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arXiv:2002.05041 · Physical Review A

Cooperative cooling in a one-dimensional chain of optically bound cold atoms

Angel T. Gisbert, N. Piovella, Romain Bachelard

Published Jul 14, 2020• 2 citations
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Abstract

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.

DOI
10.1103/physreva.102.013312

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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.
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.
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.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.
Collective behavior in many-body systems, where the dynamics of an individual element depend on the state of the entire ensemble, play an important role in both basic science research and applied technologies. Over the last twenty years, studies of such effects in cold atomic vapors have lead to breakthroughs in areas such as quantum information science and atomic and condensed matter physics. Nevertheless, in order to generate photon-mediated atom-atom coupling strengths that are large enough to produce collective behavior, these studies employ techniques that intrinsically limit their applicability. In this thesis, I describe a novel nonlinear optical process that enables me to overcome these limitations and realize a new regime of collective light-matter interaction. My experiment involves an anisotropic cloud of cold rubidium atoms illuminated by a pair of counterpropagating optical (pump) fields propagating at an angle to the trap's long axis. When the pump beam intensities exceed a threshold value, a collective instability occurs in which new beams of light are generated spontaneously and counterpropagate along the trap's long axis. In order to understand the physical mechanism responsible for this behavior, I study first the system's nonlinear optical response when driven below the instability threshold. I find that the incident optical fields produce an optical lattice that causes the atoms to become spatially organized on the sub-wavelength length scale. This organization corresponds to the formation of an atomic density grating, which effectively couples the involved fields to one another and enables the transfer of energy between them. The loading of atoms into this grating is enhanced by my choice of field polarizations, which simultaneously results in cooling of the atoms from T~30 μK to T~3 μK via the Sisyphus effect. As a result, I observe a fifth-order nonlinear susceptibility χ^{(5)}=1.9x10^-12 (m/V)^4 that is 7 orders of magnitude larger than previously observed. In addition, because of the unique scaling of the resulting nonlinear response with material parameters, the magnitude of the nonlinearity can be large for small pump intensities (\\ie, below the resonant electronic saturation intensity 1.6 mW/cm^2) while simultaneously suffering little linear absorption. I confirm my interpretation of the nonlinearity by developing a theoretical model that agrees quantitatively with my experimental observations with no free parameters. The collective instability therefore corresponds to the situation where the cold vapor transitions spontaneously from a spatially-homogeneous state to an ordered one. This emergent organization leads to the simultaneous emission of new optical fields in a process that one can interpret either in terms of mirrorless parametric self-oscillation or superradiance. By mapping out the phase diagram for this transition, I find that the instability can occur for pump intensities as low as 1 mW/cm^2, which is approximately 50 times smaller than previous observations of similar phenomena. The intensity of the emitted light can be up to 20% of the pump beam intensity and depends superlinearly on the number of atoms, which is a clear signature of collective behavior. In addition, the generated light demonstrates temporal correlations between the counterpropagating modes of up to 0.987 and is nearly coherent over several hundred μs. The most significant attributes of the light, though, are that it consists of multiple transverse spatial modes and persists in steady-state. This result represents the first observation of such dynamics, which have been shown theoretically to lead to a rich array of new phenomena and possible applications.
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.