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Faraday Discussions

Self-organisation and cooling of a large ensemble of particles in optical cavities

Yongkai Zhao, Weiping Lu, P. F. Barker, Guangjiong Dong

Published Jan 1, 2009• 5 citations
Publisher

Abstract

We present an investigation of the dynamics of centre-of-mass of a neutral particle cloud in a cavity pumped by an optical field. We derive an expression for the pump threshold for spatial self-organization of the particles and analyze its scaling laws in terms of the system parameters. Using a newly developed statistical model, we simulate the dynamics of the particles and numerically obtain the scaling laws. We show good agreement between the analytic formulae and simulations. We further use the scaling relation to discuss the operating conditions for cavity cooling a large ensemble of particles. Finally, we study cavity cooling of an ensemble of molecules with an initial temperature of around 10 mK. We show that 35% of the molecules are trapped by the optical field intensity in the cavity and a final temperature below 1 mK is reached.

DOI
10.1039/b818653g

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We present an investigation of the dynamics of centre-of-mass of a neutral particle cloud in a cavity pumped by an optical field. We derive an expression for the pump threshold for spatial self-organization of the particles and analyze its scaling laws in terms of the system parameters. Using a newly developed statistical model, we simulate the dynamics of the particles and numerically obtain the scaling laws. We show good agreement between the analytic formulae and simulations. We further use the scaling relation to discuss the operating conditions for cavity cooling a large ensemble of particles. Finally, we study cavity cooling of an ensemble of molecules with an initial temperature of around 10 mK. We show that 35% of the molecules are trapped by the optical field intensity in the cavity and a final temperature below 1 mK is reached.
The ability to cool and trap atoms has revolutionized atomic and ultra-cold physics. Molecular physics is currently undergoing a similar transformation. This thesis aims to research a general cooling method that will be applicable to wide range of molecular and atomic species and other particles. We studied the dynamics of molecules in optical fields, focusing in particular on exploring the molecular self-organisation phenomena in optical cavities to cool molecular ensembles to sub-mK temperatures. Firstly, the general model of cavity cooling from atoms to molecules and the dynamics of a particle in a single cavity mode were discussed. We extended the existing cooling scheme for two-level atoms to an ensemble of multi-level molecules. Then we studied the spatial dynamics of molecules in the new parameter conditions, focusing in particular on exploring the molecular self-organisation phenomena in optical cavities to cool molecular ensembles to sub-mK temperatures. The scheme complements well with our present experimental work on the deceleration and focusing of cold molecules and can extend our present capability to simultaneously cool and trap a large cold molecular ensemble. For simulation of a large ensemble of molecules, we proposed a new statistical model based on the Boltzmann equation beside the traditional discrete model and studied two solution methods. The comparison of the theory and numerical simulations between discrete model and statistical model showed a good agreement, which validated this new model. We then explored the scaling laws with a view to the self-organization and cooling of a large ensemble of species. We studied the cooling of a CN molecular cloud of the density 10/cm, with an initial temperature at 10 mK in an optical cavity. We found that more than a third of the molecules are stably trapped by the intracavity field and the final temperature is below 1mK. We discussed the scaling laws in the case when a large ensemble of species is involved. Finally we argue that cavity cooling using a far
We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on a laboratory time scale, a hysteresis masks the mean-field behavior. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of ``defects'' appear in the organized phase and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase-space density with the atom number is also studied.
We have studied theoretically and numerically the cooling of CN molecules in a high-finesse optical cavity and show that these molecules can be cooled from 100 mK temperatures to submillikelvin temperatures in less than 1 ms. We establish that the cooling time does not change significantly with molecular numbers and initial temperatures over a wide range. We have further studied the scaling of the system for extending the current results for hundreds of molecules to a very large molecular ensemble. The results indicate that a gas of 109 molecules can be cooled in the cavity by use of a far-off-resonant and high-intensity pump source. © 2007 The American Physical Society.
We show that an ensemble of two-level atoms commonly coupled to a single, driven, damped high-QQQ cavity mode could be cooled and trapped via the correlated dynamics of cavity field and the atomic motion. For sufficiently large detuning between the atoms and the field, spontaneous emission plays no role in the dynamics, and the cooling scheme can be applied to all particles with a sufficient optical dipole moment. The time scale of this collective cooling process increases with the particle number and can be optimized by suitably tailoring the pump field amplitude and frequency. The key properties of the underlying mechanism are discussed using a linearized model, where one can derive a closed set of equations for certain ensemble averages and the field. The results are then compared with N-particle dynamical simulations of the full equations.
We discuss a scheme to cool, trap and manipulate an ensemble of polarizable particles moving in the field of a multimode optical cavity via the correlated dynamics of the field and the particle motion. Using a large detuning between the atoms and the field, spontaneous emission plays a negligible role in the dynamics and the cooling scheme only requires a sufficiently large optical dipole moment. Increasing the particle number slows down the cooling process but it can be accelerated using an increasing number of field modes with higher pump amplitudes. For the special case of a two mode ring cavity and assuming small deviations of the particle positions from the potential minima, the frequencies and damping rates of the vibrational excitation modes can be explicitly calculated. We find a rapid damping of the centre-of-mass motion and relatively slow damping rates for the relative particle oscillations. These predictions agree quite well with a quantum treatment of the atomic motion as used for the excitations of a non-interacting Bose gas (at T = 0) inside the cavity field. Due to the position-dependent mode coupling, the cooling process in a multimode configuration in general happens much faster than for a standing wave geometry. These analytical results are confirmed by N-particle simulations of the semiclassical equations and show even enhanced damping due to the anharmonicity of the full potential.