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Physical Review A

Atomic-beam and cavity-field correlation functions in the micromaser

James D. Cresser, Stephen M. Pickles

Published Aug 1, 1994• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.r925

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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.

Physical Review A•Oct 1, 1996•8 citations
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.
A general theory of the micromaser is described. The model is based on treating the input atomic beam as a two-component quantum field so that the two-level atoms in the beam are ``quanta'' of this field. This approach makes it possible to formulate a general quantum Langevin description of the dynamics with the input atomic field as a source of quantum noise. The passage to a master-equation description is then effected by use of an adjoint-operator method, and by introducing a general class of statistical states for the atomic beam known as generalized shot noise. The result is a (non-Markovian) master equation for the field inside the cavity which is valid for a broad range of statistical properties of the input atomic beam. The approximate steady-state solutions to this master equation for the photon statistics of the cavity field for sub-Poissonian (antibunched) atomic beams found by other researchers are regained. The theory is then extended to treat super-Poissonian (bunched) atomic beams. An exact result is found in the limit of a strongly bunched beam in which the cavity-field state is shown to converge to a mixture of a thermal-field state and the state produced by a random beam of twice the intensity. A physical explanation of this result is also presented.
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.
Stimulated emission of two-level atoms in a high-Q cavity is considered under conditions when pumping produces correlated many-atomic states. Based on the many-body problem, a kinetic equation is obtained for the Glauber–Sudarshan probability, which describes the field in the Fokker–Planck approximation. The statistics of light in this approximation are determined by the atomic correlation functions of the order of no higher than the second. The noise of light is found in the regime of micromaser operation for two types of pumping producing the initial separable states with a classical correlation and entangled states. It is shown that the presence of the initial diatomic correlation enhances the intensity noise. The entangled state of atoms is found from which nonclassical light is generated with a steady-state phase and noise, which can be almost completely suppressed in the low-frequency spectral region.
We present a general method for the derivation of various statistical quantities describing the detection of a beam of atoms emerging from a micromaser. The use of non-normalized conditioned density operators and a linear master equation for the dynamics between detection events is discussed as are the counting statistics, sequence statistics, and waiting time statistics. In particular, we derive expressions for the mean number of successive detections of atoms in one of any two orthogonal states of the two-level atom. We also derive expressions for the mean waiting times between detections. We show that the mean waiting times between detections of atoms in like states are equivalent to the mean waiting times calculated from the uncorrelated steady state detection rates, although like atoms are indeed correlated. The mean waiting times between detections of atoms in unlike states exhibit correlations. We evaluate the expressions for various detector efficiencies using numerical integration, reporting results for the standard micromaser arrangement in which the cavity is pumped by excited atoms and the excitation levels of the emerging atoms are measured. In addition, the atomic inversion and the Fano-Mandel function for the detection of deexcited atoms are calculated for comparison to the experimental results of Weidinger et al. [Phys. Rev. Lett. 82, 3795 (1999)], who report the observation of trapping states.
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.