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Physical Review Letters

Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity

Mark G. Raizen, Robert J. Thompson, Robert J. Brecha, Harry J. Kimble, H. J. Carmichael

Published Jul 17, 1989• 468 citations
Publisher

Abstract

An investigation of the radiative processes for a collection of N two-state atoms strongly coupled to the field of a high-finesse optical cavity is presented. Observations of the spectral response of the composite system to weak external modulation reveal a coupling-induced normal-mode splitting. Linewidth averaging leads to linewidths below the free-space atomic width.

DOI
10.1103/physrevlett.63.240

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The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.

Nonlinear Dynamics in Optical Systems•Jan 1, 1990•4 citations
An investigation of the radiative processes for a collection of N two-state atoms strongly coupled to the field of a high-finesse optical cavity is presented. Observations of the spectral response of the composite system to weak external modulation reveal a coupling-induced normal-mode splitting. Linewidth averaging leads to linewidths below the free-space atomic width.
Experimental and theoretical investigations of the radiative processes of a collection of two-state atoms contained in a high-finesse optical cavity are reported. To make contact with previous work on this subject, we consider the usual regimens in which either the cavity or the atomic damping is dominant. However, of greater interest and relevance to our experiments is the regime of strong coupling that generates splittings and new features in the normal-mode structure of the composite atom-field system. We identify possible mechanisms for producing line shapes with subnatural linewidths. Our experimental investigations are conducted with two-state sodium atoms that interact with a single mode of an ultra-high-finesse optical cavity. The incoherent spectral density of the transmitted field is detected by optical heterodyne. We obtain good qualitative agreement between theory and experiment for the general features of the composite atom-field system as manifested in the spectral density of the transmitted field. Experiments to probe the response of the system to weak modulation of the incident field are in progress.
Investigations of the radiative processes for the composite system of N two-state atoms coupled to the field of a high finesse optical cavity are reported. In an experiment employing an atomic beam of optically prepared sodium atoms (3S1/2, F = 2, mF = 2 → 3P3/2, F = 3, mF = 3 transition at 589 nm), we make direct spectroscopic measurements of the normal mode splitting for the coupled oscillator system of atoms and cavity field over a 20 ≤ N ≤ 600 range. Linewidth reduction below the atomic free-space width is observed and results from dynamic linewidth averaging due to the strong coherent interaction of atoms and cavity. The dependence of the normalmode structure on atom-cavity detuning is explored, and the decoupling of the system with detuning is described. A second experimental program employs a cesium atomic beam (6S1/2, F = 4, mF = 4 → 6P3/2, F = 5, mF = 5 transition at 852 nm), for which the single-atom coupling coefficient can be made larger than the free-space atomic and cavity damping rates. Our initial efforts are directed both toward the investigation of the spectroscopic properties of this system and toward the observation of photon antibunching for the field transmitted from the cavity. More generally our measurements of intensity correlations can be applied to the problem of continuous quantum measurement for a dissipative system.
We calculate the spontaneous-emission spectrum and the spectrum of weakly driven fluorescence for a two-level atom coupled to a resonant-cavity mode. For strong atom-cavity coupling the spectra split into two peaks that can have subnatural linewidths. If the cavity linewidth is negligible, the spontaneous-emission spectrum has half the radiative linewidth of the atom; the spectrum of weakly driven fluorescence shows an additional 36% squeezing-induced narrowing. These effects can be observed using coupled-field and collective-polarization oscillators excited in a cavity containing N two-level atoms.
Of fundamental importance in quantum optics has been the investigation of the radiative coupling of a collection of atoms to the field of a resonant cavity1. Within this context we are conducting a research program to investigate the interaction of optically prepared two-state atoms with the fields of high finesse optical cavities. With regard to our specific observations, we have employed a sodium atomic beam apparatus to make direct spectroscopic measurements of the normal-mode splitting for the coupled oscillator system formed by the collective atomic polarization of N two-state atoms and a single mode of a resonator of finesse of approximately 2x10⁴. At the transition wavelength of 589 nm (³, S_(1/2), F = 2, m_F = 2→3 P_(3/2), m_F = 3 and for one of our spherical mirror standing-wave cavities, the relevant parameters for the system are as follows: transverse atomic decay rate γ_⊥ = 2πX5X10⁶/S, cavity damping rate K/γ⊥= 0.18, and single-atom coupling coefficient g/γ_⊥ = 0.2.
The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.