Feshbach Resonance Management for Bose-Einstein Condensates

Kevrekidis, P. G.; Theocharis, G.; Frantzeskakis, D. J.; Malomed, Boris A.

doi:10.1103/physrevlett.90.230401

Cited by 275 publications

(253 citation statements)

References 30 publications

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“…On the contrary, in the absence of a tight transversal trapping, higher dimensional extensions of 1D solitons are generally unstable [12]. However, by restricting the transverse direction(s) of the condensate, it is possible to obtain higher † † This technique was suggested in earlier works in various important applications, as e.g., a means to prevent collapse of higher-dimensional attractive BECs [193,203,410], to produce periodic waves [107], robust matter-wave breathers [241,242,411,412], and so on. dimensional soliton solutions that are stabilized for times longer than the lifespan of the experiments [414][415][416].…”

Section: Multidimensional Solitons and Collapsementioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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Section: Multidimensional Solitons and Collapsementioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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“…The investigation of the soliton dynamics in inhomogeneous BEC is of interest, in particular with inhomogeneities periodic in time or space. Time variations can be achieved with the Feshbach resonance (FR) management technique and it has been studied in [6,7,8,9]. New type of solitons can be generated by this way, and stabilization of higher-dimensional solitons in attractive condensate has been shown.…”

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confidence: 99%

Propagation of matter-wave solitons in periodic and random nonlinear potentials

2005

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We study the motion of bright matter wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.

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“…(2) to determine the time evolution of the size of the BEC [33]. In particular, we are interested in the dynamics associated with the modulation of a using a Feshbach resonance, which has been proposed previously [34,35]. In a magnetic field B, the scattering length near a Feshbach resonance may be described by…”

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Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

Pollack

Dries²,

Hulet³

et al. 2010

Phys. Rev. A

102

113

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We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior. Collective excitation of a Bose-Einstein condensate (BEC) is an essential diagnostic tool for investigating properties of the ultracold quantum state. Fundamental information about condensate dynamics can be determined from observations of collective modes [1][2][3], including the effects of temperature [4][5][6], and the dimensionality of the system [7]. In addition, the interplay between these modes and external agents, such as random potentials [8,9], lattices [10,11], as well as other atoms [12][13][14][15][16], can be investigated. Examining the excitation spectrum of the BEC allows for a detailed comparison with theoretical models [17][18][19][20] and related quantum systems such as superfluid helium [21,22] and superconductors [23,24].Generically, a collective excitation is generated by the modification of the trapping potential of the condensate [25]. One convenient method is to apply a sudden magnetic field gradient, thereby shifting the center of the trap and exciting a dipole oscillation about the trap center. One may also suddenly change the curvature of the trap to excite quadrupole modes. The lowest-lying m = 0 quadrupole mode is characterized by out-of-phase axial and radial oscillations.If the condensate is not the only occupant of the trap (i.e., there exists a thermal component or another species of atoms) then the other atoms may also be excited through these processes. The evolution of a collective excitation can therefore be complicated because the multiple components may affect damping or induce frequency shifts of the oscillation [12][13][14][15][16]. Therefore, modulating the trap, although an extremely useful tool for an isolated condensate, can be cumbersome when the system to be studied is multispecied. An alternative approach is to excite the condensate alone, leaving the other occupants of the trap untouched.In this work, we demonstrate the excitation of the lowestlying quadrupole mode in a BEC of 7 Li by modulating the atomic scattering length via a magnetic Feshbach resonance. In contrast to abruptly changing the scattering length [26], sinusoidal modulation enables the controlled excitation of a single mode at a specific frequency. In addition, by using this method, a coexisting thermal component will be minimally excited by the mean-field coupling to the normal gas [27,28]. In the case of a multispecies experiment, resonant modulation of the scattering length of one species will not necessarily excite the others, depending on the details of other F...

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Feshbach Resonance Management for Bose-Einstein Condensates

Cited by 275 publications

References 30 publications

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Propagation of matter-wave solitons in periodic and random nonlinear potentials

Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

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