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Journal of Applied Physics

Nonlinear optical phase shift obtained from two-level atoms confined in a planar microcavity

Hisaki Oka, Hideki Fujiwara, Shigeki Takeuchi, Keiji Sasaki

Published Mar 1, 2010• 0 citations
Publisher

Abstract

We investigate the nonlinear optical phase shift obtained from a thin atomic layer confined in a distributed Bragg reflector (DBR) microcavity with reflection geometry. The optical response of the atom-cavity system is numerically analyzed using finite-difference time-domain method with the optical Bloch equations. The optimal position of atomic layer, at which a maximal phase shift of π is realized, drastically changes with the quality factor Q of the cavity. We show that for high Q the maximal phase shift of π can be obtained anywhere in the cavity field independently of atomic layer position. This result is in contrast to that obtained from a one-dimensional atom model in the limit of bad cavity, where a maximal phase shift of π is obtained only at the antinode of the cavity field. We also show that the independence of phase shift on atom position realized in high-Q regime is due to an interference effect in the surface layers of the DBR cavity.

DOI
10.1063/1.3327411

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We investigate the nonlinear optical phase shift obtained from a thin atomic layer confined in a distributed Bragg reflector (DBR) microcavity with reflection geometry. The optical response of the atom-cavity system is numerically analyzed using finite-difference time-domain method with the optical Bloch equations. The optimal position of atomic layer, at which a maximal phase shift of π is realized, drastically changes with the quality factor Q of the cavity. We show that for high Q the maximal phase shift of π can be obtained anywhere in the cavity field independently of atomic layer position. This result is in contrast to that obtained from a one-dimensional atom model in the limit of bad cavity, where a maximal phase shift of π is obtained only at the antinode of the cavity field. We also show that the independence of phase shift on atom position realized in high-Q regime is due to an interference effect in the surface layers of the DBR cavity.
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We investigate the effects of decoherence on the nonlinear phase shift obtained from a one-dimensional atom implemented by a one-sided microcavity. The one-dimensional atom is realized by coupling a single atom confined in the cavity to the one-dimensional input-output fields of the cavity. The nonlinear optical response obtained from the one-dimensional atom can then be analyzed by using the optical Bloch equations. It is shown that the nonlinear phase shift depends on the coupling efficiency η, which is defined by the ratio of the coherent atom-field coupling rate and the total dipole relaxation rate. In particular, a maximal phase shift of π is obtained on resonance for coupling efficiencies η larger than one half, while the maximal phase shifts for coupling efficiencies η smaller than one half are obtained off resonance and are always smaller than π/2.
The nonlinear optical response obtained from a single two level atom in a one-sided cavity is studied using a model system, where a infinite atomic layer sits in front of a reflecting mirror. When the atomic layer is placed at the antinode of input field, the result given by finite difference time domain method coupled with the optical Bloch equations is consistent with previous analytical result [ H F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B 5, 218 (2003) ] based on one-dimensional atom model.
Abstract We investigate the optical properties of a hybrid solid-state optomechanical microcavity containing two coupled quantum wells interacting with the cavity mode in the presence of a third-order nonlinear medium and a mechanically compliant distributed Bragg reflector (MC-DBR). The MC-DBR interacts with the cavity mode via the nonlinear radiation pressure effect. The steady state mean-field analysis shows the existence of optical bistability, which can be utilized to design all optical tunable switch. The coupling between the two quantum wells, the interaction between the excitons and the optical mode, the Kerr nonlinearity, and the optomechanical interaction can be tuned to operate the optical switch at lower input laser power. The fluctuation dynamics demonstrate the presence of optomechanically induced transparency (OMIT) and optomechanically induced absorption (OMIA). We find that both OMIT and OMIA can be manipulated efficiently by optomechanical coupling strength and the quantum well tunneling rate.
We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Particular attention is given to the parallel dipole in the $\ensuremath{\lambda}/2$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.