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arXiv:quant-ph/0606079 · Physical Review A

Cavity QED with multiple hyperfine levels

Kevin M. Birnbaum, A. S. Parkins, Harry J. Kimble

Published Dec 4, 2006• 20 citations
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Abstract

We calculate the weak-driving transmission of a linearly polarized cavity mode strongly coupled to the $D2$ transition of a single cesium atom. Results are relevant to future experiments with microtoroid cavities, where the single-photon Rabi frequency $g$ exceeds the excited-state hyperfine splittings, and photonic band-gap resonators, where $g$ is greater than both the excited- and ground-state splitting.

DOI
10.1103/physreva.74.063802

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We calculate the weak-driving transmission of a linearly polarized cavity mode strongly coupled to the D2D2D2 transition of a single cesium atom. Results are relevant to future experiments with microtoroid cavities, where the single-photon Rabi frequency ggg exceeds the excited-state hyperfine splittings, and photonic band-gap resonators, where ggg is greater than both the excited- and ground-state splitting.
The steady-state transmission spectrum of a cavity with two modes of orthogonal polarization strongly coupled to a single atom with multiple Zeeman states is computed. Effects due to cavity birefringence and atomic ac-Stark shifts are included. The transmission spectrum is compared to experimental results for a single Cesium atom trapped via an intracavity FORT in a Fabry-Perot cavity. The excellent agreement of the theory with the data is used to infer the distribution of the position of the trapped atom. The intensity correlation function of this system is also calculated, and found to be strongly antibunched and sub-Poissonian. This effect is explained in terms of photon blockade, based on the structure of the lowest energy eigenvalues. Experimental results confirm the strong nonlinearity at the single-photon level. We present theoretical predictions of the weak field spectra of microtoroid and photonic bandgap cavities strongly coupled to the D2 transition of single Cesium atoms. These calculations include all hyperfine and Zeeman states of the transition and model the cavity as a single-mode, linearly polarized resonator. Finally, we outline a technique for using multiple hyperfine and Zeeman levels of a single atom in a strongly coupled atom-cavity system to generate polarized single photons on demand in a well-defined temporal mode via adiabatic passage. The technique is insensitive to cavity birefringence and only weakly sensitive to atomic position. Variations of this technique for generating entanglement of photon polarization and atomic Zeeman state are also discussed.
We calculate the probe spectrum for multilevel atoms in a damped, weakly driven cavity supporting two degenerate orthogonally polarized modes. One mode is weakly driven by a linearly polarized external field. The atoms, initially prepared in a mF=0{m}_{F}=0mF​=0 hyperfine ground state, couple to the driven mode by making a $\ensuremath{\Delta}{m}_{F}=0$ transition and to the orthogonally polarized mode by making $\ensuremath{\Delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ transitions to other hyperfine sublevels. We compare probe spectra, the intensity of the driven mode, the undriven mode, and the atomic excitation probability as a function of the detuning of the driving laser from the cavity resonance for three- and four-level atomic models. In both cases the spectrum of the driven mode is a vacuum Rabi doublet familiar from the driven, damped Jaynes-Cummings model. The undriven mode spectrum is a triplet with the maximum on resonance for the three-level model while the four-level model has a four-peaked spectrum. We discuss the role of strong coupling to the undriven mode in accounting for the qualitative difference between the models.
We propose a quantum simulation of a two-level atom coupled to a single mode of the electromagnetic field in the ultrastrong-coupling regime based upon resonant Raman transitions in an atom interacting with a high finesse optical cavity mode. We show by numerical simulation the possibility of realizing the scheme with a single rubidium atom, in which two hyperfine ground states make up the effective two-level system, and for cavity QED parameters that should be achievable with, for example, microtoroidal whispering-gallery-mode resonators. Our system also enables simulation of a generalized model in which a nonlinear coupling between the atomic inversion and the cavity photon number occurs on an equal footing with the (ultrastrong) dipole coupling and can give rise to critical-type behavior even at the single-atom level. Our model takes account of dissipation, and we pay particular attention to observables that would be readily observable in the output from the system.
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 study the nonlinear dynamics of an ensemble of cold trapped atoms with a hyperfine transition magnetically coupled to a resonant microwave cavity mode. Despite the minute single-atom coupling, one obtains strong coupling between collective hyperfine qubits and microwave photons, enabling coherent transfer of an excitation between the long-lived atomic qubit state and the mode. Evidence of strong coupling can be obtained from the cavity transmission spectrum even at finite thermal photon number. The system makes it possible to study further prominent collective phenomena such as superradiant decay of an inverted ensemble or the building of a narrowband stripline micromaser locked to an atomic hyperfine transition.