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Physical Review A

Intensity-intensity correlations for the micromaser: Spectral and antibunching characteristics

Satish Kumar, G. S. Agarwal

Published Jul 1, 1994• 6 citations
Publisher

Abstract

We report results on different types of two-photon correlations for the micromaser field. We calculate these two-time correlations using the master equation for the micromaser field. We also present detailed results on the behavior of the eigenvalues of the Liouville operator for a range of excitation conditions and cavity parameters. We demonstrate the antibunching and the multiple-exponential decay of the micromaser field. We also discuss probing of the two-photon correlations.

DOI
10.1103/physreva.50.680

Related papers

Dynamics, correlations, and phases of the micromaser

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The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time of flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time of flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times of flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them. \textcopyright{} 1996 The American Physical Society.

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Collective two-atom effects and trapping states in the micromaser

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We investigate signals of trapping states in the micromaser system in terms of the average number $⟨n⟩$ of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number, $ϵ$, of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for $ϵ\ensuremath{\ne}0$, even for a mean number of atoms inside the cavity close to one. We, however, argue more importantly that the trapping states are more pronounced in terms of the correlation length as compared to $⟨n⟩$, i.e., we suggest that trapping states can be more clearly revealed experimentally in terms of the atom correlation length. For axion detection in the micromaser this observable may, therefore, be an essential ingredient.

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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.

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Atomic beam correlations and the quantum state of the micromaser

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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.

arXiv:cond-mat/9506058•Physica Scripta•Jun 1, 1997•5 citations
We report results on different types of two-photon correlations for the micromaser field. We calculate these two-time correlations using the master equation for the micromaser field. We also present detailed results on the behavior of the eigenvalues of the Liouville operator for a range of excitation conditions and cavity parameters. We demonstrate the antibunching and the multiple-exponential decay of the micromaser field. We also discuss probing of the two-photon correlations.
The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time of flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time of flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times of flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them. \textcopyright{} 1996 The American Physical Society.
Explicit expressions are derived for calculating the two-time coincidence probability density, the Mandel Q parameter of the counting statistics, and the waiting-time distribution between detector clicks for the detection of de-excited atoms leaving a micromaser with Poissonian pumping. The procedure is illustrated by applying it to the simplest trapped micromaser state for which all results can be obtained analytically. Moreover, by making use of a symmetry relation which determines the properties of the time-dependent micromaser master equation solution, it is shown that in the stationary regime for negligible thermal photon number the normalized two-time intensity correlation function of the cavity field with respect to a given time difference is equal to the normalized two-time coincidence probability density of detecting two de-excited atoms with the same time difference at the exit of the micromaser.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.
We investigate signals of trapping states in the micromaser system in terms of the average number ⟨n⟩⟨n⟩⟨n⟩ of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number, ϵϵϵ, of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for $ϵ\ensuremath{\ne}0$, even for a mean number of atoms inside the cavity close to one. We, however, argue more importantly that the trapping states are more pronounced in terms of the correlation length as compared to ⟨n⟩⟨n⟩⟨n⟩, i.e., we suggest that trapping states can be more clearly revealed experimentally in terms of the atom correlation length. For axion detection in the micromaser this observable may, therefore, be an essential ingredient.
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.
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.