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Physical Review A

Laser cooling of molecules by zero-velocity selection and single spontaneous emission

C. H. Raymond Ooi

Published Nov 9, 2010• 5 citations
Publisher

Abstract

A laser-cooling scheme for molecules is presented based on repeated cycle of zero-velocity selection, deceleration, and irreversible accumulation. Although this scheme also employs a single spontaneous emission as in [Raymond Ooi, Marzlin, and Audretsch, Eur. Phys. J. D 22, 259 (2003)], in order to circumvent the difficulty of maintaining closed pumping cycles in molecules, there are two distinct features which make the cooling process of this scheme faster and more practical. First, the zero-velocity selection creates a narrow velocity-width population with zero mean velocity, such that no further deceleration (with many stimulated Raman adiabatic passage (STIRAP) pulses) is required. Second, only two STIRAP processes are required to decelerate the remaining hot molecular ensemble to create a finite population around zero velocity for the next cycle. We present a setup to realize the cooling process in one dimension with trapping in the other two dimensions using a Stark barrel. Numerical estimates of the cooling parameters and simulations with density matrix equations using OH molecules show the applicability of the cooling scheme. For a gas at temperature $T=1$ K, the estimated cooling time is only $2$ ms, with phase-space density increased by about 30 times. The possibility of extension to three-dimensional cooling via thermalization is also discussed.

DOI
10.1103/physreva.82.053408

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A laser-cooling scheme for molecules is presented based on repeated cycle of zero-velocity selection, deceleration, and irreversible accumulation. Although this scheme also employs a single spontaneous emission as in [Raymond Ooi, Marzlin, and Audretsch, Eur. Phys. J. D 22, 259 (2003)], in order to circumvent the difficulty of maintaining closed pumping cycles in molecules, there are two distinct features which make the cooling process of this scheme faster and more practical. First, the zero-velocity selection creates a narrow velocity-width population with zero mean velocity, such that no further deceleration (with many stimulated Raman adiabatic passage (STIRAP) pulses) is required. Second, only two STIRAP processes are required to decelerate the remaining hot molecular ensemble to create a finite population around zero velocity for the next cycle. We present a setup to realize the cooling process in one dimension with trapping in the other two dimensions using a Stark barrel. Numerical estimates of the cooling parameters and simulations with density matrix equations using OH molecules show the applicability of the cooling scheme. For a gas at temperature T=1T=1T=1 K, the estimated cooling time is only 222 ms, with phase-space density increased by about 30 times. The possibility of extension to three-dimensional cooling via thermalization is also discussed.
We propose a laser cooling concept for the translational motion of molecules which does not require repeated spontaneous emission by each molecule. The cooling works by repetition of three main steps; velocity selection of a narrow momentum width, deceleration of velocity selected molecules by repeated STIRAP and accumulation of decelerated molecules via one time spontaneous emission. We use single spontaneous emission for irreversible accumulation of narrow velocity selected and decelerated populations. We develop an analytical model to describe the evolution of the molecular gas system, internal subsystem and external (center of mass) subsystem density matrices and entropies. Simulation results show cooling from an arbitrary momentum width towards final width of about hbark\\hbar khbark. The external entropy is reduced while the internal entropy is increased. The external entropy is shown to decrease during coherent laser interactions, a possibility of translational cooling via unitary evolution. The system entropy increases in consistency with the Araki-Lieb inequality.
Ultracold molecular gases are promising as an avenue to rich many-body physics, quantum chemistry, quantum information, and precision measurements. This richness, which flows from the complex internal structure of molecules, makes the creation of ultracold molecular gases using traditional methods (laser plus evaporative cooling) a challenge, in particular due to the spontaneous decay of molecules into dark states. We propose a way to circumvent this key bottleneck using an all-optical method for decelerating molecules using stimulated absorption and emission with a single ultrafast laser. We further describe single-photon cooling of the decelerating molecules that exploits their high dark state pumping rates, turning the principal obstacle to molecular laser cooling into an advantage. Cooling and deceleration may be applied simultaneously and continuously to load molecules into a trap. We discuss implementation details including multilevel numerical simulations of strontium monohydride. These techniques are applicable to a large number of molecular species and atoms with the only requirement being an electric dipole transition that can be accessed with an ultrafast laser.
We present a study of Sisyphus cooling of molecules: The scattering of a single photon removes a substantial amount of the molecular kinetic energy and an optical pumping step allows one to repeat the process. A review of the produced cold molecules so far indicates that the method can be implemented for most of them, making it a promising method able to produce a large sample of molecules at sub-mK temperatures. Considerations of the required experimental parameters, for instance the laser power and linewidth or the trap anisotropy and dimensionality, are given. Rate equations, as well as scattering and dipolar forces, are solved using kinetic Monte Carlo methods for several lasers and several levels. For NH molecules, such detailed simulation predicts a 1000-fold temperature reduction and an increase of the phase-space density by a factor of 107{}^{7}7. Even in the case of molecules with both low Franck-Condon coefficients and a nonclosed pumping scheme, 60% of trapped molecules can be cooled from 100 mK to sub-mK temperatures in a few seconds. Additionally, these methods can be applied to continuously decelerate and cool a molecular beam.
In the last several years we have discovered a variety of remarkable pulse strategies for manipulating molecular motion by employing a design strategy we call “local optimization.'' Here we review the concept of local optimization and contrast it with optimal control theory. By way of background, we give highlights from two recent examples of the method: (1) a strategy for eliminating population transfer to one or many excited electronic states during strong field excitation, an effect we call ‘optical paralysis’; (2) a generalization of the counterintuitive STIRAP (stimulated Raman adiabatic passage) pulse sequence from three levels to N levels, a strategy we call ‘straddling STIRAP.' We then turn to a third example, which is the main subject of this paper: laser cooling of molecular internal degrees of freedom. We study a model that includes both coherent interaction with the radiation field and spontaneous emission; the latter is necessary to carry away the entropy from the molecule. An optimal control calculation was performed first and succeeded in producing vibrational cooling, but the resulting pulse sequence was difficult to interpret. Local optimization subsequently revealed the cooling mechanism: the instantaneous phase of the laser is locked to the phase of the transition dipole moment between the excited state amplitude and v=0 of the ground state. Thus, the molecules that reach v=0 by spontaneous emission become decoupled from the field, and no longer absorb, while molecules in all other states are continually repumped. The mechanism could be called “vibrationally selective coherent population trapping,'' in analogy to the corresponding mechanism of velocity selective coherent population trapping in atoms for sub-Doppler cooling of translations.
We present a study of Sisyphus cooling of molecules: the scattering of a single-photon remove a substantial amount of the molecular kinetic energy and an optical pumping step allow to repeat the process. A review of the produced cold molecules so far indicates that the method can be implemented for most of them, making it a promising method able to produce a large sample of molecules at sub-mK temperature. Considerations of the required experimental parameters, for instance the laser power and linewidth or the trap anisotropy and dimensionality, are given. Rate equations, as well as scattering and dipolar forces, are solved using Kinetic Monte Carlo methods for several lasers and several levels. For NH molecules, such detailed simulation predicts a 1000-fold temperature reduction and an increase of the phase space density by a factor of 10^7 . Even in the case of molecules with both low Franck-Condon coefficients and a non-closed pumping scheme, 60% of trapped molecules can be cooled from 100 mK to sub-mK temperature in few seconds. Additionally, these methods can be applied to continuously decelerate and cool a molecular beam