Searcharxiv⌕ Search

arXiv subjects

Tin-Lun Ho

Publications and source records attributed to Tin-Lun Ho.

68 records · Page 4Linked to original sources
arXiv1999

The General Structure of Bose Gases with Arbitrary Spin

Motivated by the recent discoveries of spin-1 and spin-1/2 Bose gas, we have studied the general structure of the Bose gases with arbitrary spin. A general method is developed to uncover the elementary building blocks of the angular momentum eigenstates, as well as the relations (or interactions) between them. Applications of this method to Bose gases with integer spins (f=1,2,3) and half integer spins (f=1/2,3/2) reveal many surprising structures.

cond-mat↗
arXiv1999

Fragmented and Single Condensate Ground States of Spin-1 Bose Gas

We show that the ground state of a spin-1 Bose gas with an antiferro- magnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order $N$) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and the method of detecting fragmented states are presented.

cond-mat↗
arXiv1998

Pairing of Fermions with Arbitrary Spin

Motivated by the recent success of optical trapping of alkali Bose condensate, we have studied the superfluid state of optically trapped alkali fermions, which can have Cooper pairs with total spin $J\geq 2$. In this paper, we shall discuss the general structure of these large spin Cooper pairs and their close relation with singlet Cooper pairs with non-zero orbital angular momentum. We also present the exact solution for the J=2 pairing which shows a surprising change of ground state as the spin $f$ of the constituent fermion increases.

cond-mat↗
arXiv1998

Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a ferromagnetic state respectively.

cond-mat↗
arXiv1998

Quasi 1 and 2d Dilute Bose Gas in Magnetic Traps : Existence of Off-Diagonal Order and Anomalous Quantum Fluctuations

Current magnetic traps can be made so anisotropic that the atomic gas trapped inside behaves like quasi one or two dimensional system. Unlike the homogeneous case, quantum phase fluctuations do not destroy macroscopic off-diagonal order of trapped Bose gases in $d\leq 2$. In the dilute limit, quantum fluctuations increase, remain constant, and decrease with size for $% 3, 2, 1d$ respectively. These behaviors are due to the combination of a finite gap and the universal spectrum of the collective mode.

cond-mat↗
arXiv1997

First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures ($0.6<T/T_{c}<1.2$) and for systems with $10^4$ to $10^8$ particles. The second sound modes (which exist only below $T_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near $T_{c}$ recently observed at JILA in systems with $10^3$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

cond-mat↗
arXiv1997

The Hydrodynamic Equations of Superfluid Mixtures in Magnetic Traps

The hydrodynamics equations of binary mixtures of Bose gases, Fermi gases, and mixtures of Bose and Fermi gases in the presence of external potentials are derived. These equations can be applied to current experiments on mixtures of atomic gases confined in magnetic traps.

cond-mat↗
arXiv1996

Alkali Bose Condensate Mixtures

We show that binary mixtures of Bose-condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of these states, and have worked out their phase diagrams within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought $^{3}$He-$^{4}$He interpenetrating superfluids in ultra-low temperature physics.

cond-mat↗
arXiv1996

Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity ${\bf u}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static" traps, ${\bf u}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\bf Ω}_{c1}$, and can lead to {\em vortex ground states}. The inversion symmetry of ${\bf Ω}_{c1}$, however, is not broken in ``dynamic" traps. Rotations of the atom cloud can be generated by adiabatic effects without physically rotating the entire trap.

cond-mat↗
arXiv1995

The Broken Symmetry of Two-Component $ν=1/2$ Quantum Hall States

We show that the recently discovered $ν=1/2$ quantum Hall states in bilayer systems are triplet p-wave pairing states of composite Fermions, of exactly the same form as $^{3}$He superfluids. The observed persistence (though weakening) of the $ν=1/2$ state in the two- to one-component crossover region corresponds to a continuous deformation of the so-called (331) state towards the ``Pfaffian" state, identical to the well known A to A$_{1}$ transition in $^{3}$He. This deformation also demonstrates the remarkable fact that electrons can release and capture ``vortices" in a continuous and incompressible manner through spin rotations. The broken symmetry of the triplet pairing state is a ``pairing" vector ${\bf d}$. It also implies a (pseudo-spin) magnetization $\propto i{\bf d}\times {\bf d}^{\ast}$. In the presence of layer tunneling, the (331) state ({\bf d} real) is unstable against other states with a magnetization ({\bf d} complex). The recently observed persistence of the $ν=5/2$ state in single layer systems in the two- to one-component crossover region is also consistent with triplet pairing interpretation.

cond-mat↗
arXiv1995

Wigner Crystals Phases in Bilayer Quantum Hall Systems

(This is a substantially shortened version of the original abstract:) The Wigner crystal phase diagram of the bilayer systems have been studied using variational methods. Five crystal phases are obtained. As the layer spacing increases, the system will undergo a sequence of phase transitions. A common feature of most bilayer Wigner crystals is that they have mixed (pseudo-spin) ferromagnetic and antiferromagnetic order.

cond-mat↗
arXiv1994

Oscillatory Tunneling between Quantum Hall Systems

Electron tunneling between quantum Hall systems on the same two dimensional plane separated by a narrow barrier is studied. We show that in the limit where inelastic scattering time is much longer than the tunneling time, which can be achieved in practice, electrons can tunnel back and forth through the barrier continously, leading to an oscillating current in the absence of external drives. The oscillatory behavior is dictated by a tunneling gap in the energy spectrum. We shall discuss ways to generate oscillating currents and the phenomenon of natural ``dephasing" between the tunneling currents of edge states. The noise spectra of these junctions are also studied. They contain singularites reflecting the existence of tunneling gaps as well as the inherent oscillation in the system. (Figures will be given upon requests).

cond-mat↗
arXiv1994

Quantum Hall Ferromagnets

It is pointed out recently that the $ν=1/m$ quantum Hall states in bilayer systems behave like easy plane quantum ferromagnets. We study the magnetotransport of these systems using their ``ferromagnetic" properties and a novel spin-charge relation of their excitations. The general transport is a combination of the ususal Hall transport and a time dependent transport with $quantized$ time average. The latter is due to a phase slippage process in $spacetime$ and is characterized by two topological constants. (Figures will be provided upon requests).

cond-mat↗