arXiv subjects

Ryan M. Wilson

Publications and source records attributed to Ryan M. Wilson.

At least 19 recordsLinked to original sources

arXiv2020

Bogoliubov theory of a Bose-Einstein condensate of rigid rotor molecules

We consider a BEC of rigid rotor molecules confined to quasi-2d through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipole-dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules "tilt". The character of these instabilities is clarified by means of momentum-space density-density structure factors. A peak at zero momentum in the spin-spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability.

cond-mat.quant-gas↗

arXiv2017

Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems

We study theoretically and experimentally the competing blockade and anti-blockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system's behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qualitative agreement with previous experimental results. We further predict that as the atomic density is increased, the Rydberg population's dependence on Rabi frequency will transition from quadratic to linear dependence at lower Rabi frequencies. We study this behavior experimentally by observing this crossover at two different atomic densities. We confirm that the larger density system has a smaller crossover Rabi frequency than the smaller density system. The second theoretical approach is a set of phenomenological inhomogeneous rate equations. We compare the results of our rate equation model to the experimental observations in [E. A. Goldschmidt, et al., PRL 116, 113001 (2016)] and find that these rate equations provide quantitatively good scaling behavior of the steady-state Rydberg population for both resonant and off-resonant drive.

quant-ph↗

arXiv2017

Gutzwiller Monte Carlo approach for a critical dissipative spin model

We use the Gutzwiller Monte Carlo approach to simulate the dissipative XYZ-model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior, while neglecting non-local quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to describe critical behavior which is completely missed by the widely applied Gutzwiller decoupling of the density matrix.

quant-ph↗

arXiv2016

Emergent equilibrium in many-body optical bistability

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

quant-ph↗

arXiv2016

Collective phases of strongly interacting cavity photons

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

quant-ph↗

arXiv2016

Anomalous supersolidity in a weakly interacting dipolar Bose mixture on a square lattice

We calculate the mean-field phase diagram of a zero-temperature, binary Bose mixture on a square optical lattice, where one species possesses a non-negligible dipole moment. Remarkably, this system exhibits supersolidity for anomalously weak dipolar interaction strengths, which are readily accessible with current experimental capabilities. The supersolid phases are robust, in that they occupy large regions in the parameter space. Further, we identify a first-order quantum phase transition between supersolid and superfluid phases. Our results demonstrate the rich features of the dipolar Bose mixture, and suggest that this system is well-suited for exploring supersolidity in the experimental setting.

cond-mat.quant-gas↗

arXiv2015

Resonant wavepackets and shock waves in an atomtronic SQUID

The fundamental dynamics of ultracold atomtronic devices are reflected in their phonon modes of excitation. We probe such a spectrum by applying a harmonically driven potential barrier to a $^{23}$Na Bose-Einstein condensate in a ring-shaped trap. This perturbation excites phonon wavepackets. When excited resonantly, these wavepackets display a regular periodic structure. The resonant frequencies depend upon the particular configuration of the barrier, but are commensurate with the orbital frequency of a Bogoliubov sound wave traveling around the ring. Energy transfer to the condensate over many cycles of the periodic wavepacket motion causes enhanced atom loss from the trap at resonant frequencies. Solutions of the time-dependent Gross-Pitaevskii equation exhibit quantitative agreement with the experimental data. We also observe the generation of supersonic shock waves under conditions of strong excitation, and collisions of two shock wavepackets.

cond-mat.quant-gas↗

arXiv2015

Two-state Bogoliubov theory of a molecular Bose gas

We present an analytic Bogoliubov description of a BEC of polar molecules trapped in a quasi-2D geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and dynamic structure factors. This method can be applied to any homogeneous, two-component system with linear coupling, and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. These instabilities are clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave response in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $Λ$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$Σ$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.

cond-mat.quant-gas↗

arXiv2015

Beliaev damping in quasi-2D dipolar condensates

We study the effects of quasiparticle interactions in a quasi-two dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly non-trivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, the low energy phonons experience no damping, and the higher energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. Further, we find a qualitative anisotropy in the damping rates when the dipoles are tilted off the axis of symmetry. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and non-equilibrium dynamics in these systems.

cond-mat.quant-gas↗

arXiv2014

Half-Quantum Vortex Molecules in a Binary Dipolar Bose Gas

We study the ground state phases of a rotating two-component, or binary Bose-Einstein condensate, wherein one component possesses a large magnetic dipole moment. A variety of non-trivial phases emerge in this system, including a half-quantum vortex (HQV) chain phase and a HQV molecule phase, where HQVs of opposite charge bind at short distances. We attribute the emergence of these phases to the development of a minimum in the adiabatic HQV interaction potential, which we calculate explicitly. We thus show that the presence of dipolar interactions in this system leads to a rich phase diagram, and the formation of HQV molecules.

cond-mat.quant-gas↗

arXiv2013

Spin Waves and Dielectric Softening of Polar Molecule Condensates

We consider an oblate Bose-Einstein condensate of heteronuclear polar molecules in a weak applied electric field. This system supports a rich quasiparticle spectrum that plays a critical role in determining its bulk dielectric properties. In particular, in sufficiently weak fields the system undergoes a polarization wave rotonization, leading to the development of textured electronic structure and a dielectric instability that is characteristic of the onset of a negative static dielectric function.

cond-mat.quant-gas↗

arXiv2013

Meron Ground State of Rashba Spin-Orbit-Coupled Dipolar Bosons

We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.

cond-mat.quant-gas↗

arXiv2013

Landau damping in a collisionless dipolar Bose gas

We present a theory for the Landau damping of low energy quasi-particles in a collisionless, quasi-2D dipolar Bose gas and produce expressions for the damping rate in uniform and non-uniform systems. Using simple energy-momentum conservation arguments, we show that in the homogeneous system, the nature of the low energy dispersion in a dipolar Bose gas severely inhibits Landau damping of long wave-length excitations. For a gas with contact and dipolar interactions, the damping rate for phonons tends to decrease with increasing dipolar interactions; for strong dipole-dipole interactions, phonons are virtually undamped over a broad range of temperature. The damping rate for maxon-roton excitations is found to be significantly larger than the damping rate for phonons.

cond-mat.quant-gas↗

arXiv2013

Geometric Stability Spectra of Dipolar Bose Gases in Tunable Optical Lattices

We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the features emerge only when the polarization axis is tilted into the plane of the condensate. Our results suggest that the stability diagram may be used as a novel means to spectroscopically measure rotons in dipolar condensates.

cond-mat.quant-gas↗

arXiv2013

Stability Spectroscopy of Rotons in a Dipolar Bose Gas

We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate (dBEC) that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.

cond-mat.quant-gas↗

arXiv2012

Roton immiscibility in a two-component dipolar Bose gas

We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a roton-like IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled non-local Gross-Pitaevskii equations.

cond-mat.quant-gas↗

arXiv2012

A Dielectric Superfluid of Polar Molecules

We show that, under achievable experimental conditions, a Bose-Einstein condensate (BEC) of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasiparticle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.

cond-mat.quant-gas↗

arXiv2010

Emergent structure in a dipolar Bose gas in a one-dimensional lattice

We consider an ultracold dipolar Bose gas in a one-dimensional lattice. For a sufficiently large lattice recoil energy, such a system becomes a series of non-overlapping Bose-Einstein condensates that interact via the long-range dipole-dipole interaction (ddi). We model this system via a coupled set of non-local Gross-Pitaevskii equations (GPEs) for lattices of both infinite and finite extent. We find significantly modified stability properties in the lattice due to the softening of a discrete roton-like mode, as well as "islands" in parameter space where biconcave densities are predicted to exist that only exist in the presence of the other condensates on the lattice. We solve for the elementary excitations of the system to check the dynamical stability of these solutions and to uncover the nature of their collapse. By solving a coupled set of GPEs exactly on a full numeric grid, we show that this emergent biconcave structure can be realized in a finite lattice with atomic $^{52}$Cr.

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