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Physical Review A

Generation of pure states in a two-photon micromaser: Effects of finite detuning and cavity losses

Miguel Orszag, Luis Roa, R. Ramírez

Published Dec 1, 1993• 20 citations
Publisher

Abstract

In this paper, we study the generation of pure states in a two-photon micromaser with finite detuning of the intermediate atomic level. This study was done via the temporal evolution of the discrete master equation. We show that it is possible to generate the ideal squeezed vacuum for a broad range of detunings in a lossless cavity and away from the trapping condition. We also consider the effect of cavity losses.

DOI
10.1103/physreva.48.4648

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In this paper, we study the generation of pure states in a two-photon micromaser with finite detuning of the intermediate atomic level. This study was done via the temporal evolution of the discrete master equation. We show that it is possible to generate the ideal squeezed vacuum for a broad range of detunings in a lossless cavity and away from the trapping condition. We also consider the effect of cavity losses.
We study the effect of finite atomic lifetimes on a micromaser from temporal evolution. A stream of finite-lifetime two-level atoms is injected inside a cavity in a coherent superposition of their upper and lower levels. We study the effect of the atomic decay on the generation of quasipure states of the inner electromagnetic field. First, we study the stationary photon number distribution when the atoms are injected in their upper level. We compare our results with previous calculations by Zhu, Wang, and Fearn [Phys. Rev. A 44, 737 (1991)]. We find that quasinumber states can be generated for a long time, in a range of physical parameters that allows their experimental realization. Second, we investigate the effect of finite atomic lifetimes on the generation of cotangent states, and we study their squeezing properties.
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.
I consider a lossless micromaser with cascade three-level atoms in a coherent superposition of its three levels. I find that for some values of the atomic flight time and some probability amplitudes for the intermediate atomic level, the field evolves to a pure state which is the well-known general squeezed state, and the squeeze and displacement parameters are functions of the atomic input parameters. Therefore it is possible to choose atomic parameters which produce squeezing in the phase or in the amplitude of the field inside the cavity.
We study the dynamics of a two-photon micromaser driven by a sequence of polarized Rydberg atoms. If cavity losses are neglected, the density matrix of the cavity mode consists of four dynamically decoupled components. Under appropriate trapping conditions, similar to those for the one-photon micromaser, it evolves to a stationary state. When the bare two-photon frequency cancels the ac Stark shift we cannot satisfy the trapping conditions for odd and even photon number states simultaneously. For specific initial conditions, where either only odd or only even number states are initially populated, we may find, however, stationary states that are pure and that can lead to macroscopic superpositions. These pure states are analogous to the cotangent and tangent states of the one-photon micromaser. When the two atomic levels are in resonance with the bare two-photon transition, trapping conditions for odd and even photon number states can be fulfilled simultaneously. Although the ac Stark shift does not allow for pure stationary states, the stationary state resembles an incoherent superposition of only two pure states, to within a relative deviation of 10-3 off purity.
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.