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Physical Review A

Decelerating and bunching molecules with pulsed traveling optical lattices

Guangjiong Dong, Weiping Lu, P. F. Barker

Published Jan 23, 2004• 31 citations
Publisher

Abstract

We investigate the deceleration and bunching of cold molecules in a pulsed supersonic jet using a far-off-resonant optical lattice traveling with a constant velocity. Using an analytical treatment, we show that by choosing the lattice velocity equal to half the supersonic beam velocity and by optimizing the pulse duration, a significant fraction $(\ensuremath{\sim}33%)$ of translationally cold (1 K) CO molecules from a supersonic molecular beam can be decelerated to zero velocity, and simultaneously bunched in velocity space. Due to the large difference of polarizability to mass ratio between the buffer gas and the CO molecules in the pulsed jet, the buffer gas can be precluded from the fraction of stationary molecules by choosing a suitable pulse duration. Furthermore, we find that spatial bunching within the optical lattice is induced and the position of the bunch within the lattice can be chosen by varying the lattice velocity.

DOI
10.1103/physreva.69.013409

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This work presents the proposed schemes for decelerating cold molecules created in pulsed supersonic expansions using pulsed optical lattices. The first scheme relies on the application of a decelerating optical lattice with a dipole-potential well depth of approximately 1 K, created by rapidly chirping medium-intensity fields in the 10 W/cm/sup 2/ range. This scheme is an optical analog of the Start decelerator that has been successfully used to slow a range of polar molecules. A significant fraction (about 10%) of the very heavy I/sub 2 /molecules in an Ar buffer gas is shown to be slowed by using this method over sub-microsecond time scales. In the second technique, an optical lattice with larger well depth in the 100 K range travelling at half the supersonic beam velocity is used to trap a significant fraction of the cold, high-velocity molecules. This technique is developed based on the property of periodic motion of the trapped molecules in the optical lattice; the molecules reverse their initial (relative) velocities in the lattice reference frame after half a period. Using this method the cold molecules can be transferred from high speed to zero velocity on nanosecond time scales. As an example, 33% of a CO molecule beam (1 K) with a velocity of 230 m/s is slowed utilising optical intensities of less than 10/sup 12/ W/cm/sup 2/.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 20, 2004•8 citations
We investigate the deceleration and bunching of cold molecules in a pulsed supersonic jet using a far-off-resonant optical lattice traveling with a constant velocity. Using an analytical treatment, we show that by choosing the lattice velocity equal to half the supersonic beam velocity and by optimizing the pulse duration, a significant fraction (\ensuremath∼33(\ensuremath{\sim}33%)(\ensuremath∼33 of translationally cold (1 K) CO molecules from a supersonic molecular beam can be decelerated to zero velocity, and simultaneously bunched in velocity space. Due to the large difference of polarizability to mass ratio between the buffer gas and the CO molecules in the pulsed jet, the buffer gas can be precluded from the fraction of stationary molecules by choosing a suitable pulse duration. Furthermore, we find that spatial bunching within the optical lattice is induced and the position of the bunch within the lattice can be chosen by varying the lattice velocity.
This work presents the proposed schemes for decelerating cold molecules created in pulsed supersonic expansions using pulsed optical lattices. The first scheme relies on the application of a decelerating optical lattice with a dipole-potential well depth of approximately 1 K, created by rapidly chirping medium-intensity fields in the 10 W/cm/sup 2/ range. This scheme is an optical analog of the Start decelerator that has been successfully used to slow a range of polar molecules. A significant fraction (about 10%) of the very heavy I/sub 2 /molecules in an Ar buffer gas is shown to be slowed by using this method over sub-microsecond time scales. In the second technique, an optical lattice with larger well depth in the 100 K range travelling at half the supersonic beam velocity is used to trap a significant fraction of the cold, high-velocity molecules. This technique is developed based on the property of periodic motion of the trapped molecules in the optical lattice; the molecules reverse their initial (relative) velocities in the lattice reference frame after half a period. Using this method the cold molecules can be transferred from high speed to zero velocity on nanosecond time scales. As an example, 33% of a CO molecule beam (1 K) with a velocity of 230 m/s is slowed utilising optical intensities of less than 10/sup 12/ W/cm/sup 2/.
The deceleration of molecules from cold molecular beams using electric and magnetic fields has become an important means for producing stationary, cold dipolar or paramagnetic molecular gases that can be trapped and potentially cooled to ultra-cold temperatures in the μK range. We report on a general scheme for the creation of cold molecules of essentially any type by deceleration of a cold molecular beam using intense optical fields. Deceleration of benzene molecules to zero velocity is achieved by utilizing a single half oscillation of the center-of-mass motion of the molecules within a moving optical lattice. The lattice traveling at half the speed of the molecular beam is created by the interference of two near-counter-propagating fields at different frequencies. We show that by rapidly switching on the optical lattice for approximately the time required for a half oscillation, a bunch of approximately 10 5 benzene molecules can be rapidly decelerated and brought to rest in the laboratory frame.
Cryogenic buffer-gas beams are a promising method for producing bright sources of cold molecular radicals for cold-collision and chemical-reaction experiments. In order to use these beams in studies of reactions with controlled collision energies or in trapping experiments, one needs a method of controlling the forward velocity of the beam. A Stark decelerator can be an effective tool for controlling the mean speed of molecules produced by supersonic jets, but efficient deceleration of buffer-gas beams presents new challenges due to longer pulse lengths. Traveling-wave decelerators are uniquely suited to meet these challenges because of their ability to confine molecules in three dimensions during deceleration and their versatility afforded by the analog control of the electrodes. We have created ground-state $\mathrm{CH}(X{\phantom{\rule{0.16em}{0ex}}}^{2}\ensuremath{\Pi})$ radicals in a cryogenic buffer-gas cell with the potential to produce a cold molecular beam of 1011{10}^{11}1011 molecules/pulse. We present a general protocol for Stark deceleration of beams with a large position and velocity spread for use with a traveling-wave decelerator. Our method involves confining molecules transversely with a hexapole for an optimized distance before deceleration. This rotates the phase-space distribution of the molecular packet so that the packet is matched to the time-varying phase-space acceptance of the decelerator. We demonstrate with simulations and an analytic one-dimensional model that this method can decelerate a significant fraction of the molecules in successive wells of a traveling-wave decelerator to produce energy-tuned beams for cold and controlled-molecule experiments.
We propose a promising scheme to realize the deceleration of a pulsed subsonic molecular beam by using a multistage optical Stark decelerator (i.e., a 1D quasi-cw traveling optical lattice), which is composed of two nearly counter-propagating, time-varying, red-detuned light fields with an intensity of ~10⁷Wcm⁻² and a fixed frequency difference between them. We also study the influence of the velocity reduced amount of the traveling lattice, the lattice power, the synchronous phase angle, the deceleration-stage number and the temporal profile of laser pulses on the molecular slowing results by using 3D Monte-Carlo method. Our study shows that the proposed decelerator cannot only be used to slow a pulsed subsonic beam from 240m/s to standstill, but also to obtain a cold molecular packet with a temperature of a few µK, and the corresponding fraction of cold molecules is 10⁻⁶-10⁻⁷, which strongly depends on the synchronous phase angle. And we also find that a pair of appropriate rising and falling times of laser pulses will lead to a better slowing effect than that produced by the top-hat temporal ones.
We propose a new scheme to realize a multistage optical Stark deceleration for a supersonic molecular beam using a time-varying red-detuned quasi-cw optical lattice with a length of up to 10 mm. We analyze the motion of the slowed molecules inside the optical decelerator, and study the dependences of the velocity of the slowed molecular packet on the synchronous phase angle and the number of the deceleration stages (i.e., the number of the optical-lattice cells) by using Monte-Carlo method. Our study shows that the proposed optical Stark decelerator cannot only efficiently slow a pulsed supersonic beam from 230 m/s to zero (standstill), but also obtain an ultracold molecular packet with a temperature of sub-mK due to bunching effect in the multistage optical Stark decelerator, which can be trapped in the optical lattice by rapidly turning off the modulation signal of the lattice. Also, we compare the decelerated results of our multistage optical Stark decelerator with a single-stage optical one, and find that our scheme cannot only obtain a colder molecular packet under the same molecular-beam parameters and deceleration conditions, but also be directly used to trap the slowed cold molecules after the deceleration, while don't need to use another molecular trap.
Analysis of the trapped and untrapped motion of particles, combined with direct numerical simulation of the 1D non-stationary Boltzmann equation, demonstrates that atoms and molecules initially at room temperature can be accelerated to velocities in the 10 to 100 km/s range over distances of 100's microns using an optical lattice. The quantity, final velocity, and velocity/energy spread of the accelerated distribution controlled by tailoring the fluence, duration and frequency chirp of the laser beam that make the lattice, indicating the potential for a compact, versatile, and configurable hyper-thermal accelerator/decelerator. Using similar lattice potentials, differential transport of atomic and molecular species with different polarizability/mass ratios leads towards the possibility of gas mixture separation in short pulses or in hollow fibers. A bulk drift can be induced in a gas by the lattice forces, even when the mean kinetic energy is much greater that the maximum dipole potential of the optical field. In this process the transfer of energy from the slowly traveling optical lattice to the gas is analogous to Landau damping of a plasma wave by charged particles.