arXiv subjects
Publications and source records attributed to Weiping Zhang.
A nonlinear Schrödinger equation is derived for the dynamics of a beam of ultracold fermionic atoms traversing a Bose-Einstein condensate. The condensate phonon modes are shown to provide a nonlinear medium for the fermionic atoms. A two-fermion bound state is predicted to arise, and the signature of the bound state in a nonlinear atom optics experiment is discussed.
We study the ground state magnetic properties of ferromagnetic spinor Bose-Einstein condensates confined in a deep optical lattices. In the Mott insulator regime, the ``mini-condensates'' at each lattice site behave as mesoscopic spin magnets that can interact with neighboring sites through both the static magnetic dipolar interaction and the light-induced dipolar interaction. We show that such an array of spin magnets can undergo a ferromagnetic or anti-ferromagnetic phase transition under the magnetic dipolar interaction depending on the dimension of the confining optical lattice. The ground-state spin configurations and related magnetic properties are investigated in detail.
In a previous work (PRL 87, 140405), we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a two-fold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.
The spin dynamics of atomic Bose-Einstein condensates confined in a one-dimensional optical lattice is studied. The condensates at each lattice site behave like spin magnets that can interact with each other through both the light-induced dipole-dipole interaction and the static magnetic dipole-dipole interaction. We show how these site-to-site dipolar interactions can distort the ground state spin orientations and lead to the excitation of spin waves. The dispersion relation of the spin waves is studied and possible detection schemes are proposed.
The ground state and its structure for a rotating, harmonically trapped N-Boson system with a weak repulsive contact interaction are studied as the angular momentum L increases up to 3N. We show that the ground state is generally a fragmented condensate due to angular momentum conservation. In response to an (arbitrarily weak) asymmetric perturbation of the trap, however, the fragmented ground state can be transformed into a single condensate state. We manifest this intrinsic instability by calculating the conditional probability distributions, which show patterns analogous to the boson density distributions predicted by mean-field theory.
We show that an ensemble of spinor Bose-Einstein condensates confined in a one dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.
We demonstrate, analytically and numerically, that the ferromagnetic phase of the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains. Together with other nonlinear effects in the atomic optics of ultra-cold gases (such as coherent photoassociation and four-wave mixing) this effect provides one more analogy between coherent matter waves and light waves in nonlinear optics.
An interferometric scheme to study Abelian geometric phase shift over the manifold SU(N)/SU(N-1) is presented.
We calculate the phonon excitation spectrum in a zero-temperature boson-fermion mixture. We show how the sound velocity changes due to the boson-fermion interaction and we determine the dynamical stability regime of a homogeneous mixture. We identify a resonant phonon-exchange interaction between the fermions as the physical mechanism leading to the instability.
We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.
An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of $10^{14}$ cm$^{-3}$. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics.
We propose a scheme for the creation of skyrmions (coreless vortices) in a Bose-Einstein condensate with hyperfine spin F=1. In this scheme, four traveling-wave laser beams, with Gaussian or Laguerre-Gaussian transverse profiles, induce Raman transitions with an anomalous dependence on the laser polarization, thereby generating the optical potential required for producing skyrmions.
We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.
We use adiabatic limits to study foliated manifolds. The Bott connection naturally shows up as the adiabatic limit of Levi-Civita connections. As an application, we then construct certain natural elliptic operators associated to the foliation and present a direct geometric proof of a vanshing theorem of Connes[Co], which extends the Lichnerowicz vanishing theorem [L] to foliated manifolds with spin leaves, for what we call almost Riemannian foliations. Several new vanishing theorems are also proved by using our method.
We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.
In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.
Light scattering from a spin-polarized degenerate Fermi gas of trapped ultracold Li-6 atoms is studied. We find that the scattered light contains information which directly reflects the quantum pair correlation due to the formation of atomic Cooper pairs resulting from a BCS phase transition to a superfluid state. Evidence for pairing can be observed in both the space and time domains.