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Alexander L. Fetter

Publications and source records attributed to Alexander L. Fetter.

At least 37 records · Page 2Linked to original sources
arXiv2004

Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $Ω$ to exceed the radial harmonic frequency $ω_\perp$. In the regime $Ω\gtrsim ω_\perp$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity $Ω_h$, a central hole appears in the condensate. Numerical studies confirm the predicted value of $Ω_h$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).

cond-mat.stat-mech↗
arXiv2004

Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the Thomas-Fermi limit. The sequence of ground states (within these single-ring configurations) is determined as a function of the external rotation frequency by comparing the free energy of the various states. For each ground state, the Tkachenko-like excitations and the associated dynamical stability are analyzed.

cond-mat.other↗
arXiv2004

Kelvin mode of a vortex in a nonuniform Bose-Einstein condensate

In a uniform fluid, a quantized vortex line with circulation h/M can support long-wavelength helical traveling waves proportional to e^{i(kz-ω_k t)} with the well-known Kelvin dispersion relation ω_k \approx (\hbar k^2/2M) \ln(1/|k|ξ), where ξis the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity V of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the line's curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wavenumber k(z) upward near the trap center, and k(z) then increases still more toward the ends.

cond-mat.soft↗
arXiv2001

Vortex precession in a rotating nonaxisymmetric trapped Bose-Einstein condensate

We study the precession of an off-axis straight vortex in a rotating nonaxisymmetric harmonic trap in the Thomas-Fermi (TF) regime. A time-dependent variational Lagrangian analysis yields the dynamical equations of the vortex and the precessional angular velocity in two-dimensional (2D) and three-dimensional (3D) condensates.

cond-mat.stat-mech↗
arXiv2001

Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity Omega_{c2} occurs when the intervortex separation b becomes comparable with the vortex core radius xi. For a radial harmonic trap, the loss of confinement as Omega approaches omega_perp implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which Omega_{c2} is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of Omega_{c2} arises not only from decreasing b but also from increasing xi caused by the vanishing of the chemical potential as Omega approaches Omega_{c2}.

cond-mat.stat-mech↗
arXiv2001

Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate

We use a variational method to investigate the ground-state phase diagram of a small, asymmetric Bose-Einstein condensate with respect to the dimensionless interparticle interaction strength $γ$ and the applied external rotation speed $Ω$. For a given $γ$, the transition lines between no-vortex and vortex states are shifted toward higher $Ω$ relative to those for the symmetric case. We also find a re-entrant behavior, where the number of vortex cores can decrease for large $Ω$. In addition, stabilizing a vortex in a rotating asymmetric trap requires a minimum interaction strength. For a given asymmetry, the evolution of the variational parameters with increasing $Ω$ shows two different types of transitions (sharp or continuous), depending on the strength of the interaction. We also investigate transitions to states with higher vorticity; the corresponding angular momentum increases continuously as a function of $Ω$.

cond-mat↗
arXiv2000

Anomalous modes drive vortex dynamics in confined Bose-Einstein condensates

The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for the metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. As the condensate becomes more elongated, the number of anomalous modes increases. The largest frequency of these modes exceeds both the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe not only the critical rotation frequency for creation of the first vortex in an elongated condensate but also the vortex precession in a single-component spherical condensate.

cond-mat.stat-mech↗
arXiv1999

Stability of a Vortex in a Trapped Bose-Einstein Condensate

Based on the method of matched asymptotic expansion and on a time-dependent variational analysis, we study the dynamics of a vortex in the large-condensate (Thomas-Fermi) limit. Both methods as well as an analytical solution of the Bogoliubov equations show that a vortex in a trapped Bose-Einstein condensate has formally unstable normal mode(s) with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, the solution becomes stable above an angular velocity $Ω_m$ characterizing the onset of metastability with respect to small transverse displacements of the vortex from the central axis.

cond-mat.stat-mech↗
arXiv1999

Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.

cond-mat.stat-mech↗
arXiv1999

Vortex State Structure of a Bose Condensate in an Asymmetric Trap

Based on an analytic solution of the Gross-Pitaevskii equation in the large-condensate (Thomas-Fermi) limit we determine the structure of a stationary vortex in a Bose-Einstein condensate in a nonaxisymmetric rotating trap. The condensate velocity field has cylindrical symmetry only near the vortex core and becomes intrinsically anisotropic near the condensate boundaries. Rotating the anisotropic trap induces an additional irrotational velocity field even for a vortex-free condensate.

cond-mat.stat-mech↗
arXiv1999

Stability of a vortex in a small trapped Bose-Einstein condensate

A second-order expansion of the Gross-Pitaevskii equation in the interaction parameter determines the thermodynamic critical angular velocity Omega_c for the creation of a vortex in a small axisymmetric condensate. Similarly, a second-order expansion of the Bogoliubov equations determines the (negative) frequency omega_a of the anomalous mode. Although Omega_c = -omega_a through first order, the second-order contributions ensure that the absolute value |omega_a| is always smaller than the critical angular velocity Omega_c. With increasing external rotation Omega, the dynamical instability of the condensate with a vortex disappears at Omega*=|omega_a|, whereas the vortex state becomes energetically stable at the larger value Omega_c. Both second-order contributions depend explicitly on the axial anisotropy of the trap. The appearance of a local minimum of the free energy for a vortex at the center determines the metastable angular velocity Omega_m. A variational calculation yields Omega_m=|ω_a| to first order (hence Omega_m also coincides with the critical angular velocity Omega_c to this order). Qualitatively, the scenario for the onset of stability in the weak-coupling limit is the same as that found in the strong-coupling (Thomas-Fermi) limit.

cond-mat.stat-mech↗
arXiv1998

Theory of a dilute low-temperature trapped Bose condensate

This set of four lectures reviews various aspects of the theory of a dilute low-temperature trapped Bose gas, starting with (I) a review of the Bogoliubov description of the elementary excitations in a uniform system. The treatment is then generalized (II) to include the new physical effects of a confining harmonic trap potential on the condensate and its normal modes. An equivalent hydrodynamic description (III) focuses directly on the density and velocity fluctuations. The physics of vortices (IV) in an incompressible fluid is summarized and extended to the case of a trapped Bose condensate.

cond-mat.stat-mech↗
arXiv1998

Vortex Stability in a Trapped Bose Condensate

A vortex in a trapped Bose-Einstein condensate can experience at least two types of instabilities. (1). Macroscopic hydrodynamic motion of the vortex core relative to the center of mass of the condensate requires some process to dissipate energy. (2). Microscopic small-amplitude normal modes can also induce an instability. In one specific example, the vortex core again moves relative to the overall center of mass, suggesting that there may be only a single physical mechanism.

cond-mat.stat-mech↗
arXiv1998

Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order R^{-4}ln R and R^{-4}, where R is the number-dependent dimensionless condensate radius in units of the oscillator length. The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order R^{-4}.

cond-mat.stat-mech↗
arXiv1997

Dilute Bose-Einstein Condensate in a Trap: Characteristic Lengths and Critical Velocities

The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity $Ω_{c1}$ for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length $ξ$.

cond-mat.stat-mech↗
arXiv1997

Excited states of a dilute Bose-Einstein condensate in a harmonic trap

The low-lying hydrodynamic normal modes of a dilute Bose-Einstein gas in an isotropic harmonic trap determine the corresponding Bogoliubov amplitudes. In the Thomas-Fermi limit, these modes have large low-temperature occupation numbers, and they permit an explicit construction of the dynamic structure function $S(q,ω)$. The total noncondensate number $N'(0)$ at zero temperature increases like $R^6$, where $R$ is the condensate radius measured in units of the oscillator length. The lowest dipole modes are constructed explicitly in the Bogoliubov approximation.

cond-mat.stat-mech↗
arXiv1996

Ground state and excited states of a trapped dilute condensed Bose gas

I review recent theoretical treatments of a dilute interacting condensed Bose gas in a trap. Bogoliubov's classic results for a uniform condensate are generalized to include the effect of a trap, using the Gross-Pitaevskii formalism (for the condensate) and the Bogoliubov equations (for the linearized small-amplitude excitations of the condensate). Several recent theoretical studies are discussed along with some open questions.

cond-mat↗