Jun 2014

Jun 2-Jun 6, Jinlong Yu, Jun 9-Jun 13, Zhifang Xu, Jun 16-Jun 20, Jiyao chen, Jun 23-Jun 27, zhenyu zhou

Jun 20
1.arXiv:1406.4902 [pdf, other]
Quench between a Mott insulator and a Lieb-Liniger liquid
G. Goldstein, N. Andrei
Comments: 4 pages, 1 figure
Subjects: Quantum Gases (cond-mat.quant-gas)
In this work we study a quench between a Mott insulator and a repulsive Lieb-Liniger liquid. We find explicitly the stationary state when a long time has passed after the quench. It is given by a GGE density matrix which we completely characterize, calculating the quasiparticle density describing the system after the quench. In the long time limit we find an explicit form for the local three body density density density correlation function and the asymptotic long distance limit of the density density correlation function. The later is shown to have a Gaussian decay at large distances.

Jun 19

1.arXiv:1406.4758 [pdf, other]
Quantum magnetism with ultracold molecules
M. L. Wall, K. R. A. Hazzard, A. M. Rey
Comments: 21 pages, 6 figures, 1 table. Review article
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con)

This article gives an introduction to the realization of effective quantum magnetism with ultracold molecules in an optical lattice, reviews experimental and theoretical progress, and highlights future opportunities opened up by ongoing experiments. Ultracold molecules offer capabilities that are otherwise difficult or impossible to achieve in other effective spin systems, such as long-ranged spin-spin interactions with controllable degrees of spatial and spin anisotropy and favorable energy scales. Realizing quantum magnetism with ultracold molecules provides access to rich many-body behaviors, including many exotic phases of matter and interesting excitations and dynamics. Far-from-equilibrium dynamics plays a key role in our exposition, just as it did in recent ultracold molecule experiments realizing effective quantum magnetism. In particular, we show that dynamical probes allow the observation of correlated many-body spin physics, even in polar molecule gases that are not quantum degenerate. After describing how quantum magnetism arises in ultracold molecules and discussing recent observations of quantum magnetism with polar molecules, we survey prospects for the future, ranging from immediate goals to long-term visions.


Jun 18

1.arXiv:1406.3756 (cross-list from quant-ph) [pdf, ps, other]
Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices
Artur Barasiński, Wiesław Leoński, Tomasz Sowiński
Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)
We discuss a model with ultra-cold atoms confined in optical superlattices. In particular, we study the ground-state properties of two spin-1 bosons trapped in a double-well potential. Depending on the external magnetic field and biquadratic interactions different phases of magnetic order are realized. Applying von Neumann entropy and number of relevant orbitals, we quantify the bipartite entanglement between particles. Changing the values of the parameters determining superlattices, we can switch the system between differently entangled states.

Jun 16
1.arXiv:1406.3443 [pdf, ps, other]
Resonant atom-dimer collisions in cesium: Testing universality at positive scattering lengths
Alessandro Zenesini, Bo Huang, Martin Berninger, Hanns-Christoph Nägerl, Francesca Ferlaino, Rudolf Grimm
Subjects: Quantum Gases (cond-mat.quant-gas)
We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550G in the regime of positive s-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimov's scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates non-universal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect as suggested by observations in other atomic species. We could not confirm the presence of such a feature.

2. arXiv:1406.3572 (cross-list from quant-ph) [pdf, ps, other]
Analog quantum simulation of gravitational waves in a Bose-Einstein condensate
Tupac Bravo, Carlos Sabín, Ivette Fuentes
Comments: 9 pages. I. F. previously published as I. Fuentes-Guridi and I.Fuentes-Schuller
Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); General Relativity and Quantum Cosmology (gr-qc)
We show how to vary the physical properties of a Bose-Einstein condensate (BEC) in order to mimic an effective gravitational-wave spacetime. In particular, we focus in the simulation of the recently discovered creation of particles by real spacetime distortion in box-type traps. We show that, by modulating the speed of sound in the BEC, the phonons experience the effects of a simulated spacetime ripple with experimentally amenable parameters. These results will inform the experimental programme of gravitational wave astronomy with cold atoms.


Jun 13
1.arXiv:1406.3033 [pdf, other]
Anomalous Hall Effect in Weyl Metals
A.A. Burkov
Comments: 5 pages, 2 figures
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

We present a theory of the anomalous Hall effect (AHE) in a doped Weyl semimetal, or Weyl metal, including both intrinsic and extrinsic (impurity scattering) contributions. We demonstrate that a Weyl metal is distinguished from an ordinary ferromagnetic metal by the absence of the extrinsic and the Fermi surface part of the intrinsic contributions to the AHE, as long as the Fermi energy is sufficiently close to the Weyl nodes. The AHE in a Weyl metal is thus shown to be a purely intrinsic, universal property, fully determined by the location of the Weyl nodes in the first Brillouin zone.

2.arXiv:1406.3079 [pdf, other]
Imaginary geometric phases of quantum trajectories
Fan Yang, Ren-Bao Liu
Comments: 5 pages with 3 figures
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also experience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.

3.arXiv:1406.3094 [pdf, ps, other]
Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
Mikito Koshino, Takahiro Morimoto, Masatoshi Sato
Comments: 12 pages, 6 figures
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el)

We explore a new class of topologically stable zero energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion and rotation, the Hamiltonian can be separated into independent chiral-symmetric subsystems by the eigenvalue of the space symmetry operator. Each subsystem supports chiral zero energy modes when a topological index assigned to the block is nonzero. By applying the argument to Bloch electron systems, we detect band touching at symmetric points in the Brillouin zone. In particular, we show that Dirac nodes appearing in honeycomb lattice (e.g. graphene) and in half-flux square lattice are protected by three-fold and two-fold rotation symmetry, respectively. We also present several examples of Dirac semimetal with isolated band-touching points in three-dimensional $k$-space, which are protected by combined symmetry of rotation and reflection. The zero mode protection by spatial symmetry is distinct from that by the conventional winding number. We demonstrate that symmetry-protected band touching points emerge even though the winding number is zero. Finally, we identify relevant topological charges assigned to the gapless points.
Jun 12
1. arXiv:1406.2701 [pdf, other]
Dynamic trapping near a quantum critical point
Michael Kolodrubetz, Emanuel Katz, Anatoli Polkovnikov
Comments: 4 pages, 3 figures + 5 page supplement
Subjects: Quantum Gases (cond-mat.quant-gas); High Energy Physics - Theory (hep-th)

The study of dynamics in closed quantum systems has recently been revitalized by the emergence of experimental systems that are well-isolated from their environment. In this paper, we consider the closed-system dynamics of an archetypal model: spins near a second order quantum critical point, which are traditionally described by the Kibble-Zurek mechanism. Imbuing the driving field with Newtonian dynamics, we find that the full closed system exhibits a robust new phenomenon -- dynamic critical trapping -- in which the system is self-trapped near the critical point due to efficient absorption of field kinetic energy by heating the quantum spins. We quantify limits in which this phenomenon can be observed and generalize these results by developing a Kibble-Zurek scaling theory that incorporates the dynamic field. Our findings can potentially be interesting in the context of early universe physics, where the role of the driving field is played by the inflaton or a modulus.

2. arXiv:1406.2968 (cross-list from cond-mat.supr-con) [pdf, other]
Amplitude / Higgs Modes in Condensed Matter Physics
David Pekker, C. M. Varma
Comments: 35 pages, 12 figures
Subjects: Superconductivity (cond-mat.supr-con); Quantum Gases (cond-mat.quant-gas)

The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by a complex function \Psi({\bf r}, t). These states include superfluids, superconductors, and a sub-class of anti-ferromagnets and charge-density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and those of amplitude of \Psi({\bf r}, t). The phase oscillations are the Goldstone modes of the broken continuous symmetry. The amplitude modes, even at long wave-lengths, are well defined and de-coupled from the phase oscillations only at particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry as in particle physics. They bear close correspondence with the so-called Higgs modes in particle physics, whose prediction and discovery is very important for the standard model of particle physics. In this review, we discuss the theory and the observation of the amplitude or Higgs modes in condensed matter physics - in superconductors, cold-atoms in periodic lattices, and in uni-axial anti-ferromagnets. We discuss the necessity for at least approximate particle-hole symmetry as well as the special conditions required to couple to such modes.

Jun 11
1. arXiv:1406.2669 [pdf, other]
Observation of coherent quench dynamics in a metallic many-body state of fermions
Sebastian Will, Deepak Iyer, Marcos Rigol
Comments: 6 pages, 4 figures
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

The investigation of nonequilibrium dynamics in interacting quantum many-body systems has emerged as a key approach to characterize the nature of quantum states, to study excitation spectra, and to shed light on thermalization processes. So far, research on nonequilibrium dynamics has focused on many-body quantum states of bosonic particles, leading to the observation of coherent quench dynamics and the exploration of relaxation and thermalization in isolated quantum systems. Here we report on the observation of coherent quench dynamics in a many-body quantum state of fermionic particles. In the experiment, we prepare a metallic state of ultracold spin-polarized fermionic atoms in a shallow three-dimensional (3D) optical lattice. The delocalized fermions are in contact with a Bose-Einstein condensate (BEC) that is simultaneously loaded into the lattice. With a rapid increase of lattice depth, we take the system out of equilibrium and induce quench dynamics that is driven by the interactions between fermions and bosons. We observe the time evolution of the fermionic momentum distribution, which shows long-lived coherent oscillations for up to ten periods, both for attractive and repulsive Fermi-Bose interactions. A theoretical model reveals that the dynamics arises as a consequence of the delocalized nature of the initial fermionic state and the on-site number fluctuations of the BEC. Our work demonstrates that coherent quench dynamics constitutes a powerful technique to gain insight into the nature of fermionic quantum many-body states and to accurately determine Hamiltonian parameters used in their microscopic description.
2. arXiv:1406.2530 [pdf, ps, other]
Topological growing of Laughlin states in synthetic gauge fields
Fabian Grusdt, Fabian Letscher, Mohammad Hafezi, Michael Fleischhauer
Comments: 4 pages, 2 figures, 1 page supplementary material
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)

We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions (CF) along with magnetic flux quanta one-by-one. The topologically protected Thouless pump ("Laughlin's argument") is used to create two localized flux quanta and the resulting hole excitation is subsequently filled by a single boson, which, together with one of the flux quanta forms a CF. Using our protocol, filling 1/2 LN states can be grown with particle number N increasing linearly in time and strongly suppressed number fluctuations. To demonstrate the feasibility of our scheme, we consider two-dimensional (2D) lattices subject to effective magnetic fields and strong on-site interactions. We present numerical simulations of small lattice systems and discuss also the influence of losses.

3. arXiv:1406.2336 [pdf, other]
Optical transport of ultracold atoms using focus-tunable lenses
Julian Léonard, Moonjoo Lee, Andrea Morales, Thomas M. Karg, Tilman Esslinger, Tobias Donner
Comments: 4 pages, 3 figures
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Optics (physics.optics); Quantum Physics (quant-ph)

We present an optical setup with focus-tunable lenses to dynamically control the waist and focus position of a laser beam, in which we transport a trapped ultracold cloud of 87-Rb over a distance of 28 cm. The scheme allows us to shift the focus position at constant waist, providing uniform trapping conditions over the full transport length. The fraction of atoms that are transported over the entire distance comes near to unity, while the heating of the cloud is in the range of a few microkelvin. We characterize the position stability of the focus and show that residual drift rates in focus position can be compensated for by counteracting with the tunable lenses. Beyond being a compact and robust scheme to transport ultracold atoms, the reported control of laser beams makes dynamic tailoring of trapping potentials possible.

Jun 10
1.arXiv:1406.2176 [pdf, other]
Observing elementary excitations of correlated one-dimensional Bose gases
Nicole Fabbri, Milosz Panfil, David Clément, Leonardo Fallani, Massimo Inguscio, Chiara Fort, Jean-Sébastien Caux
Subjects: Quantum Gases (cond-mat.quant-gas)

The concept of elementary excitations lies at the core of our understanding of interacting many-body systems. In one-dimensional (1D) quantum fluids, peculiar modes have been predicted to appear which do not have any higher-dimensional equivalent [1, 2]. As revealed recently in electronic systems and spin chains [3-5], these modes can dominate the physics outside of the low-energy regime, where the celebrated Luttinger liquid paradigm applies. No evidence of these modes has been reported so far for bosonic fluids. Here, we trace the excitations of 1D strongly-interacting Bose gases at low temperature through their effects on dynamical response functions. Our experimental results are compared to a theoretical analysis of the finite-temperature Lieb-Liniger model describing repulsively interacting bosons. The excellent agreement demonstrates that both quasi-particle and quasi-hole modes are contributing to the experimental correlation signals, a regime that lies beyond the conventional Luttinger Liquid theory.

2.arXiv:1406.2102 [pdf, ps, other]
SU(2) Ginzburg-Landau theory for degenerate Fermi gases with synthetic non-Abelian gauge fields
Kuang Zhang, Yanlin Feng, Chuanwei Zhang, Gang Chen, Suotang Jia
Comments: 9 pages, 2 figures
Subjects: Quantum Gases (cond-mat.quant-gas)

The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing originally on the Fermi atoms, affect the pairing field with no extra electric charge by a local gauge-field theory,and then obtain the first and second SU(2) Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau equations, we find that the superfluid critical temperature of the intra- (inter-) band pairing increases (decreases) linearly, when increasing the strength of the synthetic non-Abelian gauge fields. More importantly, we predict a novel SU(2) non-Abelian Josephson effect, which can be used to design a new atomic superconducting quantum interference device.


Jun 9
1.arXiv:1406.1789 (cross-list from hep-th) [pdf, ps, other]
Relaxation dynamics in a strongly coupled Fermi superfluid
S. Khlebnikov
Comments: 4 pages, 2 figures
Subjects: High Energy Physics - Theory (hep-th); Quantum Gases (cond-mat.quant-gas); Superconductivity (cond-mat.supr-con)

The key feature of time-dependent dynamics in a paired Fermi superfluid is the presence of a large number of independent degrees of freedom---the pairing amplitudes of fermions with different momenta. We argue that useful prototypes of this dynamics come from D-brane constructions of string theory. Using a specific example of that kind, we identify the mechanism by which a strongly coupled Fermi superfluid relaxes to equilibrium; it involves a wave of excitation in the momentum space, propagating from the Fermi surface towards the ultraviolet. For a sudden quench induced by a change in the fermion coupling, we find that the relaxation occurs rapidly, over only a few oscillations of the quasiparticle gap.

June 6
1. arXiv:1406.1403 [pdf, other]
Phase diffusion in a Bose-Einstein condensate of light
A.-W. de Leeuw, E.C.I. van der Wurff, R.A. Duine, H.T.C. Stoof
We study phase diffusion in a Bose-Einstein condensate of light in a dye-filled optical microcavity, i.e., the spreading of the probability distribution for the condensate phase. To observe this phenomenon, we propose an interference experiment between the condensed photons and an external laser. We determine the average interference patterns, considering quantum and thermal fluctuations as well as dissipative effects due to the dye. Moreover, we show that a representative outcome of individual measurements can be obtained from a stochastic equation for the global phase of the condensate.

2. arXiv:1406.1322 [pdf, other]
A Bose-Einstein condensate of metastable helium for quantum correlation experiments
Michael Keller, Mateusz Kotyrba, Florian Leupold, Mandip Singh, Maximilian Ebner, Anton Zeilinger
We report on the realization of Bose-Einstein condensation of metastable helium-4. After exciting helium to its metastable state, the atomic beam is collimated and slowed. We then trap several 10^8 atoms in a magneto-optical trap. For subsequent evaporative cooling, the atoms are transferred into a magnetic trap. Degeneracy is achieved with typically a few 10^6 atoms. For detection of atomic correlations with high resolution, an ultra-fast delay-line detector has been installed. Consisting of four quadrants with independent read-out electronics that allow for true simultaneous detection of atoms, the detector is especially suited for quantum correlation experiments that require the detection of correlated subsystems. We expect our setup to allow for the direct demonstration of momentum entanglement in a scenario equivalent to the EPR gedankenexperiment. This will pave the way to matter-wave experiments exploiting the peculiarities of quantum correlations.

June 5
1. arXiv:1406.1095 [pdf, other]
Direct measurement of the current-phase relationship of a superfluid weak link
S. Eckel, F. Jendrzejewski, A. Kumar, C.J. Lobb, G.K. Campbell
Weak connections between superconductors or superfluids differ from classical links due to quantum coherence, which allows flow without resistance. Transport properties through such weak links can be described with a single function, the current-phase relationship, which serves as the quantum analog of the current-voltage relationship. Here, we present the first direct measurement of a current-phase relationship for a superfluid weak link. We interferometrically measure the phase gradient around a ring-shaped superfluid Bose-Einstein condensate containing a rotating weak link, allowing us to identify the current flowing around the ring. This technique can be extended to weak links in any phase-coherent quantum gas and can also measure the current-phase relationships of excitations, such as solitonic-vortices. Such measurements may open new avenues of research in quantum transport.

2. arXiv:1406.1110 [pdf, other]
Half-Quantum Vortex Molecules in a Binary Dipolar Bose Gas
Wilbur E. Shirley, Brandon M. Anderson, Charles W. Clark, Ryan M. Wilson
We study the ground state phases of a rotating two-component, or binary Bose-Einstein condensate, wherein one component possesses a large magnetic dipole moment. A variety of non-trivial phases emerge in this system, including a half-quantum vortex (HQV) chain phase and a HQV molecule phase, where HQVs of opposite charge bind at short distances. We attribute the emergence of these phases to the development of a minimum in the adiabatic HQV interaction potential, which we calculate explicitly. We thus show that the presence of dipolar interactions in this system leads to a rich phase diagram, and the formation of HQV molecules.


June 4
1. arXiv:1406.0570 [pdf, other]
Spin-orbital dynamics in a system of polar molecules
Sergey V. Syzranov, Michael L. Wall, Victor Gurarie, Ana Maria Rey
Spin-orbit coupling (SOC) in solids normally originates from the electron motion in the electric field of the crystal. It is key to understanding a variety of magnetic, spin-transport, and topological phenomena, such as Majorana fermions and recently discovered topological insulators. Implementing and controlling spin-orbit coupling is thus highly desirable and could open untapped opportunities for the exploration of unique quantum physics. In this paper we show that dipole-dipole interactions can produce an effective SOC in two-dimensional ultracold polar molecule gases. This SOC generates chiral excitations with a non-trivial Berry phase 2π. These excitations, which we call \emph{chirons}, resemble low-energy quasiparticles in bilayer graphene and manifest themselves in the dynamics of the spin density profile, spin currents, and spin coherences, even for molecules pinned in a deep optical lattice. Chirons emerge regardless of the quantum statistics and for arbitrary ratios of kinetic to interaction energies.


June 3
1. arXiv:1406.0181 [pdf, other]
Non-standard Hubbard models in optical lattices
Omjyoti Dutta, Mariusz Gajda, Philipp Hauke, Maciej Lewenstein, Dirk-Sören Lühmann, Boris A. Malomed, Tomasz Sowiński, Jakub Zakrzewski
Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schr\"odinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.


June 2
1. arXiv:1405.7745 [pdf, other]
In situ imaging of vortices in Bose-Einstein condensates
Kali E. Wilson, Zachary L. Newman, Joseph D. Lowney, Brian P. Anderson
Laboratory observations of vortex dynamics in Bose-Einstein condensates (BECs) are essential for determination of many aspects of superfluid dynamics in these systems. We present a novel application of dark-field imaging that enables \texttt{\it in situ} detection of two-dimensional vortex distributions in single-component BECs, a step towards real-time measurements of complex two-dimensional vortex dynamics within a single BEC. By rotating a 87Rb BEC in a magnetic trap, we generate a triangular lattice of vortex cores in the BEC, with core diameters on the order of 400 nm and cores separated by approximately 9 μm. We have experimentally confirmed that the positions of the vortex cores can be determined without the need for ballistic expansion of the BEC.