arXiv subjects

L. D. Carr

Publications and source records attributed to L. D. Carr.

At least 37 records · Page 2Linked to original sources

arXiv2009

Graduate Quantum Mechanics Reform

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

physics.ed-ph↗

arXiv2008

Emergent Time Scale in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices

We derive a novel lattice Hamiltonian, the \emph{Molecular Hubbard Hamiltonian} (MHH), which describes the essential many body physics of closed-shell ultracold heteronuclear molecules in their absolute ground state in a quasi-one-dimensional optical lattice. The MHH is explicitly time-dependent, making a dynamic generalization of the concept of quantum phase transitions necessary. Using the Time-Evolving Block Decimation (TEBD) algorithm to study entangled dynamics, we demonstrate that, in the case of hard core bosonic molecules at half filling, the MHH exhibits an emergent time scale over which spatial entanglement grows, crystalline order appears, and oscillations between rotational states self-damp into an asymptotic superposition. We show that this time scale is a non-monotonic function of the physical parameters describing the lattice. We also point out that experimental mapping of the static phase boundaries of the MHH can be used to measure the molecular polarizability tensor.

cond-mat.other↗

arXiv2008

Ultracold Atoms in 1D Optical Lattices: Mean Field, Quantum Field, Computation, and Soliton Formation

In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (1) the discrete nonlinear Schrödinger equation, a discrete mean-field theory, and (2) the Bose-Hubbard Hamiltonian, a discrete quantum-field theory. The former is recovered from the latter in the limit of a product of local coherent states. Using a truncated form of these mean-field states as initial conditions, we build quantum analogs to the dark soliton solutions of the discrete nonlinear Schrödinger equation and investigate their dynamical properties in the Bose-Hubbard Hamiltonian. We also discuss specifics of the numerical methods employed for both our mean-field and quantum calculations, where in the latter case we use the time-evolving block decimation algorithm due to Vidal.

cond-mat.other↗

arXiv2008

Nano-Engineering Defect Structures on Graphene

We present a new way of nano-engineering graphene using defect domains. These regions have ring structures that depart from the usual honeycomb lattice, though each carbon atom still has three nearest neighbors. A set of stable domain structures is identified using density functional theory (DFT), including blisters, ridges, ribbons, and metacrystals. All such structures are made solely out of carbon; the smallest encompasses just 16 atoms. Blisters, ridges and metacrystals rise up out of the sheet, while ribbons remain flat. In the vicinity of vacancies, the reaction barriers to formation are sufficiently low that such defects could be synthesized through the thermally activated restructuring of coalesced adatoms.

cond-mat.mtrl-sci↗

arXiv2008

Angular Pseudomomentum Theory for the Generalized Nonlinear Schrödinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schrödinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schrödinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.

nlin.PS↗

arXiv2008

The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries

We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.

cond-mat.other↗

arXiv2007

Radially Symmetric Nonlinear States of Harmonically Trapped Bose-Einstein Condensates

Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with $n_r=0,1$ and 2 radial nodes respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge $m$, i.e., vorticity. It is found that for repulsive interatomic interactions {\it only} the ground state is {\it linearly stable} throughout the parameter range examined. Furthermore, this is true for topological charges $m=0$ or $m=1$; solutions with higher topological charge can be unstable even in that case. All higher excited states are found to be unstable in a wide parametric regime. However, for the focusing/attractive case the ground state with $n_r=0$ and $m=0$ can only be stable for a sufficiently low number of atoms. Once again, excited states are found to be generically unstable. For unstable profiles, the dynamical evolution of the corresponding branches is also followed to monitor the temporal development of the instability.

cond-mat.other↗

arXiv2007

Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-anti-vortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.

cond-mat.other↗

arXiv2007

Ultracold Bosons in a Tilted Multi-level Double-Well Potential

The N -body problem in a double well requires new features for quantum information processing, macroscopic quantum superposition, and other fundamental studies of quantum many body physics in ultracold atoms. One needs (a) tilt, and (b) to go beyond the single-particle ground state in each well, i.e., to two or more energy levels. For (a), we show that a small potential difference between the wells, or tilt, causes the decoherence of Schrodinger cat states. However, these states reappear when the tilt can be compensated by atom-atom interactions; these tilted cat states constitute partial cats that are protected from decoherence by the many body wavefunction. For (b), we provide explicit criteria for when two energy levels are needed to describe the state space. For typical experimental parameters, two levels are indeed required for creation of cat states.

quant-ph↗

arXiv2007

Millimeter Wave Localization: Slow Light and Enhanced Absorption

We exploit millimeter wave technology to measure the reflection and transmission response of random dielectric media. Our samples are easily constructed from random stacks of identical, sub-wavelength quartz and Teflon wafers. The measurement allows us to observe the characteristic transmission resonances associated with localization. We show that these resonances give rise to enhanced attenuation even though the attenuation of homogeneous quartz and Teflon is quite low. We provide experimental evidence of disorder-induced slow light and superluminal group velocities, which, in contrast to photonic crystals, are not associated with any periodicity in the system. Furthermore, we observe localization even though the sample is only about four times the localization length, interpreting our data in terms of an effective cavity model. An algorithm for the retrieval of the internal parameters of random samples (localization length and average absorption rate) from the external measurements of the reflection and transmission coefficients is presented and applied to a particular random sample. The retrieved value of the absorption is in agreement with the directly measured value within the accuracy of the experiment.

cond-mat.mes-hall↗

arXiv2007

Experiments on Multidimensional Solitons

This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in Bose-Einstein condensates with repulsive interactions. We further summarize observations of planar soliton fronts undergoing the snake instability, the formation of vortex rings, and the emergence of hybrid structures.

cond-mat.other↗

arXiv2007

Theory of Multidimensional Solitons

We review a number of topics germane to higher-dimensional solitons in Bose-Einstein condensates. For dark solitons, we discuss dark band and planar solitons; ring dark solitons and spherical shell solitons; solitary waves in restricted geometries; vortex rings and rarefaction pulses; and multi-component Bose-Einstein condensates. For bright solitons, we discuss instability, stability, and metastability; bright soliton engineering, including pulsed atom lasers; solitons in a thermal bath; soliton-soliton interactions; and bright ring solitons and quantum vortices. A thorough reference list is included.

cond-mat.other↗

arXiv2006

Vortices and Ring Solitons in Bose-Einstein Condensates

The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices, and radial excitations of both. The latter are called ring solitons in two dimensions and spherical shells in three. The nonlinear Schrodinger equation is taken as the fundamental model; both extended and harmonically trapped condensates are considered. It is found that the presence of a vortex stabilizes ring solitons in a harmonic trap, in contrast to the well known instability of such solutions in the optics context. This is the first known example of a dark soliton in the cubic nonlinear Schrodinger equation which is stable in a number of dimensions greater than one.

cond-mat.other↗

arXiv2006

Quantized Vortex States of Strongly Interacting Bosons in a Rotating Optical Lattice

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of less than one atom per lattice site. The entry of vortices into the system is characterized by jumps of 2 pi in the phase winding of the condensate wavefunction. A lattice of size L X L can have at most L-1 quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasi-angular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasi-angular momentum of the ground-state changes.

cond-mat.stat-mech↗

arXiv2006

Vortices in attractive Bose-Einstein condensates in two dimensions

The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number $m$. An infinite sequence of radially excited stationary states appear for each value of $m$, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.

cond-mat.other↗

arXiv2006

Bose-Einstein Condensates in Rotating Lattices

Strongly interacting bosons in 2D in a rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.

cond-mat.other↗

arXiv2005

Macroscopic quantum tunnelling of Bose-Einstein condensates in a finite potential well

Bose-Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two, and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 milliseconds to 10 seconds.

cond-mat.other↗

arXiv2005

Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates

The band structure of a Bose-Einstein condensate is studied for lattice traps of sinusoidal, Jacobi elliptic, and Kronig-Penney form. It is demonstrated that the physical properties of the system are independent of the choice of lattice. The Kronig-Penney potential, which admits a full exact solution in closed analytical form, is then used to understand in a novel way the swallowtails, or loops, that form in the band structure. Their appearance can be explained by adiabatically tuning a second lattice with half the period. Such a two-color lattice, which can be easily realized in experiments, has intriguing new physical properties. For instance, swallowtails appear even for weak nonlinearity, which is the experimental regime. We determine the stability properties of this system and relate them to current experiments.

cond-mat.other↗