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Physical Review A

Cavity-mediated dark-state cooling without spontaneous emission

Markus Gangl, Helmut Ritsch

Published Nov 19, 2001• 11 citations
Publisher

Abstract

We extend the concept of dark state cooling to enclose the fields in a high-$Q$ resonator. Choosing a sufficiently large detuning between the atomic transition and the driving fields, spontaneous emission during the cooling process is largely suppressed and the energy dissipation occurs dominantly via cavity decay. For a ring cavity with two degenerate counterpropagating waves of opposite circular polarization, the final dark state is identical as in free space. However, we find a strong cavity mediated force with a large capture range as a precooling mechanism. In this scheme spontaneous emission is only important for the final jump to the dark state in the dynamics and the reabsorption problem is strongly reduced. In principle the scheme could also be applied to molecules with a suitable transition.

DOI
10.1103/physreva.64.063414

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We extend the concept of dark state cooling to enclose the fields in a high-QQQ resonator. Choosing a sufficiently large detuning between the atomic transition and the driving fields, spontaneous emission during the cooling process is largely suppressed and the energy dissipation occurs dominantly via cavity decay. For a ring cavity with two degenerate counterpropagating waves of opposite circular polarization, the final dark state is identical as in free space. However, we find a strong cavity mediated force with a large capture range as a precooling mechanism. In this scheme spontaneous emission is only important for the final jump to the dark state in the dynamics and the reabsorption problem is strongly reduced. In principle the scheme could also be applied to molecules with a suitable transition.
We calculate the light forces on atoms with a ground state of angular momentum F > 0 for the case that the fields are enclosed in an optical ring resonator. At the example of polarization gradient cooling using counterpropagating σ + –σ − fields coupled to a F → F + 1 transition we obtain explicit analytical expressions for the dipole-and radiation pressure forces. The additional cavity-mediated terms enhance the friction forces and yield substantial cooling even for very large atom–field detunings, where spontaneous emission is negligible. This should allow for lower final temperatures and higher densities than in free space. The new cooling force is related to stimulated Raman transitions between different ground-state sublevels, which leads to phase locking of the two polarization modes in the cavity. This provides non-destructive, detailed real-time information on the atomic motion from monitoring the output fields.
Cooling is indispensable for trapping and observing single free atoms.In atomic physics, this can be achieved efficiently by laser cooling.Conventional methods to laser cool atoms are based on repeated optical pumping cycles followed by spontaneous emission of a photon from the atom.Such pumping schemes can only be applied to certain atomic species, which have a closed optical transition.Drawbacks caused by photons spontaneously emitted from the atom can be avoided in the strongly coupled atom-cavity system in which energy and entropy can be removed by photons lost from the cavity.This thesis reports on the first observation of this cooling mechanism which does not rely on spontaneous emission.In the experiment, a single atom is captured in an intracavity dipole trap.Illuminating the system with a weak, slightly blue-detuned light beam extends the storage time of the atom in the trap.The observed cooling force is at least five times larger than the force achieved by free-space cooling methods at comparable excitation of a two-level atom.Utilising cavity cooling, single atoms are prepared strongly-coupled to the mode of a high-finesse cavity.This allows to observe two well-resolved normal-mode peaks in both the cavity transmission as well as in the trap lifetime.The experiment is in agreement with a Monte Carlo simulation, demonstrating the localisation of the atom to within a tenth of a wavelength.The ability to individually excite the normal modes opens new possibilities to use this system for applications in quantum information science, including the realisation of quantum-logic gates.In the future cavity cooling might be applied to systems which cannot be cooled by conventional methods as for instance molecules or an atom carrying a quantum bit.
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 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.
Abstract All conventional methods to laser-cool atoms rely on repeated cycles of optical pumping and spontaneous emission of a photon by the atom. Spontaneous emission in a random direction provides the dissipative mechanism required to remove entropy from the atom. However, alternative cooling methods have been proposed1, 2 for a single atom strongly coupled to a high-finesse cavity; the role of spontaneous emission is replaced by the escape of a photon from the cavity. Application of such cooling schemes would improve the performance of atom–cavity systems for quantum information processing3, 4. Furthermore, as cavity cooling does not rely on spontaneous emission, it can be applied to systems that cannot be laser-cooled by conventional methods; these include molecules2 (which do not have a closed transition) and collective excitations of Bose condensates5, which are destroyed by randomly directed recoil kicks. Here we demonstrate cavity cooling of single rubidium atoms stored in an intracavity dipole trap. The cooling mechanism results in extended storage times and improved localization of atoms. We estimate that the observed cooling rate is at least five times larger than that produced by free-space cooling methods, for comparable excitation of the atom.
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.