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Physical Review A

Photon correlation spectroscopy of the Jaynes-Cummings system

Barry C. Sanders, H. J. Carmichael, B. F. Wielinga

Published Feb 1, 1997• 13 citations
Publisher

Abstract

The spectroscopic detection of the excited-state resonances of a strongly coupled atom and optical cavity mode is complicated by inhomogeneous broadening, due to the variation of the dipole coupling constant with location in the cavity. Photon correlation spectroscopy circumvents the difficulty for slowly moving atoms using frequency-selective two-photon absorption and photon coincidence detection of the two-photon decay.

DOI
10.1103/physreva.55.1358

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The spectroscopic detection of the excited-state resonances of a strongly coupled atom and optical cavity mode is complicated by inhomogeneous broadening, due to the variation of the dipole coupling constant with location in the cavity. Photon correlation spectroscopy circumvents the difficulty for slowly moving atoms using frequency-selective two-photon absorption and photon coincidence detection of the two-photon decay.
We show that photon coincidence spectroscopy can provide an unambiguous signature of two atoms simultaneously interacting with a quantized cavity field mode. We also show that the single-atom Jaynes—Cummings model can be probed effectively via photon coincidence spectroscopy, even with deleterious contributions to the signal from two-atom events. In addition, we have explicitly solved the eigenvectors and eigenvalues of two two-level atoms coupled to a quantized cavity mode for differing coupling strengths.
Summary form only given.The Jaynes-Cummings model (JCM) of a two-level atom interacting with a single mode of a high-finesse cavity in the strong-coupling regime forms the basis of studies in strong-coupling cavity quantum electrodynamics. Jaynes and Cummings demonstrated that the semiclassical model of radiation could account for the observed properties of the coupled atom-cavity system, and it has remained a challenge to observe the nonclassical features of the JCM, specifically those that reveal quantum entanglement between the atomic internal degrees of freedom and the single-mode cavity field. The key to observing nonclassical effects is to access the nonlinear regimen of the spectrum (beyond the first couplet of the JCM ladder). This has been accomplished in the microwave domain, but the optical domain presents difficulties that are not significant in the microwave experiments. Recently, the method of photon coincidence (or correlation) spectroscopy (PCS) has been proposed to overcome these difficulties and provide an experimental signature of the nonlinear regimen of the JCM spectrum. The atom is excited directly by a bichromatic laser field, and two-photon coincidence detection is performed on the cavity output field. Here we consider the complication that arises because the two-photon de-excitation is not instantaneous: the temporal separation between the two photons in the pair is random and of the order of the cavity lifetime. We also determine the optimal window time T for detecting photon pairs in order to maximize the number of genuine pairs while minimizing the number of false pairs. Our simulations, using a Bloch function expansion for solving the master equation, yield optimal values of T.
The strong coupling of atoms and molecules to radiation field modes in optical cavities creates dressed matter/field states known as polaritons with controllable dynamical and energy transfer properties. We propose a multidimensional optical spectroscopy technique for monitoring polariton dynamics. The response of a two-level atom to the time-dependent coupling to a single-cavity mode is monitored through time-and-frequency-resolved single-photon coincidence measurements of spontaneous emission. Polariton population and coherence dynamics and its variation with cavity photon number and controlled by gating parameters are predicted by solving the Jaynes-Cummings model.
When a single atom interacts with one mode of an optical cavity and the coupling to the cavity mode is sufficiently large, the spectroscopic response of the composite system to a weak probe is a doublet, with peaks located at the eigenfrequencies of the one-quantum excited states of the Jaynes–Cummings Hamiltonian. So far as these one-quantum states are concerned the spectroscopy of the Jaynes–Cummings model is the same as that of coupled, damped harmonic oscillators. This equivalence has been used to observe a doublet spectrum (the so-called "vacuum" Rabi splitting) by exciting a collective dipole oscillator inside an optical cavity.1,2 At higher levels of excitation the spectroscopy of the Jaynes–Cummings model differs markedly from that of coupled harmonic oscillators. Coupled harmonic oscillators give a doublet at all excitation levels; because of its noncommensurate excited state energies the Jaynes–Cummings model gives a multitude of additional peaks. In this paper we show how the excited states of the Jaynes–Cummings Hamiltonian can be probed by driving a cavity containing a single atom with broadband chaotic light. For a sufficiently large dipole coupling strength the spectrum of the light scattered out of the cavity mode shows peaks at the many resonance frequencies of the Jaynes–Cummings Hamiltonian. A similar multipeaked spectrum is seen in transmission. The spectrum of the light reflected from the cavity shows corresponding absorption dips superimposed on the broadband input.