Greatly enhanced absorption of non-resonant microwave fields by ultracold molecules near a Feshbach resonance

We show that the probability of the collision-induced absorption of non-resonant microwave photons by a gas of ultracold molecules is dramatically enhanced near a Feshbach scattering resonance. This can be used for detecting Feshbach resonances of ultracold molecules by measuring the microwave field absorption and for tuning the elastic scattering cross sections of ultracold molecules by varying the frequency and intensity of the microwave field in a wide range of the field parameters

Quantum walk and Anderson localization of rotational excitations in disordered ensembles of polar molecules

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale $t \sim 1$ sec. For 3D lattices with $55$ sites in each dimension and vacancy concentration $90~\%$, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2. Our results raise a general question whether quantum particles with long-range tunnelling can undergo quantum localization in 3D lattices with substitutional disorder

Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with Gaussian processes

We explore the performance of a statistical learning technique based on Gaussian Process (GP) regression as an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PES) for polyatomic molecules. Using an example of the molecule N$_4$, we show that a realistic GP model of the six-dimensional PES can be constructed with only 240 potential energy points. We construct a series of the GP models and illustrate the convergence of the accuracy of the resulting surfaces as a function of the number of ${\it ab \ initio}$ points. We show that the GP model based on $\sim 1500$ potential energy points achieves the same level of accuracy as the conventional regression fits based on 16,421 points. The GP model of the PES requires no fitting of ${\it ab \ initio}$ data with analytical functions and can be readily extended to surfaces of higher dimensions.Comment: 2 figure

Controlling collisional decoherence of ultracold molecules in superposition states by an external magnetic field

We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of non-degenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states exhibiting Feshbach resonances

Rotational excitations of polar molecules on an optical lattice: from novel exciton physics to quantum simulation of new lattice models

Ultracold polar molecules trapped on an optical lattice is a many-body system that, under appropriate conditions, may support collective excitations reminiscent of excitons in solid state crystals. Here, we discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. We show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential. The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. As an example, we discuss the possibility of engineering the Holstein model with polar molecules on an optical lattice.Comment: 28 pages, 7 figure

Elastic and inelastic collisions of 2Σ^2\Sigma molecules in a magnetic field

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2\Sigma$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2\Sigma$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic cross section ratios under conditions corresponding to trapped molecular ensembles at $T \sim 10^{-3}$ K exceed 100 for the majority of $^2\Sigma$ molecules. The range of $^2\Sigma$ molecules expected to be collisionally unstable in magnetic traps at $T < 10^{-3}$ K is limited to molecules with the spin-rotation interaction constant $\gamma_{\rm SR} > 0.5$ cm$^{-1}$ and the rotational constant $B_e < 4$ cm$^{-1}$

Tuning bimolecular chemical reactions by electric fields

We develop a theoretical method for solving the quantum mechanical reactive scattering problem in the presence of external fields based on a hyperspherical coordinate description of the reaction complex combined with the total angular momentum representation for collisions in external fields. The method allows us to obtain converged results for the chemical reaction LiF + H -> Li + HF in an electric field. Our calculations demonstrate that, by inducing couplings between states of different total angular momenta, electric fields with magnitudes <150 kV/cm give rise to resonant scattering and a significant modification of the total reaction probabilities, product state distributions and the branching ratios for reactive vs inelastic scattering.Comment: 11 pages, 8 figures, including the Supplemental Materia

Gaussian Process Model for Collision Dynamics of Complex Molecules

We show that a Gaussian Process model can be combined with a small number (of order 100) of scattering calculations to provide a multi-dimensional dependence of scattering observables on the experimentally controllable parameters such as the collision energy or temperature) as well as the potential energy surface (PES) parameters. For the case of Ar - C$_6$H$_6$ collisions, we show that 200 classical trajectory calculations are sufficient to provide a 10-dimensional hypersurface, giving the dependence of the collision lifetimes on the collision energy, internal temperature and 8 PES parameters. This can be used for solving the inverse scattering problem, the efficient calculation of thermally averaged observables, for reducing the error of the molecular dynamics calculations by averaging over the PES variations, and the analysis of the sensitivity of the observables to individual parameters determining the PES.Trained by a combination of classical and quantum calculations, the model provides an accurate description of the quantum scattering cross sections, even near scattering resonances.Comment: 3 figure

Gaussian Process Model for Extrapolation of Scattering Observables for Complex Molecules: from Benzene to Benzonitrile

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the $-$H $\rightarrow$ $-$X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values that corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C$_6$H$_5$CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He - C$_6$H$_6$ collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C$_6$H$_5$CN with He.Comment: 7 figure

Non-adiabatic preparation of spin crystals with ultracold polar molecules

We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using dipole blockade of microwave excitations, we map the system onto an interacting spin-1/2 model possessing ground states with crystalline order, and describe a way to prepare these states by non-adiabatically driving the transitions between molecular rotational levels. The proposed technique bypasses the need to cross a phase transition and allows for the creation of ordered domains of considerably larger size compared to approaches relying on adiabatic preparation.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let