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arXiv:quant-ph/0306026 · Physical Review A

Rotational cooling of polar molecules by Stark-tuned cavity resonance

C. H. Raymond Ooi

Published Jul 22, 2003• 5 citations
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Abstract

A general scheme for rotational cooling of diatomic heteronuclear molecules is proposed. It uses a superconducting microwave cavity to enhance the spontaneous decay via Purcell effect. Rotational cooling can be induced by sequentially tuning each rotational transition to cavity resonance, starting from the highest transition level to the lowest one using an electric field. Electrostatic multipoles can be used to provide large confinement volume with essentially homogeneous background electric field.

DOI
10.1103/physreva.68.013410

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A general scheme for rotational cooling of diatomic heteronuclear molecules is proposed. It uses a superconducting microwave cavity to enhance the spontaneous decay via Purcell effect. Rotational cooling can be induced by sequentially tuning each rotational transition to cavity resonance, starting from the highest transition level to the lowest one using an electric field. Electrostatic multipoles can be used to provide large confinement volume with essentially homogeneous background electric field.
Abstract We discuss the trapping of heteronuclear diatomic molecules prepared in their electronic and vibrational ground states. We tune and shape the trapping potential for bosonic polar molecules in superpositions of rotational states by dressing rotational excitations with a static sextupole electric field. The translational motion of a molecule is treated classically. We examine the Hamiltonian which governs the center of mass dynamics. The effective potential has a global minimum that provides the trapping ability of this trap. The first term of its Taylor series expansion, corresponding to the quadratic Stark shifts, results in the integrable potential. In terms of cylindrical coordinates the center of mass Hamiltonian splits into axial and radial parts. Corresponding trajectories are parameterized by elliptic functions. At low electric fields, the non-approximated Hamiltonian is treated as a small perturbation of the mentioned integrable system described by Kolmogorov–Arnold–Moser theory. The applicability of this approximation is discussed and illustrated using the Poincaré cross-section method. We present results of numerical simulations illustrating the trapping and confinement of a polar molecule in the trap.
We present progress towards the experimental realization of optoelectrical cooling [1] which is widely applicable for producing samples of ultracold (<1 mK) polar molecules. This scheme exploits the interaction between trapped molecules and electric fields to remove energy, while a spontaneous vibrational decay removes entropy. The trap, a key element of this method, must not only provide long lifetimes, but also regions of variable homogenous electric fields, allowing the required addressing of transitions between individual rotational sublevels. We consider in detail the design of this microstructured electrical trap, where a trap depth of 1 K can be achieved. Careful patterning of the electrodes allows a suppression of trap losses by Majorana flips. [1] M. Zeppenfeld et al., Phys. Rev. A 80, 041401(R) (2009).
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.
We present an optoelectrical cooling scheme for polar molecules based on a Sisyphus-type cooling cycle in suitably tailored electric trapping fields. Dissipation is provided by spontaneous vibrational decay in a closed level scheme found in symmetric-top rotors comprising six low-field-seeking rovibrational states. A generic trap design is presented. Suitable molecules are identified with vibrational decay rates on the order of 100 Hz. A simulation of the cooling process shows that the molecular temperature can be reduced from 1 K to 1 mK in approximately 10 s. The molecules remain electrically trapped during this time, indicating that the ultracold regime can be reached in an experimentally feasible scheme.
A novel scheme is proposed for sequential cooling of rotation, translation, and vibration of molecules. More generally, this scheme manipulates and controls the states and energies of molecules. The scheme, while somewhat complex, is simpler and more feasible than simply providing a large number of synchronously but independently tunable lasers. The key component is a multiple single frequency laser (MSFL) in which a single narrow band pump laser generates an ensemble of resonant ‘‘stimulated Raman’’ (RSR) sidebands (subsequently amplified and selected) in a sample of the molecules to be cooled. Starting with a relatively cold molecular sample (e.g., a supersonic beam of Cs2), the rotation of molecules is cooled by sequential application of P branch electronic transition frequencies transverse to the molecular beam beginning at higher rotational angular momentum J. Then translation of molecules is cooled by application of multiple low J, P, and R branch transition frequencies which counterpropagate with the molecular beam and are synchronously chirped over their Doppler profiles. Finally, vibration of molecules is cooled by blocking the R(0) line of the 0–0 band. Only this specific order of rotation–translation–vibration appears feasible (using molecules produced by photoassociation of ultracold atoms avoids the requirement for translational cooling). Each step employs true dissipative cooling (i.e., reduction of system entropy in three degrees of freedom) by spontaneous emission and should yield a large translationally cold sample of molecules in the lowest (v=0, J=0) level of the ground electronic state, suitable for studies such as molecule trapping, ‘‘molecule optics,’’ or long range intermolecular states.