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Journal of Optics B Quantum and Semiclassical Optics

A two-photon one-atom micromaser with permanent optical pumping

Alexander Ya. Kazakov

Published Apr 12, 2001• 6 citations
Publisher

Abstract

A new version of the one-atom micromaser is under consideration. This micromaser is based on a three-level atom interacting simultaneously both with the quasi-resonant classical fields and with the quantized mode, which is in two-photon resonance with the third atomic transition. It is shown that such a micromaser can be a source of quantized radiation with nonclassical quantum statistical characteristics.

DOI
10.1088/1464-4266/3/3/305

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A new version of the one-atom micromaser is under consideration. This micromaser is based on a three-level atom interacting simultaneously both with the quasi-resonant classical fields and with the quantized mode, which is in two-photon resonance with the third atomic transition. It is shown that such a micromaser can be a source of quantized radiation with nonclassical quantum statistical characteristics.
We present the theory of a micromaser operating on a cascade three-level atomic transition, which is coupled to two cavity modes satisfying the resonance condition. A numerical approach is employed to integrate the master equation describing the microwave field, allowing us to obtain the semiclassical regime in the limit of large mean photon numbers. We show that the transfer rate from the excited atomic state is very close to 100% over a large interval of variation of the interaction time. The atom - field interaction time may be chosen so as to avoid transitions to the intermediate atomic state when in steady-state operation. In this case, the two cavity modes have nearly the same photon statistics, and the fluctuations in the difference of intensities may be reduced by up to 50% below the classical limit. The intensity correlation between the two cavity modes originates from the possibility of controlling the interaction time, rather than from the simultaneous generation of `twin' photons in a two-photon transition.
We formulate the theory of a micromaser operating simultaneously on a one- and a two-photon atomic transition. Departing from the complete microscopic Hamiltonian for this composite `atom plus field' system, we derive the equations governing its behaviour in the semiclassical approximation and also the fully quantum mechanical master equation. Using parameters corresponding to existing realizations of the one- and two-photon micromaser, we obtain illustrative examples of some novel aspects of this system in the steady state as well as in dynamical evolution.
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 realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a superconducting cavity. This system's ability to coherently transfer quantum states between atoms and photons made it relevant in the context of quantum computation as well. Although considerable work, both theoretical and experimental, has been devoted to this system, with a few exceptions, most cases involved only non-coherent pumping. As a result, the density matrix describing the cavity field remained diagonal, preventing the appearance of coherences. Here, our goal is to provide a summary of the progress we made toward a comprehensive understanding of the features of the coherently pumped micromaser with special respect to coherences, which are central to quantum information processing.
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.
The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity. The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n 4 , where n denotes the principle quantum number.