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arXiv:1607.02362 · Nature Communications

Observing coherence effects in an overdamped quantum system

Yu-Hung Lien, Giovanni Barontini, Michael Scheucher, Matthias Mergenthaler, J. Goldwin, Edward A. Hinds

Published Dec 21, 2016• 32 citations
arXivHTMLPDF

Abstract

It is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal-mode splitting unless the system satisfies the strong coupling condition, meaning the Rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations. Here we show that this need not be the case, but depends on the way in which the coupled system is probed. Measurements of the reflection of a probe laser from the input mirror of an overdamped cavity reveal an avoided crossing in the spectrum that is not observed when driving the atoms directly and measuring the Purcell-enhanced cavity emission. We understand these observations by noting a formal correspondence with electromagnetically induced transparency of a three-level atom in free space, where our cavity acts as the absorbing medium and the coupled atoms play the role of the control field.

DOI
10.1038/ncomms13933

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It is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal-mode splitting unless the system satisfies the strong coupling condition, meaning the Rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations. Here we show that this need not be the case, but depends on the way in which the coupled system is probed. Measurements of the reflection of a probe laser from the input mirror of an overdamped cavity reveal an avoided crossing in the spectrum that is not observed when driving the atoms directly and measuring the Purcell-enhanced cavity emission. We understand these observations by noting a formal correspondence with electromagnetically induced transparency of a three-level atom in free space, where our cavity acts as the absorbing medium and the coupled atoms play the role of the control field.
We study atomic coherence and interference in four-level atoms confined in an optical cavity and explores the interplay between cavity QED and electromagnetically induced transparency (EIT). The destructive interference can be induced in the coupled cavity-atom system with a free-space control laser tuned to the normal mode resonance and leads to suppression of the normal mode excitation. Then by adding a pump laser coupled to the four-level atoms from free space, the control-laser induced destructive interference can be reversed and the normal mode excitation is restored. When the free-space control laser is tuned to the atomic resonance and forms a Λ-type EIT configuration with the cavity-atom system, EIT is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. With the free-space pump laser driving the cavity-confined atoms in a four-level configuration, the narrow transmission peak of the cavity EIT can be split into two peaks and the dressed intra-cavity dark states are created analogous to the dressed states in free space. We report experimental studies of such coherently coupled cavity-atom system realized with cold Rb atoms confined in an optical cavity and discuss possible applications in quantum nonlinear optics and quantum information science.
Summary form only given. We consider a single two-level atom inside a resonant optical cavity, with cavity loss rate K, atomic fluorescence rate into noncavity modes A, and atom-field coupling g. For large atom cavity coupling (g>A, K) and weak driving fields, the fluorescence from this system exhibits a splitting of the spectral line, known as vacuum-Rabi splitting. When the cavity loss rate is the largest rate in the problem (K>A, g), the fluorescent spectrum is Lorentzian with a cavity-enhanced width. We examine the regime where A>g>K, and find that the spectrum exhibits a hole at line center as a result of quantum interference effects. This effect is formally identical to the phenomenon of electromagnetically induced transparency (EIT) in multilevel atomic systems. We discuss the relationship of these spectral holes to the presence of squeezing in the intracavity field, and present results also for the emission spectra, and incoherent spectra in transmission and fluorescence.
Between mirrors, the density of electromagnetic modes differs from the one in free space. This changes the radiation properties of an atom as well as the light forces acting on an atom. It has profound consequences in the strong-coupling regime of cavity quantum electrodynamics. For a single atom trapped inside the cavity, we investigate the atom-cavity system by scanning the frequency of a probe laser for various atom-cavity detunings. The avoided crossing between atom and cavity resonance is visible in the transmission of the cavity. It is also visible in the loss rate of the atom from the intracavity dipole trap. On the normal-mode resonances, the dominant contribution to the loss rate originates from dipole-force fluctuations which are dramatically enhanced in the cavity. This conclusion is supported by Monte-Carlo simulations.
When a coherently prepared atomic medium is confined in an optical cavity, the atomic coherence and interference manifested by electromagnetically induced transparency (EIT) can be manipulated and enhanced by the collective atom–cavity coupling and the cavity feedback. We present an experimental study of the light transmission through an optical cavity coupled with coherently prepared cold Rb atoms. In the frequency domain, the cavity transmission spectrum exhibits spectral peaks representing the cavity normal modes associated with the multi-atom vacuum Rabi splitting and the intra-cavity dark state manifested by the combined EIT effects of the absorption suppression and the steep normal dispersion. In the time domain, a light pulse coupled into the cavity mode propagates with a slow group velocity and the propagation time delay is significantly increased by the cavity feedback.
Between mirrors, the density of electromagnetic modes differs from the one in free space. This changes the radiation properties of an atom as well as the light forces acting on an atom. It has profound consequences in the strong-coupling regime of cavity quantum electrodynamics. For a single atom trapped inside the cavity, we investigate the atom–cavity system by scanning the frequency of a probe laser for various atom–cavity detunings. The avoided crossing between atom and cavity resonance is visible in the transmission of the cavity. It is also visible in the loss rate of the atom from the intracavity dipole trap. On the normal-mode resonances, the dominant contribution to the loss rate originates from dipole-force fluctuations which are dramatically enhanced in the cavity. This conclusion is supported by Monte Carlo simulations.
We have shown that an ultranarrow dark region can be associated with the feature of significant amount of vaccuum-Rabi splitting in the absorption spectrum of a weak coherent field probing a two-level atom strongly coupled to two degenerate cavity-modes with preselected polarizations. The cavity-induced transparency is produced by the decay-interference of the two independent cavity modes interacting with the same reservoir. It has been shown that the resonant probe transparency is independent of the individual decay rates of the cavity modes. The present model exhibits the possibility of obtaining the narrow dark transparency associated with the significant amount of Rabi splitting in the absorption spectrum with the appreciable value of the cavity-losses.