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arXiv:0705.2374 · Europhysics Letters (EPL)

Reconstruction of the photon distribution in a micromaser

Stefano Olivares, Federico Casagrande, ALFREDO LULLI, Matteo G. A. Paris

Published Nov 16, 2007• 3 citations
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Abstract

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.

DOI
10.1209/0295-5075/80/64002

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A scheme for reconstructing the Wigner function of cavity fields is proposed, and this scheme can be realized with the micromaser. We find that there is a simple relation between the Wigner function of cavity fields and the atomic populations. Therefore, we can reconstruct the Wigner function of cavity fields by measuring the atomic populations in the micromaser experiments. We test our theory with the one-photon Fock state and the Schr?dinger cat state, and find that the results are rather good.
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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.
The long lifetime of photons in a high-QQQ micromaser cavity is used to generate a ∣n〉|n〉∣n〉-state maser field by injecting atoms, one at a time. Every atom is probed for its excitation after leaving the cavity so that the precise number of photons in the field is known. We calculate the probability of obtaining nnn photons after mmm atoms have passed the cavity.
A detailed theoretical and experimental study of the atom-field interaction starting from first principles was made possible by the realization of the single-atom micromaser. The situation is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a superconducting cavity. In spite of the considerable amount of work devoted to the study of the micromaser, it still remains to be established how the system behaves under coherent pumping. We present a comprehensive study of the coherently pumped micromaser; we develop an analytic method to obtain the steady-state solution of the master equation governing the time evolution of the cavity field. We illustrate this method with a simple example and present results for the photon distribution and purity of the steady state of the coherently pumped micromaser.