Formation of high-density cold molecules via electromagnetic trap

Preparation and control of cold molecules are advancing rapidly, motivated by many exciting applications ranging from tests of fundamental physics to quantum information processing. Here, we propose a trapping scheme to create high-density cold molecular samples by using a combination of electric and magnetic fields. In our theoretical analysis and numerical calculations, a typical alkaline-earth monofluoride, MgF, is used to test the feasibility of our proposal.A cold MgF molecular beam is first produced via an electrostatic Stark decelerator and then loaded into the proposed electromagnetic trap, which is composed of an anti-Helmholtz coil, an octupole, and two disk electrodes. Following that,a huge magnetic force is applied to the molecular sample at an appropriate time, which enables further compressing of the spatial distribution of the cold sample. Molecular samples with both higher number density and smaller volume are quite suitable for the laser confinement and other molecular experiments such as cold collisions in the next step.

A crossed focused vortex beam with application to cold molecules

We report the generation of a crossed,focused,optical vortex beam by using a pair of hybrid holograms,which combine the vortex phase and lens phase onto a spatial light modulator.We study the intensity distributions of the vortex beam in free propagation space,and the relationship of its dark spot size with the incident Gaussian beam’s waist,the lens’s focal length,and its orbital angular momentum.Our results show that the crossed,focused,vortex beam’s dark spot size can be as small as 16.3μm and adjustable by the quantum number of the orbital angular momentum,and can be used to increase the density of trapped molecules.Furthermore,we calculate the optical potential of the blue-detuned,crossed vortex beam for MgF molecules.It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling,as the intensity gradient of such vortex beam is extremely high near the focal point.

Adiabatic cooling for cold polar molecules on a chip using a controllable high-efficiency electrostatic surface trap

We propose a controllable high-efficiency electrostatic surface trap for cold polar molecules on a chip by using two insulator-embedded charged rings and a grounded conductor plate. We calculate Stark energy structure pattern of ND3 molecules in an external electric field using the method of matrix diagonalization. We analyze how the voltages that are applied to the ring electrodes affect the depth of the efficient well and the controllability of the distance between the trap center and the surface of the chip. To obtain a better understanding, we simulate the dynamical loading and trapping processes of ND3 molecules in a ｜J, KM = ｜1,-1 state by using classical Monte–Carlo method. Our study shows that the loading efficiency of our trap can reach ～ 88%. Finally, we study the adiabatic cooling of cold molecules in our surface trap by linearly lowering the potential-well depth（i.e., lowering the trapping voltage）, and find that the temperature of the trapped ND3 molecules can be adiabatically cooled from 34.5 m K to ～ 5.8 m K when the trapping voltage is reduced from-35 k V to-3 k V.

Electrostatic surface trap for cold polar molecules on a chip

We propose a simple scheme for trapping cold polar molecules in low-field seeking states on the surface of a chip by using a grounded metal plate and two finite-length charged wires that half embanked in an insulating substrate, calculate the electric field distributions generated by our charged-wire layout in free space and the corresponding Stark potentials for ND3 molecules, and analyze the dependence of the trapping center position on the geometric parameters. Moreover, the loading and trapping processes of cold ND3 molecules are studied by using the Monte Carlo method. Our study shows that the loading efficiency of the trap scheme can reach 11.5%, and the corresponding temperature of the trapped cold molecules is about 26.4 mK.

Broadband Vibrational Cooling of Cold Cesium Molecules： Theory and Experiments

The use of a broadband, frequency shaped femtosecond laser on translationally cold cesium molecules has recently demonstrated to be a very efficient method of cooling also the vibrational degree of freedom. A sample of cold molecules, initially distributed over several vibrational levels, has thus been transfered into a single selected vibrational level of the singlet X^1∑g ground electronic state. Our method is based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but limited in its frequency bandwidth with a spatial light modulator. In such a way we are able to eliminate transitions from the selected level, in which molecules accumulate. In this paper we briefly report the main experimental results and then address, in a detailed way by computer simulations, the perspectives for a ＂complete＂ cooling of the molecules, including also the rotational degree of freedom. Since the pumping process strongly depends on the relative shape of the ground and excited potential curves, ro-vibrational cooling through different excited states is theoretically compared.

Electrostatic surface guiding of cold polar molecules with a single charged wire

This paper proposes a scheme to guide cold polar molecules by using a single charged wire half embanked in an insulating substrate and a homogeneous bias electric field, which is generated by a plate capacitor composed of two infinite parallel metal plates. The spatial distributions of the electrostatic field produced by the combination of the charged wire and the plate capacitor and the corresponding Stark potentials （including dipole forces） for metastable CO molecules are calculated, the relationships between the electric field and the parameters of our charged-wire layout are analysed. It also studies the influences of the insulator on the electric field distribution and the discharge effect. This study shows that the proposed scheme can be used to guide cold polar molecules in the weak-field - seeking states, and to form various molecule-optical elements, such as molecular funnel, molecular beam-splitters and molecule interferometer, even to construct a variety of integrated molecule-optical elements and their molecule chips.

Novel electrostatic trap for cold polar molecules

We propose a novel scheme in which cold polar molecules are trapped by an electrostatic field generated by the combination of a pair of parallel transparent electrodes （i.e., two infinite transparent plates） and a ring electrode （i.e., a ring wire）. The spatial distributions of the electrostatic fields from the above charged wire and the charged plates and the corresponding Stark potentials for cold CO molecules are calculated; the dependences of the trap centre position on the geometric parameters of the electrode are analysed. We also discuss the loading process of cold molecules from a cold molecular beam into our trap. This study shows that the proposed scheme is not only simple and convenient to trap, manipulate and control cold polar molecules in weak-field-seeking states, but also provides an opportunity to study cold collisions and collective quantum effects in a variety of cold molecular systems, etc.

Microwave-mediated magneto-optical trap for polar molecules

Realizing a molecular magneto-optical trap has been a dream for cold molecular physicists for a long time. However,due to the complex energy levels and the small effective Lande g-factor of the excited states, the traditional magneto-optical trap（MOT） scheme does not work very well for polar molecules. One way to overcome this problem is the switching MOT,which requires very fast switching of both the magnetic field and the laser polarizations. Switching laser polarizations is relatively easy, but fast switching of the magnetic field is experimentally challenging. Here we propose an alternative approach, the microwave-mediated MOT, which requires a slight change of the current experimental setup to solve the problem. We calculate the MOT force and compare it with the traditional MOT and the switching MOT scheme. The results show that we can operate a good MOT with this simple setup.

Optical Stark deceleration of neutral molecules from supersonic expansion with a rotating laser beam

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 of20 k W in power focused into a pot of 40 μm in waist radius, ND3 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.

AC magnetic trap for cold paramagnetic molecules

Strong-field-seeking states are the lowest-energy configurations for paramagnetic molecules in the magnetic field.Molecules in strong-field-seeking states cannot be trapped in a magnetostatic field because a magnetostatic maximum in free space is not allowed.In this paper,we propose an AC magnetic trap composed of two pairs of Helmholtz coils.The spatial magnetic field distribution is numerically calculated and the time-sequential control is depicted.We investigate the influence of the switching frequency and the electric current in the coils on the performance of our trap.Variations of the location and phase-space distribution during a whole switching cycle are simulated.Finally,we study the impact of time during which the field is switched off on the number of captured molecules in a switching cycle.

Two-dimensional novel optical lattices with multi-well traps for cold atoms or molecules

We propose some new schemes to constitute two-dimensional （2D） array of multi-well optical dipole traps for cold atoms （or molecules） by using an optical system consisting of a binary 7r-phase grating and a 2D array of rectangle microlens. We calculate the intensity distribution of each optical well in 2D array of multi-well traps and its geometric parameters and so on. The proposed 2D array of multi-well traps can be used to form novel 2D optical lattices with cold atoms （or molecules）, and form various novel optical crystals with cold atoms （or molecules）, or to perform quantum computing and quantum information processing on an atom chip, even to realize an array of all-optical multi-well atomic （or molecular） Bose- Einstein condensates （BECs） on an all-optical integrated atom （or molecule） chip.

Disassociation of a one-dimensional cold molecule via quantum scattering

Motivated by the recent experimental developments in ultracold molecules and atoms,we propose a simple theoretical model to address the disassociation,reflection,and transmission probability of a one-dimensional cold molecule via quantum scattering.First,we show the Born approximation results in the weak interaction regime.Then,by employing the Lippmann-Schwinger equation,we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths.We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum.We expect that our model can be realized in experiments in the near future.

Saturated absorption spectroscopy of buffergas-cooled Barium monofluoride molecules

We report an experimental investigation on the Doppler-free saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride(BaF)molecules in a 4 K cryogenic cell.The obtained spectra with a resolution of 19 MHz,much smaller than previously observed in absorption spectroscopy,clearly resolve the hyperfine transitions.Moreover,we use these high-resolution spectra to fit the hyperfine splittings of excited A(v=0)state and find the hyperfine splitting of the laser-cooling-relevant A^(2)Π_(1/2)(v=0,J=1/2,+)state is about 18 MHz,much higher than the previous theoretically predicted value.This provides important missing information for laser cooling of BaF molecules.

Laser cooling of internal degrees of freedom of molecules

Optical pumping techniques using laser fields combined with photo-association of ultracold atoms leads to control of tile vibrational and/or rotational population of molecules. In this study, we review tile basic concepts and main steps that should be followed, including the excitation schemes and detection techniques used to achieve to-vibrational cooling of Cs2 molecules. We also discuss the extension of this technique to other molecules. In addition, we present a theoretical model used to support the experiment. These simulations can be widely used for the preparation of various experiments because they allow the optimization of several important experimental parmneters.

A driven three-dimensional electric lattice for polar molecules

Three-dimensional(3D)driven optical lattices have attained great attention for their wide applications in the quest to engineer new and exotic quantum phases.Here we propose a 3D driven electric lattice(3D-DEL)for cold polar molecules as a natural extension.Our 3D electric lattice is composed of a series of thin metal plates in which two-dimensional square hole arrays are distributed.When suitable modulated voltages are applied to these metal plates,a 3D potential well array for polar molecules can be generated and can move smoothly back and forth in the lattice.Thus,it can drive cold polar molecules confined in the 3D electric lattice.Theoretical analyses and trajectory calculations using two types of molecules,ND3 and PbF,are performed to justify the possibility of our scheme.The 3D-DEL offers a platform for investigating cold molecules in periodic driven potentials,such as quantum computing science,quantum information processing,and some other possible applications amenable to the driven optical lattices.

Laser cooling with adiabatic passage for type-Ⅱ transitions

We extend the idea of laser cooling with adiabatic passage to multi-level type-Ⅱ transitions.We find the cooling force can be significantly enhanced when a proper magnetic field is applied.That is because the magnetic field decomposes the multi-level system into several two-level sub-systems,hence the stimulated absorption and stimulated emission can occur in order,allowing for the multiple photon momentum transfer.We show that this scheme also works on the laser-coolable molecules with a better cooling effect compared to the conventional Doppler cooling.A reduced dependence on spontaneous emission based on our scheme is observed as well.Our results suggest this scheme is very feasible for laser cooling of polar molecules.

A versatile electrostatic trap with open optical access

A versatile electrostatic trap with open optical access for cold polar molecules in weak-field-seeking state is proposed in this paper. The trap is composed of a pair of disk electrodes and a hexapole. With the help of a finite element software, the spatial distribution of the electrostatic field is calculated. The results indicate that a three-dimensional closed electrostatic trap is formed. Taking NDa molecules as an example, the dynamic process of loading and trapping is simulated. The results show that when the velocity of the molecular beam is 10 m/s and the loading time is 0.9964 ms, the maximum loading efficiency reaches 94.25% and the temperature of the trapped molecules reaches about 30.3 inK. A single well can be split into two wells, which is of significant importance to the precision measurement and interference of matter waves. This scheme, in addition, can be further miniaturized to construct one-dimensional, two-dimensional, and three-dimensional spatial electrostatic lattices.