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Quantum and Semiclassical Calculations of Cavity QED Spectra

L. Tian

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

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.

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•May 28, 2009•0 citations
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.
We present detailed numerical simulations of semiclassical and quantum spectra of a cavity QED system consisting of a single three-level atom in Λ-configuration interacting with a quantized cavity mode through one of its transitions while its other transition is driven by a coherent classical field. We compute the semiclassical and quantum spectra of the system under various levels of external driving field strengths. In the semiclassical approach, we neglect the correlations between the cavity and atomic operators, whereas in the quantum case no such assumption is made. Our results show that the two approaches yield identical results under sufficiently weak driving field conditions. However, the two approaches yield starkly different results at stronger driving field intensities: the fully quantum approach yields a well-defined multiphoton spectrum whereas the semiclassical approach results in a bistable spectrum. Furthermore, our calculations reveal a complex Raman structure at the position of the dark-state transition.
We present a numerical study comparing semiclassical and quantum models of a damped, strongly interacting cavity QED system composed of a single two-level atom interacting with a single quantized cavity mode driven externally by a tunable monochromatic field. We compute the steady state transmission spectrum of the coupled system under each model and show that in the strong coupling regime, the two models yield starkly different results. The fully quantum mechanical model of the system correctly yields the expected multiphoton transmission spectra while the semiclassical approach results in a bistable spectrum.
The spectrum of the resonance fluorescence light from a single two-level atom in a small, high-quality, optical cavity is calculated. The coupling between the atom and cavity is made sufficiently strong compared to the dissipation that single quantum frequency splitting (vacuum Rabi splitting) occurs. Under high excitation qualitatively new fluorescent spectra are predicted. The usual three-peaked resonance fluorescence spectrum now has sidebands whose width is given by the Jaynes-Cummings atom-cavity coupling coefficient rather than by the system dissipation.
Spectra of the atomic resonance fluorescence and of the cavity-transmitted light in a driven Jaynes-Cummings system are studied theoretically, where the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, anomalous resonance peaks occur at $\ifmmode\pm\else\textpm\fi{}\sqrt{n}{g}^{\ensuremath{'}} (n=2,3,\dots{}),$ with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}},$ both in the atomic fluorescence and the cavity transmission. These peaks as well as the observed shift of the vacuum Rabi splitting are explained in terms of the quasienergy levels induced dynamically by the strong driving field. For a stronger driving field, it is shown that the spectrum of the cavity transmission deviates from that of the atomic fluorescence. In the presence of significant damping, the spectrum of the cavity transmission approaches a singlet structure in the strong driving-field limit, and it is found additionally that a bimodal photon-number distribution, which results in a unique quintuplet spectrum of the atomic fluorescence, does not show up in the cavity transmission.
The cavity field spectrum of a pair of coupled two-level atoms interacting with single mode field is studied. The results for the initial fields in pure number state, coherent state or squeezed vacuum state are presented and discussed. The effect of dipole-dipole coupling constant gαp on the cavity field spectrum is analyzed. It is found that four Rabi peaks appear for small gαp and three Rabi peaks for large gα when the field is vacuum initially. When the field is pure number state initially, the structure of the cavity field spectrum is five peaks for weak field and three peaks for strong field. When the fields are in a coherent state or squeezed vacuum state, a multi-peak structure appears generally. The peak-position and peak-height of the spectrum are both influenced by gα, but this influence is evident for weak field only.
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.