Delocalizing transition in one-dimensional condensates in optical lattices due to inhomogeneous interactions

Bludov, Yuliy V.; Brazhnyi, V. A.

doi:10.1103/physreva.76.023603

Cited by 32 publications

(29 citation statements)

References 25 publications

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“…The DTS was also recently found in 1D BEC in OLs in the presence of three-body interactions [7,8] or in combined linear and nonlinear OLs [9,10], as well as in two-component BEC confined in nonlinear periodic potentials [11]. We remark that, while the nature of the DTS reported in [4,6] was intrinsically multidimensional, in all other cases cited above the DTS occurs in 1D settings, thus making the phenomenon more accessible to numerical and theoretical investigations.…”

Section: Introductionmentioning

confidence: 93%

“…when there is in the parameter space a critical threshold for the number of particles, N cr , below which no localized solutions exist. This idea was used in [9,10] to obtain the DTS in BECs with combined linear and nonlinear OLs and in binary mixtures of BECs, respectively. Also, the idea of non-existence of small amplitude solitons as a condition for the existence of the DTS allows one to predict the occurrence of DTs in other physical systems such as the nonlinear Schrödinger (NLS) equation with nonlinear OL (the existence of N cr was established using approximate arguments in [12]), the quintic NLS equation with a periodic potential (the existence of N cr was established in [7,8]), and related discrete models to which the continuum NLS-like equation is mapped using the Wannier function analysis [13].…”

Section: Introductionmentioning

confidence: 99%

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One-dimensional delocalizing transitions of matter waves in optical lattices

Cruz

Brazhnyi

Salerno

2009

Physica D: Nonlinear Phenomena

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

One-dimensional delocalizing transitions of matter waves in optical lattices

Cruz

Brazhnyi

Salerno

2009

Physica D: Nonlinear Phenomena

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“…The resulting so-called "collisionally inhomogeneous" environment provides a variety of interesting and previously unexplored dynamical phenomena and potential applications, including adiabatic compression of matter waves [33,34], atomic soliton emission and atom lasers [35], enhancement of the transmittivity of matter waves through barriers [36,37], dynamical trapping of matter-wave solitons [36], stable condensates exhibiting both attractive and repulsive interatomic interactions [38], and the delocalization transition of matter waves [39]. Particular inhomogeneous frameworks that have been investigated include linear [33,36], parabolic [40], random [41], periodic [39,42,43], and localized (step-like) [35,44,45] spatial variations. There have also been a number of detailed mathematical studies [46,47,48].…”

Section: Introductionmentioning

confidence: 99%

Matter-wave solitons with a periodic, piecewise-constant scattering length

et al. 2008

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Motivated by recent proposals of "collisionally inhomogeneous" Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewiseconstant scattering length. We use a "stitching" approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wavefunction and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that solitons can only exist at the centers of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.

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“…To this end we use spatial periodic modulations of the scattering length via optically induced Feshbach resonances, in order to change the stability properties of the Bloch states at the edges of the band. These modulations correspond to a nonlinear lattice whose amplitude, considered as a free parameter, can be used to eliminate instabilities from the band (similar stabilizing properties of nonlinear lattice were used to achieve delocalizing transitions in one dimensional (1D) case [17]). We show that the regions of parameter space for which Bloch states become unstable (almost) in the whole band coincide with those for which long-lived BO of matter waves become possible, this showing the validity of our approach.…”

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confidence: 99%

Long-Living Bloch Oscillations of Matter Waves in Periodic Potentials

2008

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It is shown that by properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of a localized wavepacket in a periodic potential. The results are supported both by analytical and numerical investigations and are interpreted in terms of matter wave dynamics displaying dozens of oscillation periods without any visible distortion of the wave packet.PACS numbers: 03.75Kk, 03.75Lm, 67.85.HjThe phenomenon of Bloch oscillations (BO), predicted by Bloch in 1928 in his celebrated paper on the dynamics of a band electron in a steady electrical field [1], represents a problem of non exhausted interest. Besides solid state physics, where the phenomenon has been observed only in recent times after the development of the superlattice technology [2], it is now possible to observe BO also in other fields such as nonlinear optics, using light beams in arrays of waveguides [3] or in photorefractive crystals [4], and atomic physics, using Bose-Einstein condensates (BEC) loaded in optical lattices (OLs) [5,6,7]. Apart its fundamental significance, the interest in BO arises mainly from perspectives of their practical applications. In this context we mention the use of BO for metrological tasks, including relatively precise definition of h/m [8] and measurement of forces at the micrometer scale like the Casimir-Polder force [9] and the gravity [10]. Recently, BO were also suggested as a tool for controlling light in coupled-resonator optical waveguides [11]. In these physical contexts BO have been observed mainly in the linear (as first proposed by Bloch) or quasi linear regimes (where the nonlinearity introduces quantitative but not yet qualitative changes). The present experimental settings (both in nonlinear optics and in BECs), however, allow for attaining essentially nonlinear regimes quite easily, this actually being a desirable condition for applications involving localized states.The fact that BO can exist in presence of interactions (nonlinearity) was first recognized in the context of nonlinear discrete systems [12]. For periodic continuous models of the nonlinear Schrödinger (NLS) type, such as ones describing matter waves in OLs, the existence of BO becomes more problematic because of nonlinearity induced instabilities in the underlying linear system. These instabilities can be simply understood by observing that in a usual OL at the edges of an allowed band the effective mass has always opposite signs. This implies that if a Bloch state is modulationally stable (in presence of a constant nonlinearity) at one edge of the band, it must be necessarily unstable at the other band edge [13]. Nonlinearity induced instabilities have been extensively investigated both theoretically [13,14] and experimentally [15]) and have been identified as primary cause for the short life-times of BO of matter waves (the oscillation survives only a few cycles) observed both in numerical [16] and in real experiments [15].In this Letter we show that by properly controlling the instabiliti...

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Delocalizing transition in one-dimensional condensates in optical lattices due to inhomogeneous interactions

Cited by 32 publications

References 25 publications

One-dimensional delocalizing transitions of matter waves in optical lattices

One-dimensional delocalizing transitions of matter waves in optical lattices

Matter-wave solitons with a periodic, piecewise-constant scattering length

Long-Living Bloch Oscillations of Matter Waves in Periodic Potentials

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