Aug 27 - Aug 31, Saubhik Sarkar
Aug 31
1.arXiv:1208.6266 [pdf, ps, other]
Composite fermion state of spin-orbit coupled bosons
Tigran A. Sedrakyan, Alex Kamenev, Leonid I. Glazman
We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in 2D. We argue that at low density its groundstate is a composite fermion state with a Chern-Simons gauge field and filling factor one. The chemical potential of such a state scales with the density as \mu \propto n^{3/2}. This is a lower energy per particle than \mu \propto n for the earlier suggested groundstate candidates: a condensate with broken time-reversal symmetry and a spin density wave state.
2.arXiv:1208.6194 [pdf, ps, other]
Approximate mean-field equations of motion for quasi-2D Bose-Einstein condensate systems
Mark Edwards, Michael Krygier, Hadayat Seddiqi, Brandon Benton, Charles W. Clark
We present a method for approximating the solution of the three-dimensional, time-dependent Gross-Pitaevskii equation (GPE) for Bose-Einstein condensate systems where the confinement in one dimension is much tighter than in the other two. This method employs a hybrid Lagrangian variational technique whose trial wave function is the product of a completely unspecified function of the coordinates in the plane of weak confinement and a gaussian in the strongly confined direction having a time-dependent width and quadratic phase. The hybrid Lagrangian variational method produces equations of motion that consist of (1) a two-dimensional, effective GPE whose nonlinear coefficient contains the width of the gaussian and (2) an equation of motion for the width that depends on the integral of the fourth power of the solution of the 2D effective GPE. We apply this method to the dynamics of Bose-Einstein condensates confined in ring-shaped potentials and compare the approximate solution to the numerical solution of the full 3D GPE.
Aug 30
1.arXiv:1208.5976 [pdf, ps, other]
Modified Bethe-Peierls boundary condition for ultracold atoms with Spin-Orbit coupling
Peng Zhang, Long Zhang, Youjin Deng
We show that the Bethe-Peierls (BP) boundary condition should be modified for ultracold atoms with spin-orbit (SO) coupling. Moreover, we derive a general form of the modified BP boundary condition, which is applicable to a system with arbitrary kind of SO coupling. Our result is helpful for the study of both few-body and many-body physics in SO-coupled ultracold gases.
2.arXiv:1208.5807 [pdf, other]
Quantum Phases of Dipolar Bosons in Bilayer Geometry
Arghavan Safavi-Naini, Sebnem G. Soyler, Guido Pupillo, H. R. Sadeghpour, Barbara Capogrosso-Sansone
We investigate the quantum phases of hard-core dipolar bosons confined to a square lattice in a bilayer geometry. Using exact theoretical techniques, we discuss the many-body effects resulting from pairing of particles across layers at finite density, including a novel pair supersolid phase, superfluid and solid phases. These results are of direct relevance to experiments with polar molecules and atoms with large magnetic dipole moments trapped in optical lattices.
Aug 29
1.arXiv:1208.5550 (cross-list from cond-mat.str-el) [pdf, other]
Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
Jie Lin, K. A. Matveev, M. Pustilnik
We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.
Aug 28
1. arXiv:1208.5450 [pdf, ps, other]
Majorana fermions in one-dimensional spin-orbit coupled Fermi gases
Ran Wei, Erich J. Mueller
We theoretically study trapped one-dimensional Fermi gases in the presence of spin-orbit coupling induced by Raman lasers. The gas changes from a conventional (non-topological) superconductor to a topological superconductor as one increases the intensity of the Raman lasers above a critical chemical-potential dependent value. Solving the Bogoliubov-de Gennes equations self-consistently, we calculate the density of states in real and momentum space at finite temperatures. We study Majorana fermions (MFs) which appear at the boundaries between topologically trivial and topologically non-trivial regions. We linearize the trap near the location of a MF, finding an analytic expression for the localized MF wavefunction and the gap between the MF state and other edge states.
Aug 27
1.arXiv:1208.4852 [pdf, other]
Quantum Dynamics of Disordered Bosons in an Optical Lattice
Chien-Hung Lin, Rajdeep Sensarma, K. Sengupta, S. Das Sarma
We study the equilibrium and non-equilibrium properties of strongly interacting bosons on a lattice in presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose Hubbard model and obtain the Mott insulator, Bose glass and superfluid phases. We also study the non equilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter and the energy pumped into the system in this process as a function of the inverse ramp rate $\tau$. For the clean case the density of excitations goes to a constant, while the order parameter and energy relaxes as $1/\tau$ and $1/\tau^2$ respectively. With disorder, the excitation density decays exponentially with $\tau$, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as $\tau$ is increased.
2.arXiv:1208.4883 [pdf, ps, other]
An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
Shintaro Taie, Rekishu Yamazaki, Seiji Sugawa, Yoshiro Takahashi
The Hubbard model, containing only the minimum ingredients of nearest neighbor hopping and on-site interaction for correlated electrons, has succeeded in accounting for diverse phenomena observed in solid-state materials. One of the interesting extensions is to enlarge its spin symmetry to SU(N>2), which is closely related to systems with orbital degeneracy. Here we report a successful formation of the SU(6) symmetric Mott insulator state with an atomic Fermi gas of ytterbium (173Yb) in a three-dimensional optical lattice. Besides the suppression of compressibility and the existence of charge excitation gap which characterize a Mott insulating phase, we reveal an important difference between the cases of SU(6) and SU(2) in the achievable temperature as the consequence of different entropy carried by an isolated spin. This is analogous to Pomeranchuk cooling in solid 3He and will be helpful for investigating exotic quantum phases of SU(N) Hubbard system at extremely low temperatures.
Aug 20 - Aug 24, Xiaopeng Li
Aug 24
1. arXiv:1208.4834 [pdf, ps, other]
Genons, twist defects, and projective non-Abelian braiding statistics
Maissam Barkeshli, Chao-Ming Jian, Xiao-Liang Qi
It has recently been realized that a general class of non-abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductor-ferromagnet domain walls in conventional quantum Hall states or topological insulators. In this paper, we begin by placing these defects within the broader conceptual scheme of extrinsic twist defects associated with symmetries of the topological state. We explicitly study several classes of examples, including $Z_2$ and $Z_3$ twist defects, where the topological state with N twist defects can be mapped to a topological state without twist defects on a genus $g \propto N$ surface. To emphasize this connection we refer to the twist defects as genons. We develop methods to compute the projective non-abelian braiding statistics of the genons, and we find the braiding is given by adiabatic modular transformations, or Dehn twists, of the topological state on the effective genus g surface. We study the relation between this projective braiding statistics and the ordinary non-abelian braiding statistics obtained when the genons become deconfined, finite-energy excitations. We find that the braiding is generally different, in contrast to the Majorana case, which opens the possibility for fundamentally novel behavior. We find situations where the genons have quantum dimension 2 and can be used for universal topological quantum computing (TQC), while the host topological state is by itself non-universal for TQC.
2. arXiv:1208.4601 [pdf, other]
Why is the bulk resistivity of topological insulators so small?
Brian Skinner, Tianran Chen, B. I. Shklovskii
As-grown topological insulators (TIs) are typically heavily-doped $n$-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length.
Aug 23
1. arXiv:1208.4579 [pdf, other]
Designing Topological Bands in Reciprocal SpaceN. R. Cooper, R. Moessner
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically non-trivial band structures. Our approach is simple and direct: it amounts to considering tight-binding models directly in reciprocal space. These models naturally cause atoms to experience highly uniform magnetic flux density and lead to topological bands with very narrow dispersion, without fine-tuning of parameters. Further, our construction immediately yields instances of optical Chern lattices, as well as band structures of higher Chern number, |C|>1.
Aug 22
1. arXiv:1208.4234 [pdf, other]
Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators
A. Alexandradinata, Xi Dai, B. Andrei Bernevig
In the context of translationally-invariant insulators, Wilson loops describe the adiabatic evolution of the ground state around a closed circuit in the Brillouin zone. We propose that the Wilson-loop eigenspectrum provides a complete characterization of the inversion-symmetric topological insulator. Through the Wilson loop, we formulate a criterion for nontriviality that indicates a Z classification of 1D inversion-symmetric insulators. If the ground-state wavefunctions at momenta 0 and pi transform under different representations of inversion, we find that a subset of the Wilson-loop eigenvalues are robustly quantized to -1; we identify the number of -1 eigenvalues as a topological index N \in Z. Physical interpretations of N are provided in holonomy and in the geometric-phase theory of polarization. In addition, we identify N with the number of protected boundary modes in the entanglement spectrum. In 2D, we identify a relative winding number W which provides a Z classification of 2D inversion-symmetric insulators. For insulators with nonzero W, their Wilson-loop eigenspectra exhibit spectral flow that is protected only by inversion symmetry. Hence, W is the inversion-analog of the first Chern class C (for charge-conserving insulators) and the Z_2 invariant Xi (for time-reversal invariant insulators). Finally, we establish relations between the topological invariants (W, C, Xi) and the Wilson-loop eigenvalues at symmetric lines in the 2D Brillouin zone.
2. arXiv:1208.4232 [pdf, ps, other]
Rotational Quantum Friction
Rongkuo Zhao, J. B. Pendry
We investigate the frictional forces due to quantum fluctuations, acting on a small sphere rotating near a surface. At zero temperature, we find the frictional force near a surface to be several orders of magnitude larger than that for the sphere rotating in vacuum. For metallic materials with typical conductivity, quantum friction is maximized by matching the frequency of rotation with the conductivity. Materials with poor conductivity are favored to obtain large quantum frictions. For semiconductor materials that are able to support surface plasmon polaritons, quantum friction can be further enhanced by several orders of magnitude due to the excitation of surface plasmon polaritons.
3. arXiv:1208.4136 [pdf, other]
Magnetic field tuned dimensional crossover in spin-orbit coupled semiconductor nanowires with induced superconducting pairing
Tudor D. Stanescu, Roman M. Lutchyn, S. Das Sarma
We show that the topological Majorana quasiparticles hosted by semiconductor nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these zero-energy crossings can be tuned by an external magnetic field and are protected by the particle-hole symmetry. We study the evolution of the low-energy spectrum as a function of the magnetic field, wire length, and chemical potential, manifestly establishing that the low-energy physics of short wires is directly related to that occurring in long nanowires. In the presence of finite energy resolution, invariably operational under experimental conditions, the near-zero-energy states of a short wire give rise to a zero bias conductance peak over a finite magnetic field range.
4.arXiv:1208.4109 [pdf, other]
Synthetic Topological Degeneracy by Anyon Condensation
Yi-Zhuang You, Chao-Ming Jian, Xiao-Gang Wen
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed manifolds have been used to discover/define topological order in many-body systems, which contain excitations with fractional statistics. In this paper, we study a new type of topological degeneracy induced by condensing anyons along a line in 2D topological ordered states. Such topological degeneracy can be viewed as carried by each end of the line-defect, which is a generalization of Majorana zero-modes. The topological degeneracy can be used as a quantum memory. The ends of line-defects carry projective non-Abelian statistics, and braiding them allow us to perform fault tolerant quantum computations.
5. arXiv:1208.4299 (cross-list from quant-ph) [pdf, other]
Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
Erez Zohar, J. Ignacio Cirac, Benni Reznik
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.
Aug 21
1. arXiv:1208.4033 [pdf, other]
Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
A. J. A. James, R. M. Konik
We study the entanglement entropy and spectra of a coupled array of N one dimensional quantum Ising chains in their continuum limit. Employing a DMRG algorithm specifically adapted to the study of coupled, continuum systems, we are able to study large arrays of chains (up to N=200) both in their gapped phase and in the approach to criticality. Away from criticality the entanglement entropy obeys an area law. Close to criticality the entanglement entropy continues to obey the area law but possesses an additive piece scaling as $c_{eff}\log (N)/6$ with $c_{eff} \approx 1$. We also study the entanglement spectra of the coupled chains. Away from criticality in the disordered phase the low lying portion of the entanglement spectra appears similar to that of a single gapped quantum Ising chain. As the critical point is approached the entanglement gap closes. A finite scaling analysis shows that the entanglement gap and the energy gap vanish at the same value of interchain coupling.
2. arXiv:1208.4020 [pdf, other]
Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices
J. Heinze, J. S. Krauser, N. Fläschner, B. Hundt, S. Götze, K. Sengstock, C. Becker
We report on the first experimental observation of a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. We find a counterintuitively momentum-dependent oscillation frequency for excited particles and a fast decay of holes which we attribute to spatial trapping. Lifetime measurements reveal a significant enhancement of particle-hole recombination with increasing interactions.
3. arXiv:1102.5064 (cross-list from quant-ph) [pdf, other]
Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf (UBC)
Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation.
Aug 20
1. arXiv:1208.3608 [pdf, ps, other]
Driving phase slips in a superfluid atom circuit with a rotating weak link
K.C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, G. K. Campbell
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the weak link and hence the critical current, a feature which is difficult to implement in superconducting or superfluid helium circuits.
Aug 13 - Aug 17, Johannes Schachenmayer
Aug 17
1. arXiv:1208.3304 [pdf, ps, other]
Mott insulators in plaquettes
J.-P. MartikainenWe study small systems of Mott insulating ultracold atoms under the influence of gauge potentials and spin-orbit couplings. We use second order perturbation theory in tunneling, derive an effective theory for the Mott insulators with one atom per site, and solve it exactly. We find dramatic changes in the level structure and in the amount of degeneracies expected. We also demonstrate the dynamical behavior as the barriers between plaquettes are gradually removed and find potentially high overlap with the resonating valence bond (RVB) state of the larger system.
2. arXiv:1208.3215 [pdf, other]
Mixing, demixing, and structure formation in a binary dipolar Bose-Einstein condensate
Luis E. Young-S., S. K. AdhikariWe study static properties of disk-shaped binary dipolar Bose-Einstein condensates of 168Er-164Dy and 52Cr-164Dy mixtures under the action of inter- and intra-species contact and dipolar interactions and demonstrate the e?ect of dipolar interaction using the mean-?eld approach. Throughout this study we use realistic values of inter- and intra-species dipolar interactions and the intra-species scattering lengths and consider the inter-species scattering length as a parameter. The stability of the binary mixture is illustrated through phase plots involving number of atoms of the species. The binary system always becomes unstable as the number of atoms increases beyond a certain limit. As the inter-species scattering length increases corresponding to more repulsion, an overlapping mixed state of the two species changes to a separated demixed con?guration. During transition from a mixed to a demixed con?guration as the inter-species scattering length is increased for parameters just below the stability line, the binary condensate shows special structures in density in the form of biconcave and Jupiter-ring-like shapes, which are direct manifestations of dipolar interaction.
Aug 16
1. arXiv:1208.3005 [pdf, ps, other]
Synthetic Spin-Orbit Coupling in Two-level Cold Atoms
Qi Zhang, Jiangbin Gong, C. H. OhSynthetic spin-orbit coupling (SOC) in controlled quantum systems such as cold atoms or trapped ions has been of great interest. Here we show, both theoretically and computationally, a simplest realization of SOC using two-level cold atoms interacting with only one laser beam. The underlying mechanism is based upon the non-adiabatic nature of laser-atom interaction, with the Rabi frequency and atom's kinetic energy being comparable to each other. We use the Zitterbewegung (ZB) oscillation to further illustrate the effects of the synthesized SOC on the quantum dynamics of the two-level cold atoms. We expect our proposal to be of experimental interest in quantum simulation of SOC-related physics.
Aug 15
1. arXiv:1208.2911 [pdf, ps, other]
Steady-state crystallization of Rydberg excitations in an optically driven lattice gas
Michael Hoening, Dominik Muth, David Petrosyan, Michael Fleischhauer
We study resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential which suppresses simultaneous excitation of neighboring atoms. Considering two- and three-level excitation schemes, we analyze the dynamics and stationary state of the continuously-driven, dissipative many-body system employing time-dependent density-matrix renormalization group (t-DMRG) simulations. We show that two-level atoms can exhibit only nearest neighbor correlations, while three-level atoms under dark-state resonant driving can develop finite-range crystalline order of Rydberg excitations. We present an approximate rate equation model whose analytic solution yields qualitative understanding of the numerical results.
2. arXiv:1208.2941 [pdf, other]
Scattering bright solitons: quantum vs. mean-field behavior
Bettina Gertjerenken, Thomas P. Billam, Lev Khaykovich, Christoph WeissWe investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the quantum behavior are particularly large. On the N-particle quantum level, adding an additional harmonic confinement leads to a simple signature to distinguish quantum superpositions from statistical mixtures. While the non-linear character of the GPE does not allow quantum superpositions, the splitting of GPE-solitons takes place only partially. When the potential strength is increased, the fraction of the soliton which is transmitted or reflected jumps non-continuously. We explain these jumps via energy-conservation and interpret them as indications for quantum superpositions on the N-particle level. On the GPE-level, we also investigate the transition from this stepwise behavior to the continuous case.
3. arXiv:1208.2923 [pdf, other]
Chaos-driven dynamics in spin-orbit coupled atomic gases
Jonas Larson, Brandon Anderson, Alexander AltlandThe dynamics, appearing after a quantum quench, of a trapped, spin-orbit coupled, dilute atomic gas is studied. The characteristics of the evolution is greatly influenced by the symmetries of the system, and we especially compare evolution for an isotropic Rashba coupling and for an anisotropic spin-orbit coupling. As we break the rotational symmetry by making the spin-orbit coupling anisotropic, the underlying classical model is chaotic and the quantum dynamics is affected accordingly. Within experimentally relevant time-scales and parameters, the system thermalizes in a quantum sense. The corresponding equilibration time is found to agree with the Ehrenfest time, i.e. we numerically verify a ~log(1/h) scaling. Upon thermalization, we find the equilibrated distributions show examples of quantum scars distinguished by accumulation of atomic density for certain energies. At shorter time-scales we discuss non-adiabatic effects deriving from the spin-orbit coupled induced Dirac point. In the vicinity of the Dirac point, spin fluctuations are large and, even at short times, a semi-classical analysis fails.
4. arXiv:1208.2907 [pdf, ps, other]
Universal four-body states in heavy-light mixtures with positive scattering length
D. BlumeThe number of four-body states known to behave universally is small. This work adds a new class of four-body states to this relatively short list. We predict the existence of a universal four-body bound state for heavy-light mixtures consisting of three identical heavy fermions and a fourth distinguishable lighter particle with mass ratio $\kappa \gtrsim 9.5$ and short-range interspecies interaction characterized by a positive s-wave scattering length. The structural properties of these universal states are discussed and finite-range effects are analyzed. The bound states can be experimentally realized and probed utilizing ultracold atom mixtures.
Aug 14
1. arXiv:1208.2664 [pdf, ps, other]
Impact of photo-assisted collisions on superradiant light scattering with Bose condensates
Xinyu Luo, Kuiyi Gao, L. Deng, E. W. Hagley , Ruquan WangWe present experimental evidence supporting the postulation that the secondary effects of light-assisted collisions are the main reason that the superradiant light scattering efficiency in condensates is asymmetric with respect to the sign of the pump-laser detuning. Contrary to the recent experimental study, however, we observe severe and comparable heating with all three pump-laser polarizations. We also perform two-color, double-pulse measurements to directly study the degradation of condensate coherence and the resulting impact on the superradiant scattering efficiency.
2. arXiv:1208.2514 [pdf, ps, other]
Ground state of spin-1 Bose-Einstein condensates with spin-orbit coupling in a Zeeman field
L. Wen, Q. Sun, H. Q. Wang, A. C. Ji, W. M. LiuWe systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when the strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.
3. arXiv:1208.2349 [pdf, ps, other]
Finite temperature effects in two-mode bosonic Josephson junctions
G. Mazzarella, L. Salasnich, F. ToigoWe analyze the effects of the temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose-Hubbard Hamiltonian, we calculate the coherence visibility and the fluctuation of the on-site occupation number and study them as functions of the temperature. We show that, contrary to naive expectations, when the bos
4. arXiv:1208.2371 [pdf, ps, other]
One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential
Carlos Trallero-Giner, Rolci CipolattiBy means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.
Aug 13
1. arXiv:1208.2255 [pdf, other]
Quantum simulation of expanding space-time with tunnel-coupled condensates
Clemens Neuenhahn, Florian MarquardtWe consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent with the spatial expansion of a one-dimensional toy-Universe with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss, how to observe the freezing out of quantum fluctuations during an accelerating expansion in a possible experiment. We also discuss an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field out of quantum fluctuations.
2. arXiv:1208.1861 [pdf, other]
Quantum control of spin-correlations in ultracold lattice gases
P. Hauke, R. J. Sewell, M. W. Mitchell, M. LewensteinWe demonstrate that it is possible to prepare a lattice gas of ultracold atoms with a desired non-classical spin-correlation function using atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on quantum non-demolition (QND) measurement and feedback, and allows in particular to create on demand exponentially or algebraically decaying correlations, as well as a certain degree of multi-partite entanglement.
3. arXiv:1208.2067 [pdf, other]
Measurement of the Homogeneous Contact of a Unitary Fermi gas
Yoav Sagi, Tara E. Drake, Rabin Paudel, Deborah S. JinThe theory of strongly interacting fermions is challenging due to the many-body nature of the problem and the fact that there is no obvious small parameter for a perturbative analysis. An important universal quantity whose predicted value is sensitive to different theoretical approaches is the Tan contact of a homogeneous ensemble. Recently, we reported on the development of a technique to probe local properties of a trapped gas. Here we employ this technique and measure the local (homogeneous) contact of a unitary Fermi gas. We find a gradual decrease of the contact when the temperature is increased, with good agreement with the virial expansion at high temperatures. Several theoretical works predict an increase in the contact above the superfluid critical temperature, which we do not observe in the experiment. Out of the theories compared, our data agree best with the Nozieres-Schmitt-Rink approach with gaussian pair-fluctuations.
4. arXiv:1208.2123 [pdf, ps, other]
Energy eigenfunctions of the 1D Gross-Pitaevskii equation
Želimir Marojević, Ertan Göklü, Claus LämmerzahlThe energy eigenstates and eigenvalues for the 1D Grosss--Pitaevskii--equation for three different potentials have been determined numerically. For that a new and powerful algrorithm has been developed which is capable to work also in the regime of strong nonlinearities. The numerically found solutions completely agree with the case of known analytical solutions.
5. arXiv:1208.2147 [pdf, other]
Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
Andrej Junginger, Jörg Main, Günter Wunner, Thomas BartschWe investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the "activated complex" that mediates the collapse of the condensate. For a certain value of the s-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows to smoothly pass the bifurcation.
6. arXiv:1208.2198 [pdf, other]
Roton immiscibility in a two-component dipolar Bose gas
Ryan M. Wilson, Christopher Ticknor, John L. Bohn, Eddy Timmermans
We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a roton-like IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled non-local Gross-Pitaevskii equations.
7. arXiv:1208.2206 [pdf, ps, other]
Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches
D. Rubeni, A. Foerster, I. RoditiIn this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground state energy of the relative motion of a system of two fermions with spin up and down interacting via a delta-function potential in a 1D harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.
8. arXiv:1208.2211 [pdf, other]
Phase Separation in Mixtures of Repulsive Fermi Gases Driven by Mass Difference
Xiaoling Cui, Tin-Lun HoWe show that phase separation must occur in a mixture of fermions with repulsive interaction if their mass difference is sufficiently large. This phenomenon is highly dimension-dependent. Consequently, the density profiles of phase separated 3d mixtures are very different from those in 1d. Noting that the ferromagnetic transition of a spin-1/2 repulsive Fermi gas is the equal mass limit of the phase separation in mixtures, we show from the Bethe Ansatz solution that a ferromagnetic transition will take place in the scattering states when the repulsive interaction passes through resonance and becomes attractive.
Aug 6 - Aug 10, Saubhik Sarkar
Aug 10
1.arXiv:1208.1980 [pdf, ps, other]
Quantum gas mixtures in different correlation regimes
Miguel Angel Garcia-March, Thomas Busch
We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a new class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically and semiclassically in both situations and show that the quantum correlations are maintained in the separated phase.
Aug 9
1. arXiv:1208.1659 [pdf, ps, other]
Superfluid drag of two-species Bose-Einstein condensates in optical lattices
Patrick P. Hofer, C. Bruder, Vladimir M. Stojanovic
We study two-species Bose-Einstein condensates in quasi two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short range) inter-species interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a non-monotonic dependence on the lattice depth. To make contact with future experiments, we quantitatively investigate the drag for mass ratios corresponding to relevant atomic species.
Aug 8
1. arXiv:1208.1455 [pdf, ps, other]
Phase diagrams of Fermi gases in a trap with mass and population imbalances at finite temperature
Jibiao Wang, Hao Guo, Qijin Chen
The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of atomic Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover with population and mass imbalances, using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of $^{6}$Li and $^{40}$K atoms. We show that there exist exotic types of phase separation in the BEC regime as well as sandwich-like shell structures at low temperature with superfluid or pseudogapped normal state in the central shell in the BCS and unitary regimes, especially when the light species is the majority. Such a sandwich-like shell structure appear when the mass imbalance increases beyond certain threshold. Our result is relevant to future experiments on the $^6$Li--$^{40}$K mixture and possibly other Fermi-Fermi mixtures.
2. arXiv:1208.1300 [pdf, other]
Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices
Zhaochuan Shen, L. Radzihovsky, V. Gurarie
We study thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the non-monotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair/molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.
Aug 7
1. arXiv:1208.1213 [pdf, other]
Dipole excitons in coupled quantum wells: toward an equilibrium exciton condensate
David W. Snoke
In recent years, experiments by several groups have demonstrated spontaneous coherence in polariton systems, which can be viewed as a type of nonequilibrium Bose-Einstein condensation. In these systems, the polariton lifetime is longer than, but not much longer than, the polariton-polariton scattering time which leads to the thermalization. By contrast, over the past twenty years several groups have pursued experiments in a different system, which has very long exciton lifetime, up to 30 microseconds or more, essentially infinite compared to the thermalization time of the excitons. Thermal equilibrium of this type of exciton in a trap has been demonstrated experimentally. In this system, the interactions between the excitons are not short-range contact interactions, but instead are dipole-dipole interactions, with the force at long range going as $1/r^{3}$. Up to now there has not been a universally accepted demonstration of BEC in this type of system, and the way forward will require better understanding of the many-body effects of the excitons. I review what has been learned and accomplished in the past two decades in the search for an equilibrium BEC in this promising system.
2. arXiv:1208.1194 [pdf, ps, other]
Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a 2D square lattice
Luca Salasnich, Flavio Toigo
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-bound Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal-long-range-order for fermions we calculate analytically and numerically the pair binding energy, the energy gap and the condensate fraction of Cooper pairs as a function of interaction strength and filling fractor of atoms in the lattice at zero temperature.
Aug 6
1. arXiv:1208.0608 [pdf, ps, other]
Pairing instabilities in topological insulator quantum wells
Predrag Nikolic, Zlatko Tesanovi
Topological insulator quantum wells with induced attractive interactions between electrons are candidate systems for the realization of novel vortex lattice states with time-reversal symmetry, and incompressible quantum vortex liquids with fractional excitations. We analyze the competition between different pairing channels stimulated by the superconducting proximity effect in these quantum wells, and calculate the helical triplet pairing instability that can produce the mentioned phases using perturbation theory. We discuss the phase diagram tunable by gate voltage.
July 30 - Aug 3, Xiaopeng Li
Aug 3
1. arXiv:1208.0450 [pdf, ps, other]
Ultra-cold Fermi gases with resonant dipole-dipole interaction
T. Shi, S.-H. Zou, H. Hu, C.-P. Sun, S. YiThe superfluid phases in the resonant dipolar Fermi gases are investigated by the standard mean-field theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid in the Fermi gases with the isotropic interactions, the resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with the distinct internal symmetries. We point that near the resonance, the two competitive phases can coexist, and an emergent relative phase between the two order parameters spontaneously breaks the time-reversal symmetry, which could be observed in the momentum resolved rf-spectroscopy.
2. arXiv:1208.0381 [pdf, ps, other]
Excitation Transport through a Domain Wall in a Bose-Einstein Condensate
Shohei Watabe, Yusuke Kato, Yoji OhashiWe investigate the tunneling properties of collective excitations through a domain wall in the ferromagnetic phase of a spin-1 spinor Bose--Einstein condensate. Within the mean-field theory at T=0, we show that the transverse spin wave undergoes perfect reflection in the low-energy limit. This reflection property differs considerably from that of a domain wall in a Heisenberg ferromagnet where spin-wave excitations exhibit perfect transmission at arbitrary energy. When the Bogoliubov mode is scattered from this domain wall soliton, the transmission and reflection coefficients exhibit pronounced non-monotonicity. In particular, we find perfect reflection of the Bogoliubov mode at energies where bound states appear. This is in stark contrast to the perfect transmission of the Bogoliubov mode with arbitrary energy through a dark soliton in a scalar Bose--Einstein condensate.
Aug 2
1. arXiv:1208.0165 [pdf, other]
A local exchange theory for trapped dipolar gases
D. Baillie, P. B. BlakieWe develop a practical Hartree-Fock theory for trapped Bose and Fermi gases that interact with dipole-dipole interactions. This theory is applicable at zero and finite temperature. Our approach is based on the introduction of local momentum distortion fields that characterize the exchange effects in terms of a local effective potential. We validate our theory against existing theories, finding excellent agreement with full Hartree-Fock calculations.
2. arXiv:1208.0118 [pdf, ps, other]
Electromagnetic induced transparency and slow light in interacting quantum degenerate atomic gases
H. H. Jen, Xiong Bo, Ite A. Yu, Daw-Wei WangWe systematically develop the full quantum theory for the electromagnetic induced transparency (EIT) and slow light properties in ultracold Bose and Fermi gases. It shows a very different property from the classical theory which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed dramatically near the Bose-Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. From experimental point of view, such quantum EIT property is mostly manifested in the counter-propagating excitation schemes in either the low-lying Rydberg transition with a narrow line width or in the D2 transitions with a very weak coupling field. We further investigate the interaction effects on the EIT for a weakly interacting Bose-Einstein condensate, showing an inhomogeneous broadening of the EIT profile and nontrivial change of the light speed due to the quantum many-body effects beyond mean field energy shifts.
3. arXiv:1208.0170 [pdf, ps, other]
Dipolar Dynamics for Interacting Ultracold Fermions in a Trapped Optical Lattice
Jia-Wei Huo, Weiqiang Chen, U. Schollwöck, M. Troyer, Fu-Chun ZhangUsing the time-dependent density matrix renormalization group (tDMRG) method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.
4. arXiv:1208.0173 [pdf, ps, other]
Quantum phase fluctuations of a pair of interacting bosons or fermions in a symmetric double-well
Biswajit Das, Bitan Ghosal, Subhasish Dutta Gupta, Bimalendu DebWe introduce hermitian and unitary quantum phase operators of two-component fermionic fields. The phase operators of bosonic fields are the same as that of quantised radiation fields introduced long back. Using these phase operators we study quantum phase and number fluctuations of a pair of interacting bosons and those of a pair of interacting two-component fermions in a symmetric double-well potential. The fluctuations in inter-well number-difference operator can be quantified in terms of two-mode squeezing parameter which also serves as an entanglement parameter to quantify inter-well entanglement in number variables. We investigate the effects of on-site interaction on the fluctuations of the two canonically conjugate inter-well number- and phase-difference variables which are closely related to the entanglement. We also study intra-well number fluctuations. Our analytical and numerical results reveal that the fluctuation properties of a pair of bosons are quite distinct from that of a pair of two-component fermions. These findings may have implications in possible quantum information processing with ultracold atoms in confined geometries such as double-well optical lattices.
Aug 1
1. arXiv:1207.7131 [pdf, ps, other]
Elastic scattering of a quantum matter-wave bright soliton on a barrier
Christoph Weiss, Yvan CastinWe consider a one-dimensional matter-wave bright soliton, corresponding to the ground bound state of N particles of mass m having a binary attractive delta potential interaction on the open line. For a full N-body quantum treatment, we derive several results for the scattering of this quantum soliton on a short-range, bounded from below, external potential, restricting to the low energy, elastic regime where the centre-of-mass kinetic energy of the incoming soliton is lower than the internal energy gap of the soliton, that is the minimal energy required to extract particles from the soliton.
Jul 31
1. arXiv:1207.6971 [pdf, ps, other]
Three-component Fermi gas near a narrow Feshbach resonance
Yusuke NishidaA three-component Fermi gas near a broad Feshbach resonance does not have a universal ground state due to the Thomas collapse, while it does near a narrow Feshbach resonance. We explore its universal phase diagram in the plane of the inverse scattering length 1/akF and the resonance range R*kF. For a large R*kF, there exists a Lifshitz transition between superfluids with and without an unpaired Fermi surface as a function of 1/akF. With decreasing R*kF, the Fermi surface coexisting with the superfluid can change smoothly from that of atoms to trimers ("atom-trimer continuity"), imitating the quark-hadron continuity in a dense nuclear matter. Eventually, there appears a finite window in 1/akF where the superfluid is completely depleted by the trimer Fermi gas, which gives rise to a pair of quantum critical points. The boundaries of these three quantum phases are determined in regions where controlled analyses are possible and are also evaluated based on a mean-field plus trimer model.
2. arXiv:1207.6975 [pdf, ps, other]
Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions
Zhihao Xu, Linhu Li, Gao Xianlong, Shu ChenThe ground state properties of Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interaction are investigated by means of the exact diagonalization method. We show that the appearance of $N$-crests in the density profile of a trapped N-fermion system is a natural result of "fermionization" between antiparallel-spin fermions in the strongly repulsive limit and can not be taken as the only signature of Wigner crystal phase, as the static structure factor does not show any signature of crystallization. On the contrary, both the density distribution and static structure factor of Hubbard model with strong long-range interactions display clear signature of Wigner crystal. Our results indicate the important role of long-range interaction in the formation of Wigner crystal.
3. arXiv:1207.6804 [pdf, ps, other]
Response function and elementary excitations of a Bose-Einstein condensed gas with equal Rashba and Dresselhaus spin-orbit coupling
Giovanni I. Martone, Yun Li, Lev P. Pitaevskii, Sandro StringariBy calculating the dynamic density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling at zero temperature. The propagation of phonons is strongly affected by the coupling and the velocity of sound vanishes when one approaches the second-order phase transition between the spin polarized and the zero-momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, when one approaches the transition to the stripe phase.
4. arXiv:1207.6843 [pdf, ps, other]
Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study
Zi Cai, Hsiang-Hsuan Hung, Lei Wang, Yi Li, Congjun WuWe employ the determinant projector quantum Monte-Carlo method to investigate the ground state magnetic properties in the Mott insulating states of the half-filled SU(4) and SU(6) Fermi-Hubbard model in the 2D square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the SU(4) case with a small residual spin moment. The SU(6) case is a spin gapless quantum paramagnetic state with the absence of long-range antiferromagnetic, dimer, and charge flux orderings. Spin correlations exhibit power-law decay, which is consistent with a possible algebraic spin-correlation state with an odd number of fermions per unit cell.
July 30
1. arXiv:1207.6505 [pdf, ps, other]
Rotational properties of non-dipolar and dipolar Bose-Einstein condensates confined in annular potentials
E. Ö. Karabulut, F. Malet, G. M. Kavoulakis, S. M. ReimannWe investigate the rotational response of both non-dipolar and dipolar Bose-Einstein condensates confined in an annular potential. For the non-dipolar case we identify certain critical rotational frequencies associated with the formation of vortices. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms.
