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Physical Review A

Parametric oscillator pumped by a quantum current

E. G. Lima, F. A. M. de Oliveira

Published Dec 1, 1993• 1 citation
Publisher

Abstract

The interaction between a parametric oscillator and a stream of polarized two-level atoms is considered. The dynamics of the system is computer simulated and the atom-field evolutions are followed. Different steady states are obtained with enhanced squeezing and sub-Poissonian statistics, depending on the atomic and parametric oscillator pump phases. The results are interpreted in terms of damping by a rigged reservoir.

DOI
10.1103/physreva.48.4569

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The interaction between a parametric oscillator and a stream of polarized two-level atoms is considered. The dynamics of the system is computer simulated and the atom-field evolutions are followed. Different steady states are obtained with enhanced squeezing and sub-Poissonian statistics, depending on the atomic and parametric oscillator pump phases. The results are interpreted in terms of damping by a rigged reservoir.
We investigate in detail the role of a reservoir concerning the squeezing effect in a driven coupled-oscillator system. In our model, a harmonic oscillator (single cavity mode) is coupled to a two-state oscillator (two-level atom) driven by a classical field. The oscillators are coupled to their respective reservoirs, by which the oscillators are damped. The degree of squeezing in the short-time limit is found to be independent of the damping rate of the harmonic oscillator in a perturbative regime. More remarkably, the harmonic oscillator, which is in a coherent state in the absence of its reservoir, gets squeezed in the steady state when it is coupled to the reservoir. The reservoir assumes two competing roles of assisting and suppressing the squeezing effect induced by the nonlinear interaction of the coupled oscillators. As a result, the squeezing effect is increased to some extent with the damping rate of the harmonic oscillator. In addition, the ``matching condition'' for the optimal squeezing is obtained such that the pumping field intensity should be inversely proportional to the damping rate.
Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.
We investigate the dynamics of a micromaser continuously driven by a resonant coherent field and pumped by atoms injected in superposition states. We formulate a master equation for the system, and by a Monte Carlo wave-function approach we describe the steady-state behavior as a function of atomic-transit time or driving-field intensity. The combined action of polarized atoms and driving field can lead to enhancement or suppression of coherence in system dynamics, including nonclassical effects such as quadrature squeezing, sub-Poissonian photon statistics, and revival of Rabi oscillations, as well as to shifts of the induced cavity-field phase. These results show the possibility of manipulating both the photon number and the phase of the cavity field.
Abstract By a Monte Carlo wave function approach we describe the dynamics of a coherently driven micromaser pumped by coherently prepared atoms. The system can exhibit nonclassical effects such as quadrature squeezing, sub-Poissonian photonstatistics, and Rabi oscillations revival. The interplay between driving field and polarised atoms allows manipulating both the photon number and the phase of the cavity field. By varying either the atomic transit time or the injected field intensity, the coherence of the system dynamics can be enhanced or even suppressed, whereas the induced cavity field phase can be shifted.
According to the exact solution of a two-level atomic system interacting with a single-mode field in a cavity and including a pumping mechanism, sub-Poissonian photon statistics can be generated either by regular pumping or by resonance absorption of the lower level. When the atomic lifetime is much smaller than the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\gg}1), which corresponds to a usual laser system, the sub-Poissonian photon distribution can be obtained only by regular pumping. On the other hand, if the atomic lifetime is comparable with the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\le}1), the sub-Poissonian photon distribution can be generated by both mechanisms.
The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a $4\ensuremath{\pi}$ squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=1/2$ transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath--atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number NNN and the squeezing phase $\ensuremath{\varphi}$. We present results of a detailed analytical and numerical study.