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Journal of Physics B Atomic Molecular and Optical Physics

Cavity-enhanced polarization gradient cooling

Markus Gangl, Helmut Ritsch

Published Nov 4, 2002• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/35/22/301

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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.
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 present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion 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.
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 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.