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Lincoln D. Carr

Publications and source records attributed to Lincoln D. Carr.

At least 91 records · Page 5Linked to original sources
arXiv2012

Nonlinear Scattering of a Bose-Einstein Condensate on a Rectangular Barrier

We consider the nonlinear scattering and transmission of an atom laser, or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several new physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark soliton train from a phonon-like standing wave.

cond-mat.quant-gas↗
arXiv2012

Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality

Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical, and that do not have a simple description in terms of weakly interacting quasi-particles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by more than 20 orders of magnitude in temperature, but they were shown to exhibit very similar hydrodynamic flow. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and it also serves as an introduction to the Focus Issue of New Journal of Physics on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas. The presentation is made accessible to the general physics reader and includes discussions of the latest research developments in all three areas.

hep-th↗
arXiv2012

Out of equilibrium dynamics with Matrix Product States

Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states called Matrix Product States (MPSs). However, DRMG suffers from inherent accuracy restrictions when multiple states are involved due to multi-state targeting and also the approximate representation of the Hamiltonian and other operators. By formulating the variational approach of DMRG explicitly for MPSs one can avoid errors inherent in the multi-state targeting approach. Furthermore, by using the Matrix Product Operator (MPO) formalism, one can exactly represent the Hamiltonian and other operators. The MPO approach allows 1D Hamiltonians to be templated using a small set of finite state automaton rules without reference to the particular microscopic degrees of freedom. We present two algorithms which take advantage of these properties: eMPS to find excited states of 1D Hamiltonians and tMPS for the time evolution of a generic time-dependent 1D Hamiltonian. We properly account for time-ordering of the propagator such that the error does not depend on the rate of change of the Hamiltonian. Our algorithms use only the MPO form of the Hamiltonian, and so are applicable to microscopic degrees of freedom of any variety, and do not require Hamiltonian-specialized implementation. We benchmark our algorithms with a case study of the Ising model, where the critical point is located using entanglement measures. We then study the dynamics of this model under a time-dependent quench of the transverse field through the critical point. Finally, we present studies of a dipolar, or long-range Ising model, again using entanglement measures to find the critical point and study the dynamics of a time-dependent quench through the critical point.

cond-mat.stat-mech↗
arXiv2012

Symmetry breaking and singularity structure in Bose-Einstein condensates

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wavefunction, showing less 0.5% error for impulse strength of (v=0.00005). We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry breaking potential does not significantly change the dynamics of the system as long as the strength is below (v=0.0005).

cond-mat.quant-gas↗
arXiv2011

Macroscopic superposition states of ultracold bosons in a double-well potential

We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a new mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.

cond-mat.quant-gas↗
arXiv2011

Macroscopic Quantum Tunneling of Solitons in Bose-Einstein Condensates

We study the quantum tunneling dynamics of many-body entangled solitons composed of ultracold bosonic gases in 1D optical lattices. A bright soliton, confined by a potential barrier, is allowed to tunnel out of confinement by reducing the barrier width and for varying strengths of attractive interactions. Simulation of the Bose Hubbard Hamiltonian is performed with time-evolving block decimation. We find the characteristic $1/e$ time for the escape of the soliton, substantially different from the mean field prediction, and address how many-body effects like quantum fluctuations, entanglement, and nonlocal correlations affect macroscopic quantum tunneling; number fluctuations and second order correlations are suggested as experimental signatures. We find that while the escape time scales exponentially in the interactions, the time at which both the von Neumann entanglement entropy and the slope of number fluctuations is maximized scale only linearly.

cond-mat.quant-gas↗
arXiv2011

Macroscopic Superposition of Ultracold Atoms with Orbital Degrees of Freedom

We introduce higher dimensions into the problem of Bose-Einstein condensates in a double-well potential, taking into account orbital angular momentum. We completely characterize the eigenstates of this system, delineating new regimes via both analytical high-order perturbation theory and numerical exact diagonalization. Among these regimes are mixed Josephson- and Fock-like behavior, crossings in both excited and ground states, and shadows of macroscopic superposition states.

cond-mat.quant-gas↗
arXiv2011

Chaotic Spin-Wave Solitons in Magnetic Film Feedback Rings

Chaotic spin-wave solitons in magnetic film active feedback rings were observed for the first time. At some ring gain level, one observes the self-generation of a single spin-wave soliton pulse in the ring. When the pulse circulates in the ring, its amplitude varies chaotically with time. Numerical simulations based on a gain-loss nonlinear Schrödinger equation reproduce the observed responses.

cond-mat.mes-hall↗
arXiv2011

Grey solitons in a strongly interacting superfluid Fermi Gas

The Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS to BEC) crossover problem is solved for stationary grey solitons via the Boguliubov-de Gennes equations at zero temperature. These \emph{crossover solitons} exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitary the velocity has a nearly linear dependence on phase difference over an extended range. For fixed phase difference the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power law relationship to express this fact: the density of grey crossover solitons varies as the square of the gap amplitude in the BEC limit and a power of about 1.5 at unitarity.

cond-mat.quant-gas↗
arXiv2011

Generalized Local Induction Equation, Elliptic Asymptotics, and Simulating Superfluid Turbulence

We prove the generalized induction equation and the generalized local induction equation (GLIE), which replaces the commonly used local induction approximation (LIA) to simulate the dynamics of vortex lines and thus superfluid turbulence. We show that the LIA is, without in fact any approximation at all, a general feature of the velocity field induced by any length of a curved vortex filament. Specifically, the LIA states that the velocity field induced by a curved vortex filament is asymmetric in the binormal direction. Up to a potential term, the induced incompressible field is given by the Biot-Savart integral, where we recall that there is a direct analogy between hydrodynamics and magnetostatics. Series approximations to the Biot-Savart integrand indicate a logarithmic divergence of the local field in the binormal direction. While this is qualitatively correct, LIA lacks metrics quantifying its small parameters. Regardless, LIA is used in vortex filament methods simulating the self-induced motion of quantized vortices. With numerics in mind, we represent the binormal field in terms of incomplete elliptic integrals, which is valid for $\mathbb{R}^{3}$. From this and known expansions we derive the GLIE, asymptotic for local field points. Like the LIA, generalized induction shows a persistent binormal deviation in the local-field but unlike the LIA, the GLIE provides bounds on the truncated remainder. As an application, we adapt formulae from vortex filament methods to the GLIE for future use in these methods. Other examples we consider include vortex rings, relevant for both superfluid $^4$He and Bose-Einstein condensates.

math-ph↗
arXiv2010

Distinguishing Fact from Fiction: Pattern Recognition in Texts Using Complex Networks

We establish concrete mathematical criteria to distinguish between different kinds of written storytelling, fictional and non-fictional. Specifically, we constructed a semantic network from both novels and news stories, with $N$ independent words as vertices or nodes, and edges or links allotted to words occurring within $m$ places of a given vertex; we call $m$ the word distance. We then used measures from complex network theory to distinguish between news and fiction, studying the minimal text length needed as well as the optimized word distance $m$. The literature samples were found to be most effectively represented by their corresponding power laws over degree distribution $P(k)$ and clustering coefficient $C(k)$; we also studied the mean geodesic distance, and found all our texts were small-world networks. We observed a natural break-point at $k=\sqrt{N}$ where the power law in the degree distribution changed, leading to separate power law fit for the bulk and the tail of $P(k)$. Our linear discriminant analysis yielded a $73.8 \pm 5.15%$ accuracy for the correct classification of novels and $69.1 \pm 1.22%$ for news stories. We found an optimal word distance of $m=4$ and a minimum text length of 100 to 200 words $N$.

cs.CL↗
arXiv2010

Finite Temperature Matrix Product State Algorithms and Applications

We review the basic theory of matrix product states (MPS) as a numerical variational ansatz for time evolution, and present two methods to simulate finite temperature systems with MPS: the ancilla method and the minimally entangled typical thermal state method. A sample calculation with the Bose-Hubbard model is provided.

cond-mat.quant-gas↗
arXiv2010

Metastable Quantum Phase Transitions in a One-Dimensional Bose Gas

This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."

cond-mat.quant-gas↗
arXiv2010

Embedded Ribbons of Graphene Allotropes: An Extended Defect Perspective

Four fundamental dimer manipulations can be used to produce a variety of localized and extended defect structures in graphene. Two-dimensional templates result in graphene allotropes, here viewed as extended defects, which can exhibit either metallic or semiconducting electrical character. \emph{Embedded allotropic ribbons}--i.e. thin swaths of the new allotropes--can also be created within graphene. We examine these ribbons and find that they maintain the electrical character of their parent allotrope even when only a few atoms in width. Such extended defects may facilitate the construction of monolithic electronic circuitry.

cond-mat.mes-hall↗
arXiv2010

Dynamical Realization of Macroscopic Superposition States of Cold Bosons in a Tilted Double Well

We present exact expressions for the quantum sloshing of Bose-Einstein condensates in a tilted two-well potential. Tunneling is suppressed by a small potential difference between wells, or tilt. However, tunneling resonances occur for critical values of the tilt when the barrier is high. At resonance, tunneling times on the order of 10-100 ms are possible. Furthermore, such tilted resonances lead to a dynamical scheme for creating few-body NOON-like macroscopic superposition states which are protected by the many body wavefunction against potential fluctuations.

quant-ph↗
arXiv2009

Formation of Random Dark Envelope Solitons from Incoherent Waves

This letter reports experimental results on a new type of soliton: the random temporal dark soliton. One excites an incoherent large-amplitude propagating spin-wave packet in a ferromagnetic film strip with a repulsive, instantaneous nonlinearity. One then observes the random formation of dark solitons from this wave packet. The solitons appear randomly in time and in position relative to the entire wave packet. They can be gray or black. For wide and/or very strong spin-wave packets, one also observes multiple dark solitons. In spite of the randomness of the initial wave packets and the random formation processes, the solitons show signatures that are found for conventional coherent dark solitons.

cond-mat.mes-hall↗
arXiv2009

Spatial Dependence of Entropy in Trapped Ultracold Bose Gases

We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can be strongly manipulated with the mean field.

cond-mat.quant-gas↗