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Physical Review A

Time-dependent micromaser spectrum

Bimalendu Deb, Deb Shankar Ray

Published Jun 1, 1994• 3 citations
Publisher

Abstract

We examine the growth of a cavity field built up from a vacuum in a micromaser in terms of a ``physical spectrum'' or a time-dependent spectrum and the photon distributions. We find that the photon distribution attains the steady state earlier than the spectrum becomes steady. The short-time decrease of the half-width at half maximum of the spectrum obeys a power-law behavior with time.

DOI
10.1103/physreva.49.5015

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We examine the growth of a cavity field built up from a vacuum in a micromaser in terms of a ``physical spectrum'' or a time-dependent spectrum and the photon distributions. We find that the photon distribution attains the steady state earlier than the spectrum becomes steady. The short-time decrease of the half-width at half maximum of the spectrum obeys a power-law behavior with time.
We study the spectrum of a one-photon micromaser through the approach of the two-time correlation function. First, we derive two general formulas for the two-time correlation function and for the micromaser spectrum. Then, we focus our attention on trapped states of the micromaser. We examine the line shapes and linewidth of the micromaser spectrum. We find that the half width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density matrix elements ${\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$n+1{\mathit{n}}_{+1}n+1​(t), that a hole can appear at the center of the spectrum, and that the spectrum can be split by shifted spectral components. Using a simple example in which the micromaser spectrum is exactly Lorentzian, we also show that two very close photon-number distributions can correspond to two very different natural linewidths.
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.
We present a study on the quantum statistical properties of radiation in a one-photon micromaser. In particular, the possibility of generating steady-state squeezing is investigated. The spectral properties of the radiation field in a micromaser are also studied. \n \nWe show that the steady-state squeezing can be generated in a lossless micromaser by injecting the atoms in a coherent superposition of upper and lower states. It is shown by considering initial vacuum number and thermal state of the cavity field, that for a particular choice of the interaction time field evolves to a squeezed state. Steady- state squeezing is found to be independent of the initial state of the cavity field. However, the temporal evolution of the squeezing depends on the initial state of the field. Effects of cavity losses and pump fluctuations on steady-state squeezing are also investigated. \n \nFinally, an exact analytic expression for the linewidth of a micromaser in the absence of cavity losses is obtained by evaluating the two-time correlation function. A comparison with the natural linewidth of laser shows that under certain conditions gain contribution to the linewidth is same in both the cases. We also, derive an exact expression for the phoston distribution function and show that for a particular choice of the interaction time, the number state of the field can be generated.
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.
By calculating the two-time correlation function of a one-photon micromaser, we study the line shapes and linewidth of the micromaser spectrum. We find that the half-width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density-matrix elements ${\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$n+1{\mathit{n}}_{+1}n+1​, that a hole can appear in the spectrum, and that the spectrum can be split by shifted spectral components.