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Physical Review Letters

Normal-Mode Line Shapes for Atoms in Standing-Wave Optical Resonators

James Childs, Kyungwon An, Michael S. Otteson, Ramachandra Rao Dasari, Michael S. Feld

Published Sep 30, 1996• 67 citations
Publisher

Abstract

A high finesse standing-wave cavity mode resonantly interacting with a beam of two-level ${}^{138}\mathrm{Ba}$ atoms is weakly driven by a tunable laser. Transmitted and sidelight scattered line shapes are recorded. With mean intracavity atomic number, $〈\overline{N}〉\ensuremath{\approx}1$, we observe one-, two-, and three-peaked line shapes for strong coupling. In addition, two-peaked spectra observed in intermediate coupling demonstrate that line-shape splitting is not necessarily indicative of oscillatory atom-cavity energy exchange. Several atoms are required for $〈\overline{N}〉\ensuremath{\approx}1$, so this is not a true single-atom regime.

DOI
10.1103/physrevlett.77.2901

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A high finesse standing-wave cavity mode resonantly interacting with a beam of two-level 138Ba{}^{138}\mathrm{Ba}138Ba atoms is weakly driven by a tunable laser. Transmitted and sidelight scattered line shapes are recorded. With mean intracavity atomic number, 〈N‾〉\ensuremath≈1〈\overline{N}〉\ensuremath{\approx}1〈N〉\ensuremath≈1, we observe one-, two-, and three-peaked line shapes for strong coupling. In addition, two-peaked spectra observed in intermediate coupling demonstrate that line-shape splitting is not necessarily indicative of oscillatory atom-cavity energy exchange. Several atoms are required for 〈N‾〉\ensuremath≈1〈\overline{N}〉\ensuremath{\approx}1〈N〉\ensuremath≈1, so this is not a true single-atom regime.
Summary form only given. We report on the observation of the many-atom dipole-dipole interaction in an ensemble of ultracold rubidium atoms strongly coupled to the standing-wave field of a weakly driven high-finesse optical cavity. The atoms split the cavity resonance into two normal modes. The many-atom light force changes the spatial distribution of the atoms, creating an asymmetry in the usually symmetric normal-mode spectrum, for intracavity photon numbers much less than one. This asymmetry is investigated as a function of the number of atoms and as a function of the intracavity photon number. Moreover, analytical expressions have been derived for the dipole force and the diffusion coefficient for an atom in presence of other atoms. These expressions allow us to simulate the trajectories of several atoms simultaneously. The calculated and measured spectra agree only if the full motional dynamics of all atoms is taken into account.
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.
We study the optomechanical interaction of a Bose–Einstein condensate with a single longitudinal mode of an ultra-high finesse standing wave optical resonator. As a unique feature the resonator combines three extreme regimes, previously not realized together, i.e., strong cooperative coupling, cavity dominated scattering with a Purcell factor far above unity, and sub-recoil resolution provided by a cavity damping rate smaller than four times the single photon recoil frequency. We present experimental observations in good agreement with a two-mode model predicting highly nonlinear dynamics with signatures as bistability, hysteresis, persistent oscillations, and superradiant back-scattering instabilities.
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.