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Physical Review Letters

Force and diffusion measurements in sub-Doppler laser cooling

Maarten D. Hoogerland, H. F. P. de Bie, Herman C. W. Beijerinck, K. A. H. van Leeuwen, P. van der Straten, Edgar J. D. Vredenbregt, H. Metcalf

Published May 23, 1994• 7 citations
Publisher

Abstract

We present the first direct measurements of the velocity dependence of the average force and diffusion constant for the metastable neon atoms in a one-dimensional ${\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ laser cooling configuration. Force and diffusion are determined, respectively, from the deflection and broadening of a highly collimated atomic beam by its interaction with a pair of counter-running laser beams. The interaction time is much shorter than the characteristic damping time of the cooling process. The resulted force and diffusion measurements are compared with the results of both semiclassical and quantum Monte Carlo calculations.

DOI
10.1103/physrevlett.72.3332

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 24, 2010•0 citations
We present the first direct measurements of the velocity dependence of the average force and diffusion constant for the metastable neon atoms in a one-dimensional {\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}} laser cooling configuration. Force and diffusion are determined, respectively, from the deflection and broadening of a highly collimated atomic beam by its interaction with a pair of counter-running laser beams. The interaction time is much shorter than the characteristic damping time of the cooling process. The resulted force and diffusion measurements are compared with the results of both semiclassical and quantum Monte Carlo calculations.
We present an extensive set of measurements on one-dimensional sub-Doppler cooling and channeling in counterpropagating light beams. The experimental method consists of the measurement of the profile of an initially subrecoil collimated atomic beam, which is deflected by the interaction with the light field. The initial velocity of the atoms in the direction of the laser beams is varied in the range -1\ensuremath{\le}${\mathit{v}}_{\mathrm{\ensuremath{\perp}}}$(${\mathrm{ms}}^{\mathrm{\ensuremath{-}}1}$)\ensuremath{\le}1 by changing the angle between atomic and laser beams. For the orthogonal circular polarization (${\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$) sub-Doppler cooling configuration, the force and the diffusion coefficient characterizing the cooling process have been determined as a function of the initial velocity ${\mathit{v}}_{\mathrm{\ensuremath{\perp}}}$ from the average deflection and broadening of the atomic beam profile. We observe transient effects due to the slow evolution of the distribution over the magnetic sublevels to an equilibrium. The experimental results agree very well with quantum Monte Carlo simulations and semiclassical calculations. For the orthogonal linear polarization (${\mathrm{\ensuremath{\pi}}}^{\mathit{x}}$${\mathrm{\ensuremath{\pi}}}^{\mathit{y}}$) configuration, we demonstrate the validity of the well-known Sisyphus picture for the cooling mechanism by comparing the experimental data to the results of a simple semiclassical Monte Carlo model incorporating only the dipole force and optical pumping. In weak standing waves of either circular or linear polarization, we demonstrate the characteristic features of channeling. \textcopyright{} 1996 The American Physical Society.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.
A theoretical analysis is given for 1-D laser cooling below the Doppler limit of J = 1/2 ground- state atoms. The laser field consists of a pair of counterpropagating, linearly polarized low- power beams, whose polarization directions differ by an angle θ (0 ≤ θ ≤ π/2). For θ ≪ 1, the effective optical pumping time is shown to increase strongly near the nodes of the standing wave and the cooling force can be much larger than that for θ ~1. Moreover, for θ ≪ 1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for θ ~ 1. As a consequence it is possible to achieve an equilibrium atomic distribution that, for θ ≪ 1, is characterized by a mean kinetic energy lower than that predicted to occur for θ = π/2. The equilibrium velocity distribution is not necessarily Maxwellian and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms are trapped in the vicinity of the laser field nodes. An explanation for these effects is given in terms of Sisyphus cooling.
Optical forces using lasers allow precise control over the motion of atoms. The bichromatic optical force (BF) is unique in its large magnitude and velocity range, arising from the absorption and stimulated emission processes. These properties were used to transversely collimate a beam of metastable helium (He∗ ) using the 2^{3}S − 2^{3}P transition. The collimation created a very bright beam of He∗ , allowing experiments of neutral atom lithography. The He∗ beam was used to pattern material surfaces using a resist-based lithography technique, where the pattern was determined by either mechanical or optical masks. The optical masks produced features with a separation of half the wavelength of the light used. Patterning was successfully demonstrated with both IR and UV optical masks. The etched pattern resolution was ∼ 100 nm and limited by the material surface. Further experiments were performed studying the ability of the bichromatic force to cool. The finite velocity range of the BF allows estimation of a characteristic cooling time which is independent of the excited state lifetime, only depending on the atomic mass and optical transition energy. Past experiments, including the helium collimation used for neutral atom lithography, have demonstrated that the BF can collimate and longitudinally slow atomic beams, but required long interaction times that included many spontaneous emission (SE) events. The effect of SE can be mitigated, and is predicted to not be necessary for BF cooling. Since the BF cooling time is not related to the excited state lifetime, a transition can be chosen such that the cooling time is shorter than the SE cycle time, allowing direct laser cooling on atoms and molecules that do not have cycling transitions. Experiments using the helium 2^{3}S− 3^{3}P transition were chosen because the BF cooling time (285 ns) is on the order of the average SE cycle time (260 ns). Numerical simulations of the experimental system were run predicting compression of the atomic velocity distribution. Our experimental results demonstrate the stimulated nature of the force through many atomic recoils from the light in less than one SE cycle time. A large range of the atomic velocity distribution is accelerated and accumulates at the velocity limit of the force. This accumulation results in an increase in the velocity space density, demonstrating cooling. | 112 pages
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.
A quantum mechanical Monte Carlo simulation is carried out for one-dimensional laser cooling of Chromium atoms. Chromium atom beam collimation via transverse laser cooling is essential for the fabrication of periodic nanometer scale structures by laser-focused atomic deposition. Such structures can be used as precision pitch standards for nanometer scale measurement and engineering. We explore the roles played by several factors, such as laser intensity and detuning, in the cooling process. Calculation results show different dependencies for cooling rate and ultimate temperature to be reached with given sets of parameters. Also, for atoms with different initial velocities in the transverse direction, the conditions under which optimal collimation effect is achieved can differ. Consequently, the current experimental setup, which utilizes LIF spots from marginal beams to monitor the laser collimation, can produce cooling effects which are not optimal for the end product.