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Physical Review A

Optical Stark decelerator for molecules with a traveling potential well

Lianzhong Deng, Shunyong Hou, Jianping Yin

Published Mar 10, 2017• 3 citations
Publisher

Abstract

We propose a versatile scheme to slow supersonically cooled molecules using a decelerating potential well, obtained by steering a focusing laser beam onto a pair of spinning reflective mirrors under a high-speed brake. The longitudinal motion of molecules in the moving red-detuned light field is analyzed and their corresponding phase-space stability is investigated. Trajectories of $\mathrm{C}{\mathrm{H}}_{4}$ molecules under the influence of the potential well are simulated using the Monte Carlo method. For instance, with a laser beam of power 20 kW focused onto a spot of waist radius 40--100 \ensuremath{\mu}m, corresponding to a peak laser intensity on the order of $\ensuremath{\sim}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$, a $\mathrm{C}{\mathrm{H}}_{4}$ molecule of $\ensuremath{\sim}250\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}$ can be decelerated to $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}$ over a distance of a few centimeters on a time scale of hundreds of microseconds.

DOI
10.1103/physreva.95.033409

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We propose a versatile scheme to slow supersonically cooled molecules using a decelerating potential well, obtained by steering a focusing laser beam onto a pair of spinning reflective mirrors under a high-speed brake. The longitudinal motion of molecules in the moving red-detuned light field is analyzed and their corresponding phase-space stability is investigated. Trajectories of CH4\mathrm{C}{\mathrm{H}}_{4}CH4​ molecules under the influence of the potential well are simulated using the Monte Carlo method. For instance, with a laser beam of power 20 kW focused onto a spot of waist radius 40--100 \ensuremath{\mu}m, corresponding to a peak laser intensity on the order of \ensuremath∼108W/cm2\ensuremath{\sim}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}\ensuremath∼108W/cm2, a CH4\mathrm{C}{\mathrm{H}}_{4}CH4​ molecule of \ensuremath∼250m/s\ensuremath{\sim}250\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}\ensuremath∼250m/s can be decelerated to \ensuremath∼10m/s\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}\ensuremath∼10m/s over a distance of a few centimeters on a time scale of hundreds of microseconds.
Cold molecules have great scientific significance in high-resolution spectroscopy, precision measurement of physical constants, cold collision, and cold chemistry. Supersonic expansion is a conventional and versatile method to produce cold molecules with high kinetic energies. We theoretically show here that fast-moving molecules from supersonic expansion can be effectively decelerated to any desired velocity with a rotating laser beam. The orbiting focus spot of the red-detuned laser serves as a two-dimensional potential well for the molecules. We analyze the dynamics of the molecules inside the decelerating potential well and investigate the dependence of their phase acceptance by the potential well on the tilting angle of the laser beam. ND 3 molecules are used in the test of the scheme and their trajectories under the impact of the decelerating potential well are numerically simulated using the Monte Carlo method. For instance, with a laser beam of 20 kW in power focused into a pot of in waist radius, ND 3 molecules of 250 m/s can be brought to a standstill by the decelerating potential well within a time interval of about 0.73 ms. The total angle covered by the rotating laser beam is about 5.24° with the distance travelled by the potential well being about 9.13 cm. In fact, the molecules can be decelerated to any desired velocity depending on the parameters adopted. This scheme is simple in structure and easy to be realized in experiment. In addition, it is applicable to decelerating both molecules and atoms.
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We propose a novel scheme to decelerate a cw precooled molecular beam by using an optical Stark decelerator, which is composed of a red-detuned cw semi-Gaussian beam. The dynamical process of the optical Stark deceleration for a cw methane molecular beam is studied by Monte Carlo simulations. It is realized that the proposed optical Stark decelerator can be used to continuously slow a cw methane molecular beam with a longitudinal temperature of 30 mK, and a maximum reduction in the most probable speed of 0.388 m/s (corresponding to a relative change of 9.93%) can be obtained by using a single semi-Gaussian beam with a power of 500 W and a maximum central intensity of about 7.96 × 10 7 W/cm 2 .
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.
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 repeatedly decelerate a pulsed molecular beam using a red-detuned quasi-cw semi-Gaussian laser beam (SGB) and an electrostatic storage ring. Using the Monte-Carlo simulation method, we demonstrate that this promising optical Stark decelerator can be used to efficiently slow a pulsed ND 3 molecular beam extracted from a Stark decelerator or a cryogenic reservoir by using a single SGB. The deceleration effect of this scheme on the intensity of the SGB is discussed in detail.