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Journal of Physics A Mathematical and General

Optical processes of a single-atom model in the phonon field

Wang Zhonghe, Zhang Guang-Yin, PAN SHI-HONG

Published Mar 21, 1994• 0 citations
Publisher

Abstract

The optical processes of a single-atom model in the phonon field have been studied. To deal with the quantum electrodynamics phenomena in condensed matter microcavities, the influence of electron-phonon interactions has to be taken into account. As a clear picture, the effect of the lattice's oscillation on the optical transition in condensed matter microcavities is reduced to a model of a single atom in a phonon field. We deduce that in the case with a phonon participating, the Bloch equation is still satisfied. In the process of spontaneous emission for an electron interacting with a phonon, we derive the Rabi oscillation for the simple atom in the phonon field.

DOI
10.1088/0305-4470/27/6/038

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The optical processes of a single-atom model in the phonon field have been studied. To deal with the quantum electrodynamics phenomena in condensed matter microcavities, the influence of electron-phonon interactions has to be taken into account. As a clear picture, the effect of the lattice's oscillation on the optical transition in condensed matter microcavities is reduced to a model of a single atom in a phonon field. We deduce that in the case with a phonon participating, the Bloch equation is still satisfied. In the process of spontaneous emission for an electron interacting with a phonon, we derive the Rabi oscillation for the simple atom in the phonon field.
This chapter presents simple theoretical models which take into account the effect of dephasing of the vacuum fields on the spontaneous emission in a microcavity. This would be necessary to evaluate the limit of the capability of microcavity-based solid-state optical devices. The dephasing of the quantized fields, i.e., the vacuum fields, which is our main concern, results from the energy exchange between fields and medium polarizations interacting with phonon reservoirs, that is, from the dispersion. A symmetric structure of the system allows us to use the one-way time-evolution of field b, in order to obtain a motion equation of the field, which is in general derived from a round-trip time-evolution of the field. The alteration of the spontaneous emission in a microcavity can be viewed as a manifestation of the self-interference of the quantized fields, which are vacuum fields.
We present a microscopic optical-Bloch-equation model for N two-level atoms being driven by a monochromatic radiation field. The model is obtained from the equations of motion that result from the microscopic Hamiltonian by introducing at a certain stage an Ansatz that accounts for spontaneous emission and bath dephasing in a unitary manner. The equations of motion are a numerically tractable set of coupled c-number differential equations with a discrete, stochastic term deduced from the quantum-mechanical equations of motion. We apply these equations to various model problems and show that they correctly describe such varied optical phenomena as superradiance, photon echoes, and absorptive bistability. In particular, they yield an interesting microscopic picture of the dynamical phase transition that occurs in the latter example. We conclude that this unified approach has advantages that make it useful for studying a number of problems of current interest.
We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.
We investigate a quantum-dot-based cavity system via the master-equation approach. The dynamics of the system is greatly affected by dissipation and dephasing processes. We include these phenomena to the theory through the master equation. The dissipation effects such as cavity loss, spontaneous recombination of excitons, and incoherent pumping are considered. The dephasing process is included as an electron--acoustic-phonon interaction. An intrinsic feature of solid-state cavity systems is the presence of electron-phonon interaction, which distinguishes this system from atomic cavity quantum electrodynamics. Due to the temperature dependence of phonons we use the complete form of the master equation (temperature dependence of dissipation rates) in this paper. We study the emission spectrum and photon statistics of the system. We show that cavity mode emission depends on temperature, and temperature strongly affects the photon statistics.
Spontaneous emission in a planar microcavity by two identical and spatially separated two-level atoms, both of them initially excited, is considered under fourth-order perturbation approximation in atom-field coupling constants. A delay-differential equation with proper retardation times for the probability of both atoms in the upper state is derived and expressions for the emitted-light intensity and spectrum are given. It is numerically shown that, while two-atom cooperation is enhanced for small interatomic distances, the two-atom vacuum Rabi oscillation is somewhat suppressed compared to the single-atom oscillation level when the interatomic separation is close to the cavity transverse coherence length.
Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms. In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis. In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.