Session X27: Dipolar Interactions in Ultracold Gases

Pairing superfluidty in a Weyl semimetal with dipolar interaction

We study the topological superfluid phase of a three-dimensional Weyl semimetal realized in a single-component dipolar Fermi gas. The system is constructed by employing both the nearest and second-nearest hopping, and generating periodic gauge potentials in an anisotropic cubic lattice. By calculating the superfluid pairing induced by dipole-dipole interaction, we determine the phase diagram of this system and obtained many novel properties.   

Dipolar lattice bosons in the presence of long-range hopping

We report on numerical results based on quantum Monte Carlo simulations of a system of two-dimensional hard-core lattice bosons in the presence of long-range hopping and long-range two-body interactions resulting from dipole-dipole interactions. This is equivalent to the XXZ model in the presence of dipolar interactions which can be realized by a lattice gas of polar molecules, creating a flexible platform for the study of quantum magnetism. The system features three phases: a superfluid, a supersolid, and a checkerboard solid. Next we mimic the current experimental conditions, that is a lattice of polar molecules away from unit filling, by adding static disorder. Under these conditions we study the localization of particles and the stabilization of a disorder-induced insulating phase.   

Developments in driving atomic transitions using the ponderomotive interaction

We describe recent developments in a novel spectroscopic method that couples Rydberg states using an intensity-modulated optical lattice. The method is fundamentally different from traditional microwave spectroscopy: it engages the $\mathbf{A} \cdot \mathbf{A}$ (ponderomotive) term rather than the $\mathbf{A} \cdot \mathbf{p}$ term of the atom-field interaction Hamiltonian. The method allows us to drive GHz-frequency transitions between Rydberg states with optical spatial resolution and is not subject to the usual electric-dipole selection rules (i.e., higher-order multipole transitions are driven in first-order time-dependent perturbation)\footnote{K.R. Moore, S.E. Anderson, and G. Raithel, \textbf{Nat. Comm.} 6, 6090 (2015)},\footnote{K.R. Moore and G. Raithel, \textbf{Phys. Rev. Lett.}, 115, 163003 (2015)},\footnote{B. Knuffman and G. Raithel, \textbf{Phys. Rev. A}, 75, 053401, (2007)}. We review our previous experimental results using cold atoms, including an extension of this method into the near-sub-THz regime via modulation harmonics. We present new theoretical results showing extensions of this method to odd-parity transitions. Finally, we discuss the proposed application of this method to a precision measurement of the Rydberg constant using circular-state Rydberg atoms.   

Heat Transfer Through Dipolar Coupling: Sympathetic cooling without contact

We consider two parallel layers of dipolar ultracold gases at different temperatures and calculate the heat transfer through dipolar coupling. As the simplest model we consider a system in which both of the layers contain two-dimensional spin-polarized Fermi gases. The effective interactions describing the correlation effects and screening between the dipoles are obtained by the Euler-Lagrange Fermi-hypernetted-chain approximation in a single layer. We use the random-phase approximation (RPA) for the interactions across the layers. We find that heat transfer through dipolar coupling becomes efficient when the layer separation is comparable to dipolar interaction length scale. We characterize the heat transfer by calculating the time constant for temperature equilibration between the layers and find that for the typical experimental parameter regime of dipolar molecules this is on the order of milliseconds. We generalize the initial model to Boson-Boson and Fermion-Boson layers and suggest that contactless sympathetic cooling may be used for ultracold dipolar molecules.   

Finite Temperature RPA Calculations of 2D Dipolar Bosons at Arbitrary Tilt Angles

We present finite-T Random Phase Approximation (RPA) calculations on a system of 2D dipolar bosons, with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane. Our calculations are done over a wide range of density, temperature, and dipolar strength, for various dipolar tilt angles. For a given temperature, we find the system to be in a quasi-condensate phase, which undergoes a collapse transition at large tilt angles, and a finite momentum instability, signaling a striped phase, at sufficiently large values of dipolar coupling strength. Within RPA, we also consider the effect of additional repulsive and attractive contact interactions. Finally, we explore the effect of a trap on the 2D system. We construct phase diagrams depicting the phases and instabilities. We discuss how our results may apply to ultracold dense Bose gas of polar molecules, such as $^{41}$K$^{87}$Rb, that has been realized experimentally.   

Dynamics of correlations in long-range quantum systems follwing a quantum quench

We study how and how fast correlations can spread in a quantum system abruptly driven out of equilibrium by a quantum quench. This protocol can be experimentally realized and it allow to address fundamental questions concerning the quasi-locality principle in isolated quantum systems with both short- and long-range interactions. We focus on two different models describing, respectively, lattice bosons, and spins. Our study is based on a combined approach, based on one hand on accurate many-body numerical calculations and on the other hand on a quasi-particle microscopic theory. We find that, for sufficiently fast decaying interaction potential the propagation is ballistic and the Lieb-Robinson bounds for long-range interactions are never attained. When the interactions are really long-range, the scenario is completely different in the two cases. In the bosonic system the locality is preserved and a ballistic propagation is still present while in the spin system an instantaneous propagation of correlations completely destroys locality. Using the microscopic point of view we can quantitatively describe all the different regimes, from instantaneous to ballistic, found in the spin model and we explain how locality is protected in the bosonic model leading to a ballistic propagation.   

Assessing approximations to spin dynamics using a geometric representation of spin correlations

We have developed a geometric way to visualize spin correlations, including their dynamical evolution. Phenomena that look complicated and mysterious when analyzed by the components of their correlations become simple and intuitive when described geometrically. We will describe how this geometric representation provides insight into the accuracy of various approximations to the dynamics, such as truncated Wigner approximations.   

Geometric interpretation of spin correlations and applications to ultracold physics

Abstract: We develop a general method to visualize spin correlations and demonstrate its broad usefulness for different models realized in ultracold matter, from fermions in lattices to trapped ions and ultracold molecules. We provide a one-to-one map between the spin correlations and certain three-dimensional objects, analogous to the map between single spins and Bloch vectors. This makes the geometric structure of the correlations manifest. Moreover, much as one can reason geometrically about dynamics using a Bloch vector -- e.g. a magnetic field causes it to precess and dephasing causes it to shrink -- we show that analogous reasoning holds for our visualization of correlations for real physical spin models. Applying this to ultracold matter, we find that seemingly mysterious and complicated dynamics becomes straightforward to understand in this representation.   

Enhanced fractal dynamics of a BEC induced by dipolar interactions

The escape dynamics of a Bose-Einstein condensate (BEC) from a potential well are studied computationally. Previous studies based on the Nonlinear Schr\"{o}dinger / Gross-Pitaevskii (NLS-GP) equation have predicted the fractal nature of the escaping flux. In attractive BECs (focusing NLS), the wave packet can undergo collapse. The effects of dipolar interactions suppress this collapse while also mitigating the wave packet's dispersion, resulting in enhanced fractal dynamics. This is joint work with Boaz Ilan and Kevin Mitchell.   

Casimir forces between two impurities in a lattice

One of the fundamental properties of matter is the Casimir force, i.e. interaction of classical objects via quantum fluctuations. It appears in various field, including optics, Bose-condensates, micro-structure geometry compounds, etc. The usual wisdom is that the Casimir force between two atoms decays as $r^{-(2D+1)}$, which is originated from the two boson exchange in the lowest order of the perturbation theory. Stimulated by the recent experiments on the high temperature superconductor H$_3$S under high pressure, we reconsider the Casimir forces between two impurities in solid state physics via virtual phonons at long and short distances. We found strong deviation from the standard law at short distances which depends on the masses of impurities atoms. At long distances it comes to the standard $r$-dependence, but the value of the prefactor is much larger than it's expected from the lowest orders of the perturbation theory. These differences become important when the impurity masses differ from the lattice atoms more than twice. Finally we apply our results to impurity atoms of deuterium and tritium in H$_3$S.   

Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface

Fluctuation induced interactions become most prominent in close to proximity to surfaces. Examples include van der Waals and Casimir forces. In this talk, we consider the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) interaction with a gently curved dielectric surface at sub-micron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of temperature, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural line widths and thermal broadening.