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Chinese Physics B

Periodically modulated interaction effect on transport of Bose–Einstein condensates in lattice with local defects

Kun-Qiang Zhu, Zi-Fa Yu, Ji-Ming Gao, Ai‐Xia Zhang, Hong-Ping Xu, Ju-Kui Xue

Published Jan 1, 2019• 2 citations
Publisher

Abstract

We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate (BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.

DOI
10.1088/1674-1056/28/1/010307

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We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate (BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.
We study the dynamics of dipolar gas in deep lattices described by a nonlocal nonlinear discrete Gross-Pitaevskii equation. The stabilities and the propagation properties of traveling plane waves in the system with defects are discussed in detail. For a clean lattice, both energetic and dynamical stabilities of the traveling plane waves are studied. It is shown that the system with attractive local interaction can preserve the stabilities, i.e., the dipoles can stabilize the gas because of repulsive nonlocal dipole-dipole interactions. For a lattice with defects, within a two-mode approximation, the propagation properties of traveling plane waves in the system map onto a nonrigid pendulum Hamiltonian with quasimomentum-dependent nonlinearity (induced by the nonlocal interactions). Competition between defects, quasimomentum of the gas, and nonlocal interactions determines the propagation properties of the traveling plane waves. Critical conditions for crossing from a superfluid regime with propagation preserved to a normal regime with defect-induced damping are obtained analytically and confirmed numerically. In particular, the critical conditions for supporting the superfluidity strongly depend on the defect type and the quasimomentum of the plane waves. The nonlocal interaction can significantly enhance the superfluidity of the system.
We investigate, both analytically and numerically, the quasisuperfluidity properties of periodic Bose-Einstein condensates (BECs) in a quasi-one-dimensional (1D) ring with optical lattices (OL) of different kinds (linear and nonlinear) and with a moving defect of an infinite mass inside. To study the dynamics of the condensate we used a mean-field approximation describing the condensate by use of the Gross-Pitaevskii equation for the order parameter. We show that the resonant scattering of sound Bloch waves with the defect profoundly affect BEC superfluidity. In particular, a moving defect always leads to the breakdown of superfluidity independently of the value of its velocity. For weak periodic potentials the superfluidity breakdown may occur on a very long time scale (quasisuperfluidity) but the breakdown process can be accelerated by increasing the strength of the OL. Quite remarkably, we find that when the length of the ring is small enough to imply the discreteness of the reciprocal space, it becomes possible to avoid the resonant scattering and to restore quasi-superfluidity.
Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.
Bose-Einstein condensates (BECs) have proven to be remarkable systems with which to study some of the foundational models of condensed matter physics. The observation of a critical velocity for the breakdown of superfluidity in a BEC and the superfluid to Mott insulator transition observed in a BEC trapped by an optical lattice are but two examples of the, by now, dozens of exciting results in this field, which combines theoretical tools from condensed matter physics with state-of-the-art experimental techniques from ultra-cold atomic physics. However, any real condensed matter system has to contend with the effects of disorder, a phenomena notably absent in the inherently clean BEC systems. We have developed and implemented a way to add well characterized disorder in a controlled way to the otherwise clean BEC system using the light field from a laser speckle pattern. Using this system, we have investigated the effects of disorder or a single Gaussian defect, on the collective dipole motion of a BEC of 7Li in an optical trap. In addition, we perform transport experiments on a weakly interacting BEC expanding in a disordered one-dimensional atom wave-guide. We have observed that in such a system, the wave nature of matter can lead to spectacular and counterintuitive phenomena. Specifically, we verify that this system exhibits Anderson localization, a phenomena fundamentally resulting from the interference of multiply scattered matter waves. In such a state, the localized gas behaves as an insulator in a regime where it is classically expected to be conducting.\nWe also present results of experiments regarding a repulsive BEC scattering from a semi-permeable, single defect potential. We investigate the transport properties of such a system with special emphasis on the velocity and defect strength dependent dissipation of the collective dipole motion of the BEC. Finally, we present the results of our experiments on the scattering properties of bright matter wave solitons. We have observed fragmentation of the soliton in a disordered potential as well as both splitting and recombination of a soliton after interacting with a single repulsive defect potential.
We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross–Pitaevskii equation.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.