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Physical Review A

Simultaneous cooling and trapping of atoms by a single cavity-field mode

András Vukics, P. Domokos

Published Sep 6, 2005• 25 citations
Publisher

Abstract

The optical dipole trap scheme is generalized by considering the laser as a dynamical cavity field mode. For a large enough finesse, the far-detuned trapping field itself exerts a significant friction force on the atom. Unlike in free-space far-off resonance dipole traps, here the trapping is stable in the steady state. The scheme in principle applies to arbitrary linearly polarizable particles, e.g., molecules.

DOI
10.1103/physreva.72.031401

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The optical dipole trap scheme is generalized by considering the laser as a dynamical cavity field mode. For a large enough finesse, the far-detuned trapping field itself exerts a significant friction force on the atom. Unlike in free-space far-off resonance dipole traps, here the trapping is stable in the steady state. The scheme in principle applies to arbitrary linearly polarizable particles, e.g., molecules.
Cooling and trapping of atoms with light provides us with samples far colder and denser than possible by any other means and enables us to study and control these systems in exquisite detail [1]. We can not only learn about these systems, but can devise experiments of such precision that we test the underlying physics. It is unfortunate therefore that the most effective techniques, Doppler cooling and the Magneto Optical Trap, rely on a simple energy level structure found only in a handful of elements. Finally, I will present an approach in which a particle can be cooled using the dipole, rather than the scattering, force. The dipole force is conservative, but by allowing the potential to vary in time, one can change the energy of a trapped particle. Specifically, if the potential depends on the position of the particle with some time delay, we can create a friction-like force [5, 6], and we are currently building an experiment to demonstrate this effect. This technique is not restricted to atoms with a simple structure, but requires only that the particle be polarisable; in principle, therefore, it can be extended without significant change to direct optical cooling of molecules.
The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.
By integrating the techniques of laser cooling and trapping with those of cavity quantum electrodynamics (QED), single cesium atoms have been trapped within the mode of a small, high finesse optical cavity in a regime of strong coupling. The observed lifetime for individual atoms trapped within the cavity mode is $\ensuremath{\tau}\ensuremath{\approx}28\mathrm{ms}$, and is limited by fluctuations of light forces arising from the far-detuned intracavity field. This initial realization of trapped atoms in cavity QED should enable diverse protocols in quantum information science.
A robust scheme for trapping and cooling atoms is described. It combines a deep dipole-trap which localizes the atom in the center of a cavity with a laser directly exciting the atom. In that way one obtains three-dimensional cooling while the atom is dipole-trapped. In particular, we identify a cooling force along the large spatial modulations of the trap. A feature of this setup, with respect to a dipole trap alone, is that all cooling forces keep a constant amplitude if the trap depth is increased simultaneously with the intensity of the probe laser. No strong coupling is required, which makes such a technique experimentally attractive. Several analytical expressions for the cooling forces and heating rates are derived and interpreted by analogy to ordinary laser cooling.
The dipole force, which avoids the closed cycle of pumping and spontaneous emission that renders laser cooling unsuitable for molecules, is conservative: without dissipation, particles entering a trap retain the energy to escape. Fortunately, dissipation need not involve spontaneous emission if it instead results from the decoherence or decay of the optical trapping field that is coupled to the particle. To enhance the weak attraction of an atom to its reflection, cavity-mediated cooling recycles light through multiple reflections, amplifying the force and the retardation - a process related to the mechanical amplification in a near confocal cavity [5]. Resonant cavities and structures can increase the retardation, but not the intensity, even when the atoms or particles lie outside them - e.g. when the cavity is the narrow-band coating of a single mirror. Plasmon resonances of a structured metal can enhance both the delay and the optical intensity. Such processes, possible with arrays of micromirrors, resemble speckle field cooling [6], except that spontaneous emission is again replaced by decay of the optical field, and offer a new class of cooling mechanisms in which weak cooling is extended over a broad array, rather than concentrated at the centre of a single external cavity.
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.