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Physical Review A

Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom

L. Tian, H. J. Carmichael

Published Dec 1, 1992• 284 citations
Publisher

Abstract

Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ``vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.

DOI
10.1103/physreva.46.r6801

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Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.
We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
Resonance fluorescence of a driven Jaynes-Cummings system is studied theoretically when the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, there occur anomalous resonance peaks at $\ifmmode\pm\else\textpm\fi{}\sqrt{2}{g}^{\ensuremath{'}},\ifmmode\pm\else\textpm\fi{}\sqrt{3}{g}^{\ensuremath{'}},$ etc., with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}}.$ These new peaks and the observed shift of the vacuum Rabi splitting are to be explained in the language of the quasienergy levels induced dynamically by the strong driving field. In the presence of significant damping the spectrum reflects the photon-number distribution inside the cavity, and particularly, a bimodality of the distribution results in a unique quintuplet resonance fluorescence spectrum.
We report experimental measurements of the transmission spectrum of an optical cavity coupled with cold Rb atoms. We observe the multiatom vacuum Rabi splitting of a composite cavity and atom system. When a coupling field is applied to the atoms and induces the resonant two-photon Raman transition with the cavity field in a $\ensuremath{\Lambda}$-type system, we observe a cavity transmission spectrum with two vacuum Rabi sidebands and a central peak representing the intracavity dark state. The central peak linewidth is significantly narrowed by the dark-state resonance and its position is insensitive to the frequency change of the empty cavity.
In recent years, remarkable advances in the science of laser cooling and trapping of atomic samples have lead to breakthroughs in quantum optics and, in particular, in cavity quantum electrodynamics (QED). The ability to optically trap an atom within the mode of a ultra-high finesse cavity of small mode volume for experimentally significant periods of time now allows for the continuous observation of fundamental quantum optical effects. This dissertation will focus on experiments conducted to fully characterize and exert quantum control over a strongly-coupled atom-cavity system consisting of single cesium atoms isolated by a dipole trapping in the mode of a Fabry-Perot optical resonator. In particular, we describe techniques developed and implemented for exerting coherent control over the internal and quantum motional state of these atoms using stimulated Raman processes. We also focus on the applications of this system to quantum networking and quantum information science, particularly within the context of coherently transferring quantum states from atom to quantum optical fields and back. Finally, we describe a series of measurements carried out to explore the characteristic dynamics of the Jaynes-Cummings Hamiltonian which governs the system. This includes spectroscopic measurement of the signature vacuum Rabi splitting for strongly-coupled cavity QED as well as evidence in the time domain for coherent Rabi nutation of excitation between atom and field on resonance.