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Journal of Physics B Atomic Molecular and Optical Physics

Theory of a two-mode micromaser simultaneously pumped by one- and two-photon atomic transitions

David Petrosyan, P. Lambropoulos

Published Sep 1, 1999• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/18/302

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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.
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We present the quantum theory of a microscopic maser operating on a degenerate two-photon transition between levels of the same parity. We derive both a master equation and a Fokker-Planck equation for this system, and show that quantum effects may have a substantial influence on the behavior of the maser. They modify the oscillation threshold and make external triggering of this maser unnecessary, whereas, according to semiclassical theory, such a triggering is required to start up the maser oscillation. We derive the phase-diffusion properties of the field and show that the diffusion coefficient is complex in this case, its imaginary part being associated with a frequency shift of the field inside the cavity. We show that, in steady state, the photon-number statistics is sub-Poissonian for a wide range of pumping rates.
We investigate the quantum dynamics of a two-photon micromaser pumped by atoms injected in the superposition state of the upper and intermediate levels. We simulate a master equation governing the system by the Monte Carlo wavefunction approach and analyse the steady-state behaviour as a function of the atomic transit time. The atomic coherence can effectively enhance the intensity and sub-Poissonian of the cavity field as compared with the atomic mixture. It is also discovered that the phase of the cavity field can be shifted by adjusting the detuning between the atom and field. This result shows that it is possible to manipulate the phase of the cavity field by detuning, due to atomic coherence.
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 derive the master equations for the fields in the one-mode \ensuremath{\Lambda}-type micromaser and laser with injected atoms in a superposition of their states. In terms of effective parameters, these equations are equivalent to those for a two-level micromaser and laser. The interference terms in the master equations may cancel the absorption terms independent of statistical properties of the field. Due to the atomic coherence between the two degenerate lower levels, the generation of field states with sub-Poissonian photon statistics is possible in the micromaser without the need for a population inversion. If an equivalent level system is used in a laser operating without population inversion it can produce field states with Poisson distributions of the photon number.
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.