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arXiv:1705.09646 · Physical Review A

Isotropic light versus six-beam molasses for Doppler cooling of atoms from background vapor: Theoretical comparison

S. Trémine, Emeric de Clercq, Philippe Verkerk

Published Aug 9, 2017• 5 citations
arXivHTMLPDF

Abstract

We present a three-dimensional theoretical comparison between the radiation-pressure forces exerted on an atom in an isotropic light cooling scheme and in a six-beam molasses. We demonstrate that, in the case of a background vapor where all the space directions of the atomic motion have to be considered, the mean cooling rate is equal in both configurations. Nevertheless, we also point out what mainly differentiates the two cooling techniques: the force component orthogonal to the atomic motion. If this transverse force is always null in the isotropic light case, it can exceed the radiation-pressure-force longitudinal component in the six-beam molasses configuration for high atomic velocities, hence reducing the velocity capture range.

DOI
10.1103/physreva.96.023411

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We present a three-dimensional theoretical comparison between the radiation-pressure forces exerted on an atom in an isotropic light cooling scheme and in a six-beam molasses. We demonstrate that, in the case of a background vapor where all the space directions of the atomic motion have to be considered, the mean cooling rate is equal in both configurations. Nevertheless, we also point out what mainly differentiates the two cooling techniques: the force component orthogonal to the atomic motion. If this transverse force is always null in the isotropic light case, it can exceed the radiation-pressure-force longitudinal component in the six-beam molasses configuration for high atomic velocities, hence reducing the velocity capture range.
Using six optical beams (+ and − directions on three orthogonal axes) tuned slightly to the red of resonance it is possible to cool sodium atoms to a few hundred microkelvin. The cooling occurs because the laser radiation pressure creates a damping force which reduces the atomic velocities to a rms value of ~60 cm/s, determined by random scattering. In this optical molasses, the laser beams propagate in all directions and the light acts as a viscous photon fluid which damps the atomic velocity. The resulting motion of the sodium atoms is diffusive until the atoms reach the edge of the laser beams where they escape. The process of atomic confinement by optical molasses can be modeled as a random walk in a viscous medium with a boundary. For a spherical volume of 0.2 cm3 the resulting confinement time is ~0.1 s for half of the atoms to escape. Direct time-of-flight measurement of the atomic temperature gives ~240 μK, which agrees with predictions of quantum limited cooling by resonance radiation pressure. With confinement times of 0.1 s and temperatures of ~240 μK this method provides a source of atoms sufficiently slow for even the highest resolution optical spectroscopy, collision studies, or optical traps.
We present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
We describe a numerical implementation of our semiclassical laser-cooling theory [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] for an arbitrary multilevel atom and light field. There is satisfactory agreement between experiments and temperatures obtained from Langevin-equation simulations of the motion of an atom subject to light-pressure force and the accompanying diffusion in three-dimensional (3D) optical molasses in which there are three orthogonal pairs of counterpropagating waves with a common linear polarization for the two beams in a pair, but orthogonal polarizations between the pairs. However, the velocity distribution of the atoms is anisotropic and may deviate strongly from a Gaussian, heterodyne spectra may have a sideband, and the atomic density may be a maximum at the maximum of the potential of the dipole forces of the molasses beams. Subsequent velocity-linearized analysis of atomic damping and diffusion shows that the damping tensor may have a negative eigenvalue corresponding to heating in large regions of space, even though the light is red tuned for cooling. It is also found that the position-averaged damping and diffusion tensors make a poor predictor of the temperature obtained in Langevin-equation simulations and real experiments. Based on additional simulations of a simple 1D model, we formulate a hypothesis that connects our findings. The key idea is that an atom trapped in a minimum of the potential of the dipole forces is subject to a weaker-than-average damping, and therefore tends to boil out of the trap.
The technique of laser cooling, whose basic idea was proposed in 1975 [1], provided the development of many important areas like high-resolution spectroscopy [2], atomic clocks [3] and quantum gases confined in magnetic or optical traps [4, 5]. Among the techniques applied to cooling neutral atoms is the optical molasses [6] that will be explored in this work. Here we study the standard molasses and a new alternated molasses configuration, which consists of turning on just one pair of counter-propagating laser beams per cycle, and alternating this pair between the three spatial directions. We analyse the two techniques under the lens of the radiation force, by exploring a semiclassical treatment, in order to obtain the minimum energy attained by each of them at the end of the cooling process. We compare, then, these two cooling techniques, pointing out their advantages.
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.