitly show the back-action effects that measurement has on the spectrum of the micromaser. In addition, these solutions are used to find analytic expressions for the mean number of successive detector clicks of the same kind as well as atom-atom and photon-photon correlation functions. In this way, the analytic solutions are linked to experimentally accessible data.
In lasers with strong atom-field coupling, Rabi-type oscillation effects are apparent not only in the atomic inversion and the photon number, but also in the field correlation function. Whereas the former play an important role in the standard micromaser with Poissonian injection, the latter are particularly relevant in lasers with non-Poissonian atomic injection. In such lasers, there is generally no steady state in the usual sense, and the field correlation function is really a two-point correlation. We analyze the field correlation function and the spectrum under these circumstances. Our analysis uses a stochastic simulation as well as an approximate analytical description. For lasers with a regular injection, this analysis explains the occurrence of a multipeak spectrum in simple terms. In the more general situation, the spectrum is related to the counting statistics of the atoms. Conditions for an experimental realization are discussed. \textcopyright{} 1996 The American Physical Society.
Correlation measurements on the states of two-level atoms having passed through a micromaser at different times can be used to infer properties of the quantum state of the radiation field in the cavity. Long(short) correlation length in time is to some extent associated with super(sub)-Poissonian photon statistics. The correlation length is also an indicator of a phase structure much richer than what is revealed by the usual single-time observables, like the atomic inversion or the Mandel quality factor. In realistic experimental situations the correlations may extend over many times the decay time of the cavity. Our assertions are verified by comparing theoretical calculations with a high-precision Monte-Carlo simulation of the micromaser system.
In this paper results are reported for the application of the quantum trajectory method to analysing the dynamics of the micromaser. The master equation for the cavity field is derived by a method which highlights the close relationship between the quantum trajectory method and the usual model for the one-atom micromaser. Possible quantum trajectory unravellings of the micromaser dynamics are discussed, and a simple number-state unravelling is described and used to generate simulations from which the cavity-field intensity correlation function is calculated. Attention is principally confined to the case of a Poissonian atomic beam, though a method of dealing with the non-Markovian master equation obtained for non-Poissonian beams is also examined. A formal theory of atomic detection analogous to the Glauber - Kelly - Kleiner theory of photodetection is proposed, based on a quantum-field description of the atomic beam. This theory is used to establish the connection between the atomic detection record obtained by continuous monitoring of the atoms leaving the cavity and the quantum trajectories followed by the cavity field. Results obtained by other treatments of atomic detection are regained. A classical correlation function obtained from the detection record of ground-state atoms emerging from a micromaser cavity is then shown, by use of a quantum trajectory analysis, to be identical to the cavity field intensity correlation function, apart from shot-noise-type contributions, provided the cavity reservoir is at zero temperature.
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.