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arXiv:quant-ph/0312129 · Physical Review A

Correlated motion of two atoms trapped in a single-mode cavity field

János K. Asbóth, P. Domokos, Helmut Ritsch

Published Jul 29, 2004• 45 citations
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Abstract

We study the motion of two atoms trapped at distant positions in the field of a driven standing-wave high-$Q$ optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a $90\ifmmode^\circ\else\textdegree\fi{}$ relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The physical origin of the correlation can be traced back to a cavity mediated crossfriction, i.e., a friction force on one particle depending on the velocity of the second particle. Choosing appropriate operating conditions allows for engineering these long range correlations. In addition this cross-friction effect can provide a basis for sympathetic cooling of distant trapped clouds.

DOI
10.1103/physreva.70.013414

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We study the motion of two atoms trapped at distant positions in the field of a driven standing-wave high-QQQ optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a 90\ifmmode∘\else\textdegree\fi90\ifmmode^\circ\else\textdegree\fi{}90\ifmmode∘\else\textdegree\fi relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The physical origin of the correlation can be traced back to a cavity mediated crossfriction, i.e., a friction force on one particle depending on the velocity of the second particle. Choosing appropriate operating conditions allows for engineering these long range correlations. In addition this cross-friction effect can provide a basis for sympathetic cooling of distant trapped clouds.
We review the modifications and implications of the effect of light forces on atoms when the field is enclosed in an optical resonator of high finesse. The systems considered range from a single atom strongly coupled to a single mode of a high-Q microcavity to a large ensemble of atoms in a highly degenerate quasi-confocal resonator. We set up general models that allow us to obtain analytic expressions for the optical potential, friction, and diffusion. In the bad-cavity limit the modified cooling properties can be attributed to the spectral modifications of light absorption and spontaneous emission in a form of generalized and enhanced Doppler cooling. For the strong coupling regime in a good cavity, we identify the dynamical coupling between the light field intensity and the atomic motion as the central mechanism underlying the cavity-induced cooling. The dynamical cavity cooling, which does not rely on spontaneous emission, can be enhanced by multimode cavity geometries because of the effect of coherent photon redistribution between different modes. The model is then generalized to include several distinct frequencies to account for more general trap geometries. Finally we show that the field-induced buildup of correlations between the motion of different particles plays a central role in the scaling behavior of the system. Depending on the geometry and parameters, its effect ranges from strong destructive interference, slowing down the cooling process, to self-organized crystallization, implying atomic self-trapping and faster cooling to lower temperatures by cooperative coherent scattering.
We investigate the coupled dynamics of N two-level atoms in the field of a weakly pumped multimode high-Q cavity. While the field mode amplitudes are coupled by the atoms depending on their positions, the motion of the atoms is influenced by the radiation pressure and dipole force induced by the total intracavity field. In the strong coupling regime, where the atom field coupling g dominates the atomic and cavity decay rates (\ensuremath{\Gamma}, \ensuremath{\kappa}) strong correlations between the atoms themselves and between the atoms and the light field build up. For suitable operating conditions an efficient motional cooling of the atoms occurs. At the example of two atoms coupled to two counterpropagating modes in a ring cavity, we show that this can lead to a strong binding force between atoms trapped at a large distance at different antinodes of the cavity field.
We investigate the external and internal dynamics of a two-level atom in a standing wave cavity. In the strong coupling regime, where the atom field coupling ggg dominates the atomic and cavity decay rates (\ensuremath{\Gamma},\ensuremath{\kappa}), a cooling mechanism entirely different from free-space Doppler cooling appears. Under suitable operating conditions, the cavity dynamics induces a Sisyphus type cooling, which is the dominant contribution to the total friction force acting on a moving atom. Simple equations describing the key properties of this effect are derived from a completely classical picture and confirmed by a semiclassical approach. The model is investigated in the bad and good cavity limits, and analytic expressions for the friction coefficient and the momentum diffusion for slow atoms are derived. Using a continued fractions expansion the cooling force for arbitrary velocities is evaluated numerically. The result is used to calculate the equilibrium temperatures of the atom of the order of $\mathrm{kT}\ensuremath{\approx}\ensuremath{\Elzxh}\ensuremath{\kappa},$ which can be much lower than the free-space Doppler limit and agree well to those obtained by quantum wave-function simulations.
The motion of two distant trapped particles or mechanical oscillators can be strongly coupled by light modes in a high finesse optical resonator. In a two mode ring cavity geometry, trapping, cooling and coupling is implemented by the same modes. While the cosine mode provides for trapping, the sine mode facilitates ground state cooling and mediates non-local interactions. For classical point particles the centre-of-mass mode is strongly damped and the individual momenta get anti-correlated. Surprisingly, quantum fluctuations induce the opposite effect of positively-correlated particle motion, which close to zero temperature generates entanglement. The non-classical correlations and entanglement are dissipation-induced and particularly strong after detection of a scattered photon in the sine mode. This allows for heralded entanglement by post-selection. Entanglement is concurrent with squeezing of the particle distance and relative momenta, while the centre-of-mass observables acquire larger uncertainties.
The motion of two distant trapped particles or mechanical oscillators can be strongly coupled by light modes in a high finesse optical resonator. In a two mode ring cavity geometry, trapping, cooling and coupling is implemented by the same modes. While the cosine mode provides for trapping, the sine mode facilitates ground state cooling and mediates non-local interactions. For classical point particles the centre-of-mass mode is strongly damped and the individual momenta get anti-correlated. Surprisingly, quantum fluctuations induce the opposite effect of positively-correlated particle motion, which close to zero temperature generates entanglement. The non-classical correlations and entanglement are dissipation-induced and particularly strong after detection of a scattered photon in the sine mode. This allows for heralded entanglement by post-selection. Entanglement is concurrent with squeezing of the particle distance and relative momenta, while the centre-of-mass observables acquire larger uncertainties.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.