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arXiv:physics/0511239 · Physical Review A

Coupled dynamics of atoms and radiation-pressure-driven interferometers

D. Meiser, Pierre Meystre

Published Mar 21, 2006• 67 citations
arXivHTMLPDF

Abstract

We consider the motion of the end mirror of a cavity in whose standing-wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this back action of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the back action of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the sideband spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.

DOI
10.1103/physreva.73.033417

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We consider the motion of the end mirror of a cavity in whose standing-wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this back action of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the back action of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the sideband spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.
We consider the dynamics of a movable mirror (cantilever) of a cavity coupled through radiation pressure to the light scattered from ultracold atoms in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the displacement spectrum of the cantilever. We show that for large pump intensities the steady-state displacement of the cantilever shows bistable behavior. Due to atomic back action, the displacement spectrum of the cantilever is modified and depends on the position of the condensate in the Brillouin zone. We further analyze the occurrence of splitting of the normal mode into three modes due to mixing of the mechanical motion with the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction.
In two recent articles, Meiser and Meystre describe the coupled dynamics of a dense gas of atoms and an optical cavity pumped by a laser field. They make two important simplifying assumptions: (i) the gas of atoms forms a regular lattice and can be replaced by a fictitious mirror, and (ii) the atoms strive to minimize the dipole potential. We show that the two assumptions are inconsistent: the configuration of atoms minimizing the dipole potential is not a perfect lattice. Assumption (ii) is erroneous, as in the strong coupling regime the dipole force does not arise from the dipole potential. The real steady state, where the dipole forces vanish, is indeed a regular lattice. Furthermore, the bistability predicted by Meiser and Meystre does not occur in this system.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.
In two recent articles [D. Meiser and P. Meystre, Phys. Rev. A 73, 033417 (2006); 74, 065801 (2006)], Meiser and Meystre describe the coupled dynamics of a dense gas of atoms and an optical cavity pumped by a laser field. They make two important simplifying assumptions: (i) The gas of atoms forms a regular lattice and can be replaced by a fictitious mirror and (ii) the atoms strive to minimize the dipole potential. We show that the two assumptions are inconsistent: The configuration of atoms minimizing the dipole potential is not a perfect lattice. Assumption (ii) is erroneous, as in the strong coupling regime the dipole force does not arise from the dipole potential. The real steady state, where the dipole forces vanish, is indeed a regular lattice. Furthermore, the bistability predicted by Meiser and Meystre does not occur in this system.
We study the collective motion of atoms confined in an optical lattice operating inside a high-finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the linewidth of the cavity resonance, the otherwise tiny retroaction of the atoms upon the light field becomes a significant feature of the system. As a result dispersive optical bistability can arise and the lattice positions is determined by the strength of the atom-cavity coupling rather than by the phases of the incoupled light beams. Solving the complete set of classical equations of motion confirms these findings, however, additional nonadiabatic phenomena are predicted, such as, for example, self-induced radial breathing oscillations. We compare these results with experiments involving laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms trapped in an optical lattice inside a ring cavity with a finesse of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$. Our observations are in excellent agreement with our theoretical predictions.
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.