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arXiv:1808.00275 · Physical Review A

Stochastic heating and self-induced cooling in optically bound pairs of atoms

Angel T. Gisbert, N. Piovella, Romain Bachelard

Published Jan 22, 2019• 5 citations
arXivHTMLPDF

Abstract

The light scattered by cold atoms induces mutual optical forces between them, which can lead to bound states. In addition to the trapping potential, this light-induced interaction generates a velocity-dependent force which damps or amplifies the stretching vibrational mode of the two-atom ``molecule.'' This velocity-dependent force acts on time scales much longer than the mode period or the dipole dynamics, determining the true stability of the bound state. We show that, for two atoms, the stochastic heating due to spontaneous emission always exceeds the bounding effect, so pairs of cold atoms cannot be truly stable without an extra cooling mechanism.

DOI
10.1103/physreva.99.013619

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The light scattered by cold atoms induces mutual optical forces between them, which can lead to bound states. In addition to the trapping potential, this light-induced interaction generates a velocity-dependent force which damps or amplifies the stretching vibrational mode of the two-atom ``molecule.'' This velocity-dependent force acts on time scales much longer than the mode period or the dipole dynamics, determining the true stability of the bound state. We show that, for two atoms, the stochastic heating due to spontaneous emission always exceeds the bounding effect, so pairs of cold atoms cannot be truly stable without an extra cooling mechanism.
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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.
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 theoretically the optical binding of one-dimensional chains of cold atoms shone by a transverse pump, where particles self-organize to a distance close to an optical wavelength. As the number of particles is increased, the trapping potential increases logarithmically as the contributions from all atoms add up constructively. We identify a cooperative cooling mechanism, due to the mutual exchange of photons between atoms, which can beat the spontaneous emission for chains that are long enough. Surprisingly, the cooling is optimal very close to the resonance. This peculiar cooling mechanism thus gives new insights into the cooperative physics of low-dimensional cold atom systems.
The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.