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arXiv:quant-ph/0412100 · Brazilian Journal of Physics

Cooling many particles to very low temperatures

Almut Beige, P. L. Knight, Giuseppe Vitiello

Published Jun 1, 2005• 2 citations
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Abstract

In a recent paper [Beige, Knight, and Vitiello, quant-ph/0404160], we showed that a large number N of particles can be cooled very efficiently. The particles should be excited by red-detuned laser fields while coupling to the quantized field mode inside a resonant and leaky optical cavity. When the coupling constants are for all particles the same, a collective behavior can be generated and the cooling rate can be as large as << times the single-particle coupling constants. Here we study the algebraic structure of the dynamics and the origin of the collective cooling process in detail.

DOI
10.1590/s0103-97332005000300007

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In a recent paper [Beige, Knight, and Vitiello, quant-ph/0404160], we showed that a large number N of particles can be cooled very efficiently. The particles should be excited by red-detuned laser fields while coupling to the quantized field mode inside a resonant and leaky optical cavity. When the coupling constants are for all particles the same, a collective behavior can be generated and the cooling rate can be as large as << times the single-particle coupling constants. Here we study the algebraic structure of the dynamics and the origin of the collective cooling process in detail.
We propose a mechanism for the collective cooling of a large number N of trapped particles to very low temperatures by applying red-detuned laser fields and coupling them to the quantized field inside an optical resonator. The dynamics is described by what appears to be rate equations, but where some of the major quantities are coherences and not populations. The cooperative behaviour of the system provides cooling rates of the same order of magnitude as the cavity decay rate κ. This constitutes a significant speed-up compared to other cooling mechanisms since κ can, in principle, be as large as times the single-particle cavity or laser coupling constant.
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 point out a laser cooling method for atoms, molecules, or ions at low saturation and large detuning from the particles' resonances. The moving particle modifies the field inside a cavity with a time delay characteristic of the cavity linewidth, while the field acts on the particle via the light shift. The dissipative mechanism can be interpreted as Doppler cooling based on preferential scattering rather than preferential absorption. It depends on particle properties only through the coherent scattering rate, opening new possibilities for optically cooling molecules or interacting atoms.
We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling-time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling-time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally, it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.
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.
In this paper, we identify a quantum coherence with the ability to induce collective dynamics in an atomic gas, when a cooling laser is applied. When present, the mean phonon number per particle changes at a rate, which is proportional to the total number of particles in the system. We then propose to use this effect to cool atoms in a cyclic two-stage process to very low temperatures. During each displacement stage, the atoms move freely inside an asymmetric trapping potential, thereby accumulating away from its centre. During each cooling stage, a cooling laser is applied, which returns the atoms to the centre of the trap, while decreasing their mean phonon number. Alternating both stages is shown to transfer the atoms to a final temperature, which vanishes in the infinitely-many particle limit.