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Physical Review Letters

Dynamics of Single-Atom Motion Observed in a High-Finesse Cavity

P. Münstermann, Thomas H. Fischer, Peter Maunz, Pepijn W. H. Pinkse, Gerhard Rempe

Published May 10, 1999• 174 citations
Publisher

Abstract

We investigate mechanical forces on single atoms in a high-finesse optical cavity containing less than one photon on average. We count the number of atoms strongly coupled to the cavity mode close to an antinode and measure the intensity autocorrelation function of the pump light transmitted through the cavity. Distinct features are observed and attributed to the dipole force, diffusion, and velocity-dependent force, as predicted by the work of Horak et al. Our data agree well with the results of a Monte Carlo simulation.

DOI
10.1103/physrevlett.82.3791

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We investigate mechanical forces on single atoms in a high-finesse optical cavity containing less than one photon on average. We count the number of atoms strongly coupled to the cavity mode close to an antinode and measure the intensity autocorrelation function of the pump light transmitted through the cavity. Distinct features are observed and attributed to the dipole force, diffusion, and velocity-dependent force, as predicted by the work of Horak et al. Our data agree well with the results of a Monte Carlo simulation.
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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.
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000); Pinkse et al., Nature (London) 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.
Summary form only given. We observe the quantized motion of single atoms strongly coupled to a high-finesse optical cavity and investigate dynamics of cavity-assisted atom cooling. Single caesium atoms are trapped in a blue-detuned standing-wave intracavity dipole trap, formed by a lock laser which is used to stabilize the cavity resonance frequency. A probe laser is coupled into the cavity mode and its transmission spectrum is monitored by means of photon-counting heterodyne spectroscopy [2].Measured heterodyne spectra of single atoms in the cavity are shown in Fig. 1 for two different lock-laser intensities and compared with theoretical models. The motional Raman sidebands are offset from the carrier beat signal at 1 MHz by the atomic vibrational frequency (±ν). They show asymmetric lineshapes due to the anharmonicity of the dipole potential.We investigate the dependence of the positions and lineshapes of the motional Raman sidebands on experimantal parameters such as the cavity-atom detuning, and lock-laser intensity. Information on the atomic temperature, cooling and heating rates, as well as the atomic position in the cavity with respect to an antinode of the cavity probe field are found by comparing the observed spectra with theoretical predictions [1]. In addition, this technique can also be used to analyze the cooling dynamics of a cavity-assisted EIT cooling scheme which has been recently studied and demonstrated in [3,4].