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arXiv:quant-ph/0702053 · Physical Review A

Resonance fluorescence of a cold atom in a high-finesse resonator

Marc Bienert, Juan Mauricio Torres, Stefano Zippilli, Giovanna Morigi

Published Jul 19, 2007• 15 citations
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Abstract

We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity fields. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser fields lead to the selective suppression of features of the resonance fluorescence spectrum, which are otherwise visible in the spectrum of laser-cooled atoms in free space.

DOI
10.1103/physreva.76.013410

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We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity fields. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser fields lead to the selective suppression of features of the resonance fluorescence spectrum, which are otherwise visible in the spectrum of laser-cooled atoms in free space.
In this poster we characterize the cooling dynamics of atoms confined by an external potential in a high-Q cavity, when the width of the atomic wave packet is much smaller than the field wave-length. Its form allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. In particular, parameter regimes are identified where the dynamics is characterized by quantum interference between the mechanical effects of the laser and of the resonator fields, which selectively enhance the cooling transitions and thus the efficiency. In this regime we characterize the state of the system by the spectrum of the intensity of the light scattered by the atom and at the cavity output, when atom and cavity are at steady state of the cooling dynamics. We evaluate the spectrum by implementing the model of M. Bienert et al., (2006) to atoms inside resonators. We find that, in some cases, quantum interference effects lead to the suppression of features of the resonance fluorescence spectrum, which are otherwise visible in the spectrum of atoms in free space.
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict that, in particular, for high cooperativities, interference effects mediated by the atomic transition may lead to higher efficiencies. The dynamics is compared with the cooling dynamics of a trapped atom inside a resonator studied by Zippilli and Morigi [Phys. Rev. Lett. 95, 143001 (2005)] where the atom, instead of the cavity, is driven by a laser field.
We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\ensuremath{\Lambda}$ shaped and driven at two-photon resonance by a pair of lasers, which cool the center-of-mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb-Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second-order perturbation theory. We find that the spectrum of resonance fluorescence is composed of two narrow sidebands---the Stokes and anti-Stokes components of the scattered light---while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow-type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behavior of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two levels.
We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics is a competition of the mechanical effects of the cavity and of the laser photons, which may mutually interfere. We focus on the good-cavity limit and identify novel cooling schemes, which are based on quantum interference effects and lead to efficient ground-state cooling in experimentally accessible parameter regimes.
In this thesis we investigate the dynamics of cold atoms in optical cavities. We study how the scattering properties of laser driven atoms are modified by the presence of an optical resonator. This investigation can be divided into two parts. First, we study the scaling of the scattering properties with the number of atoms, and we show in particular how Bragg scattering by an atomic lattice is modified by the presence of the resonator. In this case, the atoms are trapped at the antinodes of the cavity mode function by the mechanical potential induced by the resonator. In a second part, we show how this modification of the scattering properties can be used for efficiently cooling single atoms to the ground state of a harmonic trap. In particular, we find that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.