arXiv subjects

Weiping Zhang

Publications and source records attributed to Weiping Zhang.

At least 163 records · Page 9Linked to original sources

arXiv2010

Geometric quantization for proper actions

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M is symplectic with a Hamiltonian action of G that is proper and cocompact. This essentially solves a conjecture of Hochs and Landsman.

math.DG↗

arXiv2010

Generalized Witten Genus and Vanishing Theorems

We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.

math.DG↗

arXiv2010

Quantum Control of Light through an Atom-Molecule Dark State

We propose to use a quantized version of coherent two-color photoassociation to realize a hybrid device for quantum control of light. The dynamical features of this system are exhibited, including the slowing down or storage of light and the molecular matter-wave solitons. This may indicate a hybrid atom-molecule quantum device for storage and retrieve of optical information.

quant-ph↗

arXiv2010

Laser-catalyzed spin-exchange process in a Bose-Einstein condensate

We show theoretically that it is possible to optically control collective spin-exchange processes in spinor Bose condensates through virtual photoassociation. The interplay between optically induced spin exchange and spin-dependent collisions provides a flexible tool for the control of atomic spin dynamics, including enhanced or inhibited quantum spin oscillations, the optically-induced ferromagnetic-to-antiferromagnetic transition, and coherent matter-wave spin conversion.

quant-ph↗

arXiv2010

Hopf cyclic cohomology and Hodge theory for proper actions

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is cocompact, we develop a generalized Hodge theory for the de Rham cohomology of invariant differential forms. We prove that every cyclic cohomology class of the Hopf algebroid is represented by a generalized harmonic form. This implies that the space of cyclic cohomology of the Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we discuss properties of the Euler characteristic for a proper cocompact action.

math.DG↗

arXiv2010

Efficient production of polar molecular Bose-Einstein condensates via an all-optical R-type atom-molecule adiabatic passage

We propose a scheme of "$R$-type" photoassociative adiabatic passage (PAP) to create polar molecular condensates from two different species of ultracold atoms. Due to the presence of a quasi-coherent population trapping state in the scheme, it is possible to associate atoms into molecules with a \textit{low-power} photoassociation (PA) laser. One remarkable advantage of our scheme is that a tunable atom-molecule coupling strength can be achieved by using a time-dependent PA field, which exhibits larger flexibility than using a tunable magnetic field. In addition, our results show that the PA intensity required in the "$R$-type" PAP could be greatly reduced compared to that in a conventional "$Λ$-type" one.

cond-mat.quant-gas↗

arXiv2010

Achieving ground-state polar molecular condensates by chainwise atom-molecule adiabatic passage

We generalize the idea of chainwise stimulated Raman adiabatic passage (STIRAP) [Kuznetsova \textit{et al.} Phys. Rev. A \textbf{78}, 021402(R) (2008)] to a photoassociation-based chainwise atom-molecule system, with the goal of directly converting two-species atomic Bose-Einstein condensates (BEC) into a ground polar molecular BEC. We pay particular attention to the intermediate Raman laser fields, a control knob inaccessible to the usual three-level model. We find that an appropriate exploration of both the intermediate laser fields and the stability property of the atom-molecule STIRAP can greatly reduce the power demand on the photoassociation laser, a key concern for STIRAPs starting from free atoms due to the small Franck-Condon factor in the free-bound transition.

cond-mat.quant-gas↗

arXiv2009

Generating correlated (2+1)-photon in an active Raman gain medium

A scheme of generating controllable (2+1) photons in a double-$% Λ$ atomic system based on active-Raman-gain is presented in this paper. Such (2+1) photons can be a potential candidate to generate a correlated photon pair as the photon `1' acts as a trigger. Compared to other schemes of generating correlated photon pairs, our scheme exhibits a number of advantages due to the exploit of the stimulated Raman process.

quant-ph↗

arXiv2009

Cavity-Mediated Strong Matter Wave Bistability in a Spin-1 Condensate

We study matter wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields are accomplished via the spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter wave nonlinearity, making matter wave bistability in a cavity at the single-photon level achievable.

cond-mat.quant-gas↗

arXiv2009

Detection of Fermi Pairing via Electromagnetically Induced Transparency

An optical spectroscopic method based on the principle of electromagnetically-induced transparency (EIT) is proposed as quite a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. A quasiparticle picture is constructed to facilitate a simple physical explanation of the pairing signature in the EIT spectra.

cond-mat.quant-gas↗

arXiv2009

Storage of polarization-encoded cluster states in an atomic system

We present a scheme for entanglement macroscopic atomic ensembles which are four spatially separate regions of an atomic cloud using cluster-correlated beams. We show that the cluster-type polarization-encoded entanglement could be mapped onto the long-lived collective ground state of the atomic ensembles, and the stored entanglement could be retrieved based on the technique of electromagnetically induced transparency. We also discuss the efficiency of, the lifetime of, and some quantitative restrictions to the proposed quantum memory.

quant-ph↗

arXiv2008

Phase Separation in two-Species Atomic Bose-Einstein Condensate with Interspecies Feshbach Resonance

We consider a mixture of two-species atomic Bose-Einstein codensates coupled to a bound molecular state at zero temperature via interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multi-component condensate system.

cond-mat.mes-hall↗

arXiv2008

Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form

For a complex flat vector bundle over a fibered manifold, we consider the 1-parameter family of certain deformed sub-signature operators introduced by Ma-Zhang. We compute the adiabatic limit of the Bismut-Freed connection associated to this family and show that the Bismut-Lott analytic torsion form shows up naturally under this procedure.

math.DG↗

arXiv2008

Goos-Hänchen-Like Shifts in Atom Optics

We consider the propagation of a matter wavepacket of two-level atoms through a square potential created by a super-Gaussian laser beam. We explore the matter wave analog of Goos-Hänchen shift within the framework of atom optics where the roles of atom and light is exchanged with respect to conventional optics. Using a vector theory, where atoms are treated as particles possessing two internal spin components, we show that not only large negative but also large positive Goos-Hänchen shifts can occur in the reflected atomic beam.

quant-ph↗

arXiv2008

Rosen-Zener interferometry with Ultracold Atoms

We propose a time-domain "interferometer" based on ultracold Bose atoms loaded on a double well potential. By the adiabatic Rosen-Zener process, the barrier between two wells is ramped down slowly, held for a while, then ramped back. Starting with a coherent state of double well system, the final occupations on one well show interesting interference fringes in the time-domain. The fringe pattern is sensitive to the initial state, the interatomic interaction, and the external forces such as gravity which can change the shape of the double well. In this sense, this interferometric scheme has the potentials for precision measurements with ultracold atoms. The underlying mechanism is revealed and possible applications are discussed.

cond-mat.mes-hall↗

arXiv2007

Coherent population oscillation from a Fermi atom-molecule dark state

We show that a robust macroscopic atom-molecule dark state can exist in fermionic systems, which represents a coherent superposition between the ground molecular BEC and the atomic BCS paired state. We take advantage of the tunability offered by external laser fields, and explore this superposition for demonstrating coherent oscillations between ground molecules and atom pairs. We interpret the oscillation frequencies in terms of the collective excitations of the dark state.

cond-mat.other↗

arXiv2007

Real embeddings, eta invariant and Chern-Simons current

We present an alternate proof of the Bismut-Zhang localization formula for $η$-invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.

math.DG↗

arXiv2007

Properties of a coupled two species atom-heteronuclear molecule condensate

We study the coherent association of a two-species atomic condensate into a condensate of heteronuclear diatomic molecules, using both a semiclassical treatment and a quantum mechanical approach. The differences and connections between the two approaches are examined. We show that, in this coupled nonlinear atom-molecule system, the population difference between the two atomic species plays a significant role in the ground-state stability properties as well as in coherent population oscillation dynamics.

quant-ph↗