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EPH - International Journal of Applied Science

EXACT CALCULATIONS FOR ONE PHOTON MICROMASER WITH COHERENT INPUTS I

A. Kremid

Published Dec 27, 2021• 1 citation
Publisher

Abstract

We report a numerical simulation of the action of the one 85 Rb atom micromaser which shows that the micromaser field evolves towards a steady state equilibrium when the condition that Tp t int satisfies. In this steady state regime the cavity field reaches a steady state after a sufficient number of atoms have passed through the cavity. The cavity temperature T and the cavity quality factor Q can produce a quantitive change when one of them or the two are changed but they are not responsible for the qualitative changes in the micromaser field. Evidently the only responsible parameter for these qualitative changes is the repetition time T p namely if T p t int then the micromaser field evolution is towards a steady state equilibrium. In contrast when T p reduced to the order of t int then the micromaser field evolution is controlled by the trapping state dynamics – no steady state is apparent in this case. The first going-up trapping state at n=3 plays a significant role in the early dynamics of the micromaser field. Moreover the state of the field ultimately evolves towards a mixed state rather than a pure state.

DOI
10.53555/eijas.v7i4.40

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We report a numerical simulation of the action of the one 85 Rb atom micromaser which shows that the micromaser field evolves towards a steady state equilibrium when the condition that Tp t int satisfies. In this steady state regime the cavity field reaches a steady state after a sufficient number of atoms have passed through the cavity. The cavity temperature T and the cavity quality factor Q can produce a quantitive change when one of them or the two are changed but they are not responsible for the qualitative changes in the micromaser field. Evidently the only responsible parameter for these qualitative changes is the repetition time T p namely if T p t int then the micromaser field evolution is towards a steady state equilibrium. In contrast when T p reduced to the order of t int then the micromaser field evolution is controlled by the trapping state dynamics – no steady state is apparent in this case. The first going-up trapping state at n=3 plays a significant role in the early dynamics of the micromaser field. Moreover the state of the field ultimately evolves towards a mixed state rather than a pure state.
Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.
Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.
We have used matrix continued fraction methods pioneered previously, to solve essentially exactly for the dynamics of the one 85Rb atom micromaser. A range of cavity Q values and of average atomic input rates R equals Tp-1 and of atomic interaction times tint is studied. For Tp approximately greater than 200tint the system does evolve to a steady state. And even Q equals 5 multiplied by 1010 and temperature T equals 0.070 degrees K are apparently insufficient to avoid evolution to a steady state with finite variance of the cavity field when tint equals 1.54/44 kHz unless Tp is also substantially reduced. Only in this way are actual trapping state dynamics obtained. The field variance v is not a good diagnostic for observing such trapping state dynamics.
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.
We have investigated the steady-state cavity-field properties of a single-mode two-photon micromaser when the atoms in a cascade three-level configuration are initially prepared in a mixture of the upper and intermediate states. The mean photon number, trapping state and sub-Poissonian effect are discussed with upper (intermediate)-state population changing from 1(0) to 0(1). These properties are very different from those in a pure two- or one-photon transition process, due to the competition among different transition processes. In particular, the trapping states of nonzero photons are discovered in this system under some conditions, which is contrary to the previous findings.
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.