For experiments that require a quantum system to be in the ultra-cold regime, laser cooling is an essential tool. While techniques for laser cooling ions and neutral atoms have been refined and temperatures below the Doppler limit have been achieved, present-day techniques are limited to a small class of molecules. This paper proposes a general cooling scheme for molecules based on vibrational-state transitions. Superradiance is used to speed up the two-photon transition. Simulations of this scheme achieve temperatures comparable to those achieved by existing two-level schemes for neutral atoms and ions.
For experiments that require a quantum system to be in the ultra-cold regime, laser cooling is an essential tool. While techniques for laser cooling ions and neutral atoms have been refined and temperatures below the Doppler limit have been achieved, present-day techniques are limited to a small class of molecules. This paper proposes a general cooling scheme for molecules based on vibrational-state transitions. Superradiance is used to speed up the two-photon transition. Simulations of this scheme achieve temperatures comparable to those achieved by existing two-level schemes for neutral atoms and ions.
We have recently demonstrated that optical pumping methods combined with photo-association of ultra-cold atoms can produce ultra-cold and dense samples of molecules in their absolute rovibronic ground state. More generally, both the external and internal degrees of freedom can be cooled by addressing selected rovibrational levels on demand. Here, we recall the basic concepts and main steps of our experiments, including the excitation schemes and detection techniques we use to achieve the rovibrational cooling of Cs2 molecules. In addition, we present the determination of formation pathways and a theoretical analysis explaining the experimental observations. These simulations improve the spectroscopic knowledge required to transfer molecules to any desired rovibrational level.
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.
Slowing, cooling, and trapping molecules One of the major achievements in physics during the last two decades of the twentieth century was the ability to cool and trap atoms [1]. Laser cooling can produce previously inconceivable atomic temperatures of less than 1 μK. Atoms with sufficiently low kinetic energy can be trapped in magnetic and optical traps and thus studied for a prolonged time, thereby improving the resolution of spectroscopy by many orders of magnitude as well as reducing Doppler broadening. Furthermore, besides the external degrees of freedom, the internal degrees of freedom of the atoms can also be manipulated, leading to full control of the atoms. One of the holy grails of physics, the achievement of Bose–Einstein condensation in a dilute gas, was achieved mainly because of laser cooling and trapping of atoms. One of the natural extensions of laser cooling and trapping of atoms is the application of the techniques to molecules. Molecules offer a much richer internal structure than atoms, and thus provide extended possibilities to experimentalists. However, atomic laser cooling is based on the repetitive scattering of light and requires a closed, or at least nearly closed, two-level system. Because of the complicated internal structure of molecules, a closed two-level system cannot usually be found because they have many different electronic, vibrational, and rotational states and in general can decay to many different states after absorption of light (see Chap. 16). This requires a complete rethinking of the schemes that are used to cool atoms. Still, because of the extended possibilities cold molecules can offer with respect to cold atoms, there have been a large number of techniques developed to slow, cool, and trap them. These techniques can be divided into two classes, namely direct and indirect cooling. In the first case, molecules at cryogenic or room temperature are directly slowed and cooled. Although many different slowing techniques are used, this chapter focuses on Stark slowing of molecules since it was the first technique developed. Apart from the Stark shift of the molecules, the Zeeman and light shift of molecules can also be used to slow them. The idea behind Stark slowing is to subject the moving molecules to a continuously increasing electric field so that their kinetic energy is converted into potential energy.
Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.
We employ semiclassical theoretical analysis to study laser cooling of free atoms using three-level cascade transitions, where the upper transition is much weaker than the lower one. This represents an alternate cooling scheme, particularly useful for group II atoms. We find that temperatures below the Doppler limits associated with each of these transitions are expected. The lowest temperatures arise from a remarkable increase in damping and reduced diffusion compared to two-level cooling. They are reached at the two-photon resonance, where there is a crossing between the narrow and the partially dark dressed states, and can be estimated simply by the usual Doppler limit considering the decay rate of the optical coherence between these states.
One of three priorities of the 1994 National Research Council Report Atomic, Molecular and Optical Science is promote research … to better control and manipulate atoms, molecules, charged particles, and light. Although many techniques are available for atoms, charged particles, and light, we propose here new techniques for rapidly cooling (more generally, manipulating) the vibrational, rotational, and translational energy of simple molecules. A concrete example is manipulating Cs2 by using the B1Πn-1Σg+ bands. The key component is an optically pumped amplifier (using the same molecule, here Cs2) to provide the synchronized multiple-single-frequency laser required to optically couple a significant number of rovibronic levels while rapidly (and simultaneously) tuning over all coupled Doppler profiles (as in atomic translational cooling). Proposed molecular- beam experiments providing total cooling in ~12 ms are described.