[Show abstract][Hide abstract] ABSTRACT: We propose a Gaussian Process (GP) model 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 accuracy of the resulting surfaces as a function of the number of {\it ab
initio} points. We show that the GP model based on 1800 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We show that a Gaussian Process model can be combined with a small number of
scattering calculations to provide an accurate multi-dimensional dependence of
scattering observables on the experimentally controllable parameters (such as
the collision energy, temperature or external fields) as well as the potential
energy surface parameters. This can be used for solving the inverse scattering
problem, the prediction of collision properties of a specific molecular system
based on the information for another molecule, the efficient calculation of
thermally averaged observables and for reducing the error of the molecular
dynamics calculations by averaging over the potential energy surface
variations. We show that, trained by a combination of classical and quantum
dynamics calculations, the model provides an accurate description of the
scattering cross sections, even near scattering resonances. In this case, the
classical calculations stabilize the model against uncertainties arising from
wildly varying correlations of resonantly enhanced quantum results.
[Show abstract][Hide abstract] ABSTRACT: 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. We show that for realistic experimental
parameters this specific 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 concentrations $\leq 90
\%$, the rotational excitations generated in the middle of the lattice diffuse
to the edges of the lattice. We observe that the diffusion of rotational
excitations in highly disordered 2D and 3D lattices has three distinct time
scales. At short times, the rotational excitations diffuse as quantum particles
expanding ballistically. At later times, the diffusion character changes to be
the same as for the classical particles in Brownian motion. At still later
times, the rotational excitations transition to a sub-diffusive regime. While
the ballistic expansion is brief ($\sim 10$ ms), the classical-like diffusion
can last as long as 200-300 ms. We also 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.
New Journal of Physics 01/2015; 17(6). DOI:10.1088/1367-2630/17/6/065014 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use classical trajectory calculations to study the effects of the interaction strength and the geometry of rigid polyatomic molecules on the formation of long-lived collision complexes at low collision energies. We first compare the results of the calculations for collisions of benzene molecules with rare gas atoms He, Ne, Ar, Kr, and Xe. The comparison illustrates that the mean lifetimes of the collision complexes increase monotonically with the strength of the atom-molecule interaction. We then compare the results of the atom-benzene calculations with those for benzene-benzene collisions. The comparison illustrates that the mean lifetimes of the benzene-benzene collision complexes are significantly reduced due to non-ergodic effects prohibiting the molecules from sampling the entire configuration space. We find that the thermally averaged lifetimes of the benzene-benzene collisions are much shorter than those for Xe with benzene and similar to those for Ne with benzene.
The Journal of Chemical Physics 10/2014; 141(16):164315. DOI:10.1063/1.4898796 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We explore the collision dynamics of complex hydrocarbon molecules (benzene, coronene, adamantane, and anthracene) containing carbon rings in a cold buffer gas of (3)He. For benzene, we present a comparative analysis of the fully classical and fully quantum calculations of elastic and inelastic scattering cross sections at collision energies between 1 and 10 cm(-1). The quantum calculations are performed using the time-independent coupled channel approach and the coupled-states approximation. We show that the coupled-states approximation is accurate at collision energies between 1 and 20 cm(-1). For the classical dynamics calculations, we develop an approach exploiting the rigidity of the carbon rings and including low-energy vibrational modes without holonomic constraints. Our results illustrate the effect of the molecular shape and the vibrational degrees of freedom on the formation of long-lived resonance states that lead to low-temperature clustering.
The Journal of Chemical Physics 09/2014; 141(10):104317. DOI:10.1063/1.4894793 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Magnetic Feshbach resonances play a central role in experimental research on atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali metal molecules in the ground rovibrational state of the ground electronic 1Σ state. Unlike alkali metal atoms, 1Σ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for 1Σ molecules may exceed 1 mG, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.
Physical Review A 02/2014; 89(3). DOI:10.1103/PhysRevA.89.032716 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that the interaction of polar alkali-metal dimers in the quintet spin state leads to the formation of a deeply bound reaction complex. The reaction complex can decompose adiabatically into homonuclear alkali-metal dimers (for all molecules except KRb) and into alkali-metal trimers (for all molecules). We show that there are no barriers for these chemical reactions. This means that all alkali-metal dimers in the a^{3}Σ^{+} state are chemically unstable at ultracold temperature, and the use of an optical lattice to segregate the molecules and suppress losses may be necessary. In addition, we calculate the minimum-energy path for the chemical reactions of alkali-metal hydrides. We find that the reaction of two molecules is accelerated by a strong attraction between the alkali-metal atoms, leading to a barrierless process that produces hydrogen atoms with large kinetic energy. We discuss the unique features of the chemical reactions of ultracold alkali-metal dimers in the a^{3}Σ^{+} electronic state.
Physical Review A 11/2013; 88(5). DOI:10.1103/PhysRevA.88.050701 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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$^{-1}$.
Physical Review A 08/2013; 88(4). DOI:10.1103/PhysRevA.88.042705 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The goal of the present article is to review the major developments that have
led to the current understanding of molecule-field interactions and
experimental methods for manipulating molecules with electromagnetic fields.
Molecule-field interactions are at the core of several, seemingly distinct,
areas of molecular physics. This is reflected in the organization of this
article, which includes sections on Field control of molecular beams, External
field traps for cold molecules, Control of molecular orientation and molecular
alignment, Manipulation of molecules by non-conservative forces, Ultracold
molecules and ultracold chemistry, Controlled many-body phenomena, Entanglement
of molecules and dipole arrays, and Stability of molecular systems in
high-frequency super-intense laser fields. The article contains 853 references.
[Show abstract][Hide abstract] ABSTRACT: We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. We then show that ultracold molecules trapped in optical lattices can be used as a quantum simulator to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields. The parameters of current experiments place them in the region where one of the transitions occurs. We also propose a scheme to measure the polaron dispersion using stimulated Raman spectroscopy.
[Show abstract][Hide abstract] ABSTRACT: An elementary excitation in an aggregate of coupled particles generates a
collective excited state. We show that the dynamics of these excitations can be
controlled by applying a transient external potential which modifies the phase
of the quantum states of the individual particles. The method is based on an
interplay of adiabatic and sudden time scales in the quantum evolution of the
many-body states. We show that specific phase transformations can be used to
accelerate or decelerate quantum energy transfer and spatially focus
delocalized excitations onto different parts of arrays of quantum particles. We
consider possible experimental implementations of the proposed technique and
study the effect of disorder due to the presence of impurities on its fidelity.
We further show that the proposed technique can allow control of energy
transfer in completely disordered systems.
New Journal of Physics 09/2012; 15(6). DOI:10.1088/1367-2630/15/6/063015 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of nondegenerate 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.
Physical Review A 08/2012; 86(2). DOI:10.1103/PhysRevA.86.022703 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using a 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 nonadiabatically 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.
[Show abstract][Hide abstract] ABSTRACT: We show that the cross sections for molecule-molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for (15)NH-(15)NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground (15)NH molecules in a magnetic trap has a prospect of success.
The Journal of Chemical Physics 07/2012; 137(2):024103. DOI:10.1063/1.4733288 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Magnetic Feshbach scattering resonances play a central role in
experimental research of atomic gases at ultracold temperatures. A major
thrust of current research is to create an ultracold gas of diatomic
alkali-metal molecules in the ground rovibrational state of the ground
electronic ^1σ state. Can ultracold ^1σ molecules be
controlled by means of magnetic Feshbach resonances? Unlike alkali metal
atoms, ^1σ diatomic molecules have no unpaired electrons. The
response of ^1σ molecules to an external magnetic field is
determined entirely by the spin structure of the atomic nuclei. We
present the first calculations of molecule-molecule collisions for
^1σ molecules in a magnetic field. In particular, we calculate the
rates of hyperfine relaxation in molecule - molecule collisions and
explore the possibility of tuning magnetic Feshbach resonances in an
ultracold gas of ^87Rb^133Cs(X^1&+circ;) molecules.
[Show abstract][Hide abstract] ABSTRACT: Rotational excitation of ultracold polar molecules trapped on an optical
lattice produces rotational Frenkel excitons (collective rotational
excitations) [1]. We show that non-linear interactions between these
excitons can be tuned by applying a dc electric field. We show that, at
electric fields greater than a critical value, rotational Frenkel
excitons form bound pairs -- biexcitons [2]. Frenkel biexcitons are
strongly correlated states of two collective excitations in a molecular
crystal, which are exceedingly hard to create and observe in solid-state
crystals. We demonstrate that the binding energy of the rotational
biexcitons can be controlled by tuning the angle between the applied
field and the molecular array. Frenkel biexcitons can be used for many
applications ranging from the controlled preparation of entanglement
between quasi-particles to the study of bipolarons. [4pt] [1] ``Frenkel
biexcitons in optical lattices with polar molecules,'' Ping Xiang, M.
Litinskaya, R. V. Krems; cond-mat/1112.3942. [0pt] [2] ``Tunable
disorder in a crystal of cold polar molecules,'' F. Herrera, M.
Litinskaya, R. V. Krems, Phys. Rev. A 82, 033428 (2010).