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arXiv:quant-ph/0203052

Elements of Micromaser Physics

Berthold‐Georg Englert

Published Mar 13, 2002• 15 citations
arXivHTMLPDF

Abstract

The elements of micromaser physics are reviewed in a tutorial way. The emphasis is on the basic theoretical concepts, not on technical details or experimental subtleties. After a brief treatment of the atom-photon interaction according to the Jaynes-Cummings model, the master equation that governs the dynamics of the one-atom maser is derived. Then the more important properties of the steady states of the one-atom maser are discussed, including the trapped states. The approximations, upon which the standard theoretical model of the one-atom maser is based, are exhibited. The methods by which one calculates statistical properties of the emerging atoms are hinted at.

DOI
10.48550/arxiv.quant-ph/0203052

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The elements of micromaser physics are reviewed in a tutorial way. The emphasis is on the basic theoretical concepts, not on technical details or experimental subtleties. After a brief treatment of the atom-photon interaction according to the Jaynes-Cummings model, the master equation that governs the dynamics of the one-atom maser is derived. Then the more important properties of the steady states of the one-atom maser are discussed, including the trapped states. The approximations, upon which the standard theoretical model of the one-atom maser is based, are exhibited. The methods by which one calculates statistical properties of the emerging atoms are hinted at.
. In this paper experiments performed with the one-atom maser are reviewed. Furthermore, possible experiments to test basic quantum physics are discussed. Introduction, the One-Atom-Maser The most promising avenue to study the generation process of radiation in lasers and masers is to drive a maser consisting of a single mode cavity by single atoms. This system, at first glance, seems to be another example of a Gedanken-experiment treated in the pioneering work of Jaynes and Cummings (1963), but such a one-atom maser (Meschede, Walther and Müller, 1985) really exists and can in addition be used to study the basic principles of radiation-atom interaction. The advantages of the system are: it is the first maser which sustains oscillations with less than one atom on the average in the cavity, this setup allows to study in detail the conditions necessary to obtain nonclassical radiation, especially radiation with sub-Poissonian photon statistics in a maser system directly in a Poissonian pumping process, and it is possible to study a variety of phenomena of a quantum field including the quantum measurement process. What are the tools that make this device work: It was the enormous progress in constructing superconducting cavities together with the laser preparation of highly excited atoms – Rydberg atoms – that have made the realization of such a one-atom maser possible.
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.
We present a general theory for the calculation of various characteristic properties of the beam of atoms emerging from a resonator in one-atom-maser experiments. The beam is described in terms of the statistics of the detector clicks. The evolution of the state of the maser photons between clicks is governed by a nonlinear master equation. The nonlinearity originates in the necessity to account for the atoms that escape detection. Despite the permanent reductions of the photon state, resulting from the detections, the steady state of the conventional linear master equation determines the statistics of the detector clicks. The whole process is ergodic, in the sense that a single run of the experiment contains all reproducible statistical data, provided the duration of the run is much longer than all relevant correlation times. The nonlinear master equation is used to calculate the distribution of waiting times between detector clicks. Other statistical properties of the clicks that are derived include correlation functions and variances of the counting statistics. The formalism is applied to standard one-atom-maser experiments and to parity measurements on both unpumped and pumped cavities. We find that, for the standard one-atom-maser operation, none of the said statistical properties is a simple immediate indicator for a sub-Poissonian variance of the photon number. For example, the detector clicks may be antibunched although the photon distribution has a super-Poissonian variance.
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.
A micromaser in standard operation produces entangled two-level atoms. This entanglement can be investigated in the correlations of atoms leaving the micromaser cavity in the upper and lower maser levels. The correlations contribute to the stabilization of the photon number in the cavity and are thus vital for the generation of sub-Poissonian statistics in the maser field. We review how various statistical signatures for this entanglement are calculated in micromaser theory, and report recent measurements that demonstrate the case. Ways are described leading to an optimal entanglement for the atoms in the micromaser.