Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices

Modugno, Michèle; Tozzo, C.; Dalfovo, F.

doi:10.1103/physreva.70.043625

Cited by 70 publications

(38 citation statements)

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“…Hence, the state is unstable. Both dynamical and energetic instabilities of a lattice BEC have been investigated extensively in theory [158][159][160][161][162][163][164][165] and experiment [166][167][168]. Theoretically, once a nonlinear Bloch wave is known, its stability can be analyzed by solving the BdG equations.…”

Section: Experimental Measurement Of Dynamical Instability Using a Trmentioning

confidence: 99%

Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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The experimental and theoretical research of spin-orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin-orbit coupling parameters, we discuss the fundamental properties and general applications of spin-orbit-coupled Bose-Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin-orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin-orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin-orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

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Section: Experimental Measurement Of Dynamical Instability Using a Trmentioning

confidence: 99%

Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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“…To capture the main physics, the system can be conveniently described by means of effective 1D theories, which account for the transverse degrees of freedom through a renormalization of the coupling constant. Still, it is important to check the effect of the transverse degrees of freedom since they are known to play a relevant role in some cases 13 .…”

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Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement

Krämer

Menotti

Modugno³

2005

J Low Temp Phys

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We study the effect of the transverse degrees of freedom on the velocity of sound in a Bose-Einstein condensate immersed in a one-dimensional optical lattice and radially confined by a harmonic trap. We compare the results of full three-dimensional calculations with those of an effective 1D model based on the equation of state of the condensate. The perfect agreement between the two approaches is demonstrated for several optical lattice depths and throughout the full crossover from the 1D mean-field to the Thomas Fermi regime in the radial direction.Ever since the achievement of Bose-Einstein condensation (BEC) with atomic vapors, an extensive activity in the study of the excitations of these systems has been carried out. A particular example is the exploration of sound excitations in elongated condensates 1,2,3,4,5 . The propagation of sound in one-dimensional (1D) optical lattices has been the subject of recent studies performed both in the linear 6,7,8,9,10,11 and nonlinear regimes 12 . To capture the main physics, the system can be conveniently described by means of effective 1D theories, which account for the transverse degrees of freedom through a renormalization of the coupling constant. Still, it is important to check the effect of the transverse degrees of freedom since they are known to play a relevant role in some cases 13 .In this paper, we show that the sound velocity in presence of a 1D lattice and transverse harmonic confinement can be obtained by employing an effective 1D approach, and demonstrate that the effect of the transverse

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“…Potentially better descriptions than our simple GrossPitaevskii equation [17] have been proposed to describe transversely confined elongated condensates. Our main mechanism relies on the non-trivial band structure, but not on its particular shape, and we therefore believe that our proposal should remain generally valid.…”

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“…Theories [2,17] have proposed and experiments [19,20] have shown that condensates moving in periodic potentials become unstable for certain ranges of quasimomenta. These results are linked with the energy and momentum conserving processes identified in this paper, but they also involve the detailed properties of the transverse confinement [17].…”

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Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

Hilligsøe

Mølmer

2005

Phys. Rev. A

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We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasi-momentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasi-momentum k0 is transferred almost completely ( > 95%) into a pair of correlated atomic components with quasimomenta k1 and k2, if the system is seeded with a smaller number of atoms with the appropriate quasi-momentum k1.PACS numbers: 03.75. Kk, 03.75.Lm, Bose-Einstein condensates in optical lattices provide flexible systems for studying the behavior of coherent matter in periodic potentials. Considerable attention is given to studies in regimes far from the region of validity of mean-field analysis and the Gross-Pitaevskii equation [1], but also the highly non-trivial mean-field dynamics has been and continues to be subject to theoretical and experimental investigations [2,3,4].The process we wish to consider is a four wave mixing (FWM) process, which transfers pairs of atoms coherently from an initial momentum state k 0 to new states with momenta k 1 and k 2 . We consider a Bose-Einstein condensate in a quasi-1D geometry and we will consider only the longitudinal dynamics of the condensate. This geometry is relevant, e.g., for atomic wave guides and atom interferometers based on atom chips [5].In Refs. [6,7], it was shown that nonlinear interaction originating from the s-wave scattering between atoms leads to depletion of the condensate and emission of pairs of atoms at other momenta when a continuous matter wave beam passes through a finite region with enhanced interactions. For a larger condensate, however, the process will not be effective unless it conserves both energy and momentum, i.e., the waves must be phase-matched over the extent of the sample. We shall show how the characteristic energy band structure in a one-dimensional optical lattice can be used to ensure both energy and quasi-momentum conservation, i.e., phase-matching of the FWM process.Our tailoring of the dispersion properties of matter waves by an external potential is inspired by approaches to non-linear optics, which employ various means to ensure phase-matching, e.g., of the FWM process [8,9,10]. A similar phase-matched FWM process has been used to explain giant amplification from semiconductor microcavities, where the polariton dispersion properties can be controlled by the strong photon-exciton coupling [11]. We also note that a recent analysis [12] of the break-up of a bright matter wave soliton was analyzed in terms of dispersion and phase-matching. Phase-matched FWM has been realized in collisions of two condensates in two dimensions [13,14,15], but in the present paper we show that the process can take place with atomic motion along a single direction, for example inside an atomic waveguide.The basic idea of our proposal is illustrated in Fig. 1. In a periodic potentia...

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Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices

Cited by 70 publications

References 25 publications

Properties of spin–orbit-coupled Bose–Einstein condensates

Properties of spin–orbit-coupled Bose–Einstein condensates

Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

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