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arXiv:1212.3042 · Physical Review A

Molecular Hubbard Hamiltonian: Field regimes and molecular species

Michael L. Wall, E. Bekaroglu, Lincoln D. Carr

Published Aug 12, 2013• 19 citations
arXivHTMLPDF

Abstract

The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground-state polar alkali-metal dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to intrinsic variances in molecular structure even when the molecular symmetry is the same. We also demonstrate a wide variety of experimental controls on ${}^{1}\ensuremath{\Sigma}$ molecules via external fields, including applied static electric and magnetic fields, an ac microwave field, and the polarization and strength of optical lattice beams. We provide explicit numerical calculations of the parameters of the MHH, including tunneling and direct and exchange dipole-dipole interaction energies, for the molecules ${}^{6}$Li${}^{133}$Cs, ${}^{23}$Na${}^{40}$K, ${}^{87}$Rb${}^{133}$Cs, ${}^{40}$K${}^{87}$Rb, and ${}^{6}$Li${}^{23}$Na in weak and strong applied electric fields. As case studies of many-body physics, we use infinite-size matrix product state methods to explore the quantum phase transitions from the superfluid phase to half-filled and third-filled crystalline phases in one dimension.

DOI
10.1103/physreva.88.023605

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The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground-state polar alkali-metal dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to intrinsic variances in molecular structure even when the molecular symmetry is the same. We also demonstrate a wide variety of experimental controls on 1\ensuremathΣ{}^{1}\ensuremath{\Sigma}1\ensuremathΣ molecules via external fields, including applied static electric and magnetic fields, an ac microwave field, and the polarization and strength of optical lattice beams. We provide explicit numerical calculations of the parameters of the MHH, including tunneling and direct and exchange dipole-dipole interaction energies, for the molecules 6{}^{6}6Li133{}^{133}133Cs, 23{}^{23}23Na40{}^{40}40K, 87{}^{87}87Rb133{}^{133}133Cs, 40{}^{40}40K87{}^{87}87Rb, and 6{}^{6}6Li23{}^{23}23Na in weak and strong applied electric fields. As case studies of many-body physics, we use infinite-size matrix product state methods to explore the quantum phase transitions from the superfluid phase to half-filled and third-filled crystalline phases in one dimension.
An ultracold gas of heteronuclear alkali-metal dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The hyperfine molecular Hubbard Hamiltonian (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long-range dipole-dipole forces in a dc electric field and allows for transitions between rotational states in an ac microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the dc electric and magnetic fields and the strength of the ac field, it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state.
Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic states, 36 alkali-metal--alkaline-earth-metal molecules in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.
Strongly interacting ultracold dipolar molecules are a rich platform for quantum information and quantum simulation of phenomena relevant to condensed matter systems. This dissertation presents novel theoretical and computational studies of ultracold dipolar molecules relevant to these areas in three broad categories.First, the path integral ground state quantum Monte Carlo method is extended to simulations with both translational and rotational degrees of freedom, including the development of a novel estimator of the elementary excitation energies of a system with these degrees of freedom based on the well known Feynman-Bijl approximation. This is then used to study dipolar molecular ensembles confined to one-dimensional optical lattices. The ground state phase diagram is characterized with both a mean-field method and the aforementioned quantum Monte Carlo method. A quantum phase transition is found for very short optical lattice spacings or very large dipole moments. The prospects for experimentally realizing a system which exhibits this phase transition are discussed.Second, the path integral ground state quantum Monte Carlo method is utilized to study the ground state of dipole molecules confined to two-dimensional optical lattices. On square lattices a crossover from a weakly interacting disordered phase to a strongly interacting striped phase is found for short lattice spacings or large dipole moments. On triangular lattices a crossover between a disordered phase and a completely polarized phase is found, also for short lattice spacings or large dipole moments. The relevance of such simulations to self-assembled dipolar crystals in two dimensions is discussed and simulation results of these systems are presented. Simulations of polarized and harmonically confined molecular systems in two dimensions with translations and rotations are also presented and a realistic interaction potential using highly accurate ab initio quantum chemistry techniques is calculated for LiH--LiH interactions as a preliminary step toward developing a high quality trial wave function for the simulation of systems possessing both translational and rotational degrees of freedom.Finally, several novel applications for dipolar molecules confined to optical lattices are proposed. An experimental realization of a topological phase using 2Sigma^2\\Sigma2Sigma ground state molecules with applied near resonant microwave fields and transverse magnetic fields is proposed. A method to create an array of dipole-coupled two-level molecules exhibiting superradiance and possessing novel spectroscopic properties using 1Sigma^1\\Sigma1Sigma ground state molecules in the combination of a far off-resonant laser field and a moderate magnetic field is proposed. Additionally, a method to create entangled pairs of molecules using closed-shell dipolar molecules immersed in an intense far off-resonant laser field is reviewed and an extension in which parallel optical lattices are merged and molecules are allowed to collide in the presence of a far off-resonant laser field is proposed. Simulation results are presented indicating that a significant amount of entanglement may be generated in such a way in realistic molecular systems.
Ultracold molecules are expected to find applications in cold chemistry, quantum phases, precision measurements and quantum information. In this thesis three novel applications of cold molecules are studied. First the thesis presents a general method for coherent control of collisions between non-identical particles. It is shown that by preparing two alkali-metal atoms in a superposition of hyperfine states, the elastic-to-inelastic cross section ratio can be manipulated at ultracold temperatures by tuning laser parameters in the presence of a magnetic field. The static field is needed to induce quantum interference between scattering states. Extensions of this scheme for ultracold molecular reactive scattering are discussed. Second, the thesis describes rotational excitons and polarons in molecular ensembles trapped in optical lattices. Rotational excitons can be manipulated using static electric and magnetic fields. For a one-dimensional molecular array with substitutional impurities any localized exciton state can be delocalized by applying a suitable electric field. The electric field induces correlations between diagonal and off-diagonal disorder. It is also shown that the translational motion of polar molecules in an optical lattice can lead to phonons. The lattice dynamics and the phonon spectrum depend on the strength and orientation of a static electric field. An array of polar molecules in an optical lattice can be described by generalized polaron model with tunable parameters including diagonal and off-diagonal exciton-phonon interactions. It is shown that in a strong electric field the system is described by a generalized Holstein model, and at weak electric fields by the Su-Schrieffer-Heeger (SSH) model. The possibility of observing a sharp polaron transition in the SSH model using polar alkali-metal dimers is discussed. Finally, the thesis presents a method to generate entanglement of polar molecules using strong off-resonant laser pulses. Bipartite entanglement between alkali-metal dimers separated by hundreds of nanometers can be generated. Maximally entangled states can be prepared by tuning the pulse intensity and duration. A scheme is proposed to observe the violation of Bell’s inequality based on molecular orientation correlation measurements. It is shown that using a combination of microwave and off-resonant optical pulses, arbitrary tripartite and many-particle states can be prepared.