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arXiv:0705.3639 · Physical Review A

Prospects for the cavity-assisted laser cooling of molecules

Benjamin Lev, András Vukics, Eric R. Hudson, Brian C. Sawyer, P. Domokos, Helmut Ritsch, Jun Ye

Published Feb 4, 2008• 80 citations
arXivHTMLPDF

Abstract

Cooling of molecules via free-space dissipative scattering of photons is thought not to be practicable due to the inherently large number of Raman loss channels available to molecules and the prohibitive expense of building multiple-repumping laser systems. The use of an optical cavity to enhance coherent Rayleigh scattering into a decaying cavity mode has been suggested as a potential method to mitigate Raman loss, thereby enabling the laser cooling of molecules to ultracold temperatures. We discuss the possibility of cavity-assisted laser cooling of particles without closed transitions, identify conditions necessary to achieve efficient cooling, and suggest solutions given experimental constraints. Specifically, it is shown that cooperativities much greater than unity are required for cooling without loss, and that this could be achieved via the superradiant scattering associated with intracavity self-localization of the molecules. Particular emphasis is given to the polar hydroxyl radical (OH), cold samples of which are readily obtained from Stark deceleration.

DOI
10.1103/physreva.77.023402

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Cooling of molecules via free-space dissipative scattering of photons is thought not to be practicable due to the inherently large number of Raman loss channels available to molecules and the prohibitive expense of building multiple-repumping laser systems. The use of an optical cavity to enhance coherent Rayleigh scattering into a decaying cavity mode has been suggested as a potential method to mitigate Raman loss, thereby enabling the laser cooling of molecules to ultracold temperatures. We discuss the possibility of cavity-assisted laser cooling of particles without closed transitions, identify conditions necessary to achieve efficient cooling, and suggest solutions given experimental constraints. Specifically, it is shown that cooperativities much greater than unity are required for cooling without loss, and that this could be achieved via the superradiant scattering associated with intracavity self-localization of the molecules. Particular emphasis is given to the polar hydroxyl radical (OH), cold samples of which are readily obtained from Stark deceleration.
We present a simple and general optical cooling method based on 3D degenerate Raman sideband cooling with adiabatic release that goes significantly beyond the density and temperature limitations of optical molasses. In 10 ms we cool a sample of 3×108 cesium atoms to a temperature of 330 nK at a density of 1.1×1011 cm−3, which corresponds to a phase-space density nλdB3=1/500.We further propose to cool atoms or molecules inside an optical cavity that enhances the scattering of blue-detuned photons and show that the dissipative mechanism can be viewed as a cavity-induced generalized Doppler cooling. Since the cooling depends on the atom’s internal level structure only through the photon scattering rate, cavity Doppler cooling is applicable to particles that do not possess a closed optical transition, which may allow one to extend laser cooling to a greater class of atoms or molecules. Large samples are cooled at the same rate as single atoms if the effect of one atom on the cavity resonance frequency is small. We also show how to achieve 3D cooling with a single optical cavity.
We describe a possible method for laser cooling OH molecules. The method is based on exciting the Δ J = 2 stimulated Raman transition in the ground electronic and vibronic state. The molecules are assumed to already be trapped with a temperature of ∼10 mK or less in a spatially varying magnetic field. By exciting the molecule in a region of high magnetic field, the subsequent spontaneous photon emission at lower magnetic field removes centre-of-mass energy from the molecule. The vacuum decay rate from the J = 7/2, F = 4, M F = 4 to J = 5/2, F = 3, M F = 3 is roughly 0.31 Hz and the next cascade to J = 3/2, F = 2, M F = 2 is roughly 0.15 Hz. A cavity tuned to stimulate both transitions in a small region of space can enhance the decay. Simulations of the radiative transitions indicate that up to 20% of a population of OH molecules with an average energy of 10 mK will finish with energies less than 200 µK.
Cold and ultracold molecules are highly desirable for a diverse range of applications in physics and chemistry such as precision measurements, tests of fundamental physics, quantum simulation and information processing, quantum chemistry, and the physics of strongly correlated quantum matter. Laser cooling is usually infeasible in molecules because their rotational and vibrational transitions make is difficult to come up with a closed scattering cycle. Recently, a narrow range of diatomic molecules, one of which is CaF, has been shown to possess a convenient electronic structure and a highly-diagonal Franck-Condon matrix and thus be amenable to laser cooling. This thesis describes experiments on laser cooling of CaF radicals produced in a supersonic source. We first investigate the increased fluorescence when multi-frequency resonant light excites the molecules from the four hyperfine levels of the ground X²∑+(N = 1, v = 0) state to the first excited A²π½ (J’ = 1=2; v’ = 0) state. The number of photons scattered per molecule increases significantly from one or two in the single frequency case to more than 50 before the molecules get pumped into the X²∑+(N = 1; v = 1) state. We demonstrate laser cooling and slowing of CaF using counter-propagating laser light which causes the molecules to scatter more than a thousand photons on the X (N = 1, v = 0, 1) <->A (J’ = 1=2; v’ = 0) transition. The effect of the laser cooling is to slow a group of molecules from 600 ms-1 to about 580 ms-1 and to narrow their velocity distribution from an initial temperature of 3 K down to 300 mK. In addition, chirping the frequency of the cooling light to keep it on resonance with the decelerating molecules doubles the deceleration and further compresses the velocity distribution. The effect of the laser cooling is limited by the optical pumping of molecules in the X (N = 1, v = 2) state.
Cooling a range of molecules to ultracold temperatures (<1 mK) is a difficult but important challenge in molecular physics and chemistry. Collective cavity cooling of molecules is a promising method that does not rely on molecular energy level and thus can be applied to all molecules in principle. However, the initial lack of cold molecules leads to the difficulty in its experimental implementation. We show that efficient collective sympathetic cooling of molecules to sub-mK temperatures using a large ensemble of atoms within a cavity is feasible. This approach is a new type of sympathetic cooling which does not rely on direct collisions between atoms and molecules, but utilizes thermalization via their mutual interaction with a cavity field. Two important mechanisms are identified. This include: (1) giant enhancement of cavity optical field from the efficient scattering of the pump light by the atoms; (2) cavity-mediated collective interaction between the atoms and the molecules. We show an optimal cavity detuning for maximizing cooling, which is dependent on the atom and molecule numbers. We determine a threshold for the molecular pump strength and show that it is independent of molecule number when the number of atoms is much greater than the molecules. This can be reduced by orders of magnitude when compared to cavity cooling of single molecular species only. Using this new sympathetic cavity cooling technique, cooling molecules to sub-mK within a high-Q cavity could be within reach of experimental demonstration.
We point out a laser cooling method for atoms, molecules, or ions at low saturation and large detuning from the particles' resonances. The moving particle modifies the field inside a cavity with a time delay characteristic of the cavity linewidth, while the field acts on the particle via the light shift. The dissipative mechanism can be interpreted as Doppler cooling based on preferential scattering rather than preferential absorption. It depends on particle properties only through the coherent scattering rate, opening new possibilities for optically cooling molecules or interacting atoms.
We analyze cavity-assisted cooling schemes for polar molecules in the microwave domain, where molecules are excited on a rotational transition and energy is dissipated via strong interactions with a lossy stripline cavity, as recently proposed by André et al 2006 Nat. Phys. 2 636. We identify the dominant cooling and heating mechanisms in this setup and study cooling rates and final temperatures in various parameter regimes. In particular, we analyze the effects of a finite environment temperature on the cooling efficiency, and find minimal temperature and optimized cooling rate in the strong drive regime. Further, we discuss the trade-off between efficiency of cavity cooling and robustness with respect to ubiquitous imperfections in a realistic experimental setup, such as anharmonicity of the trapping potential.