Strongly Enhanced Inelastic Collisions in a Bose-Einstein Condensate near Feshbach Resonances

Stenger, J.; Inouye, S.; Andrews, M. R.; Miesner, H.-J.; Stamper-Kurn, Dan; Ketterle, Wolfgang

doi:10.1103/physrevlett.82.2422

Cited by 374 publications

(323 citation statements)

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“…To obtain representative numbers, we consider the Na 23 resonances observed by Stenger et al [16] for which |∆| = 0.1G, 1.G and 4G. Taking n = 10 12 cm −3 , [4] and a s = 3.3 nm (the Na triplet scattering length), we find δB = 0.03 |∆| = 3mG, 30mG, 0.12G exceeding current experimental magnetic field resolution (typically better than 1mG).…”

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“…We determine the interval size δB from |a ef f | ≥ 0.4 k −1 F with [16] a ef f = −a s (∆/δB), where a s denotes the ordinary scattering length of the unlike fermion interaction and ∆ represents the measured magnetic field 'width': δB = 2.5 × (|a 0 |k F )|∆|. To obtain representative numbers, we consider the Na 23 resonances observed by Stenger et al [16] for which |∆| = 0.1G, 1.G and 4G.…”

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Prospect of creating a composite Fermi–Bose superfluid

et al. 2001

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We show that composite fermi/bose superfluids can be created in coldatom traps by employing a Feshbach resonance or coherent photoassociation. The bosonic molecular condensate created in this way implies a new fermion pairing mechanism associated with the exchange of fermion pairs between the molecular condensate and an atomic fermion superfluid. We predict macroscopically coherent, Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the molecular energy, and suggest that these oscillations will provide an experimental signature of the pairing. PACS numbers(s):03.75. Fi, 05.30.Jp, 32.80Pj, 67.90.+z Typeset using REVT E X

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Prospect of creating a composite Fermi–Bose superfluid

et al. 2001

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“…Feshbach resonances were studied in a series of elegant experiments performed with sodium [62,63] and rubidium [64,65] condensates. Additionally, they have been used in many important experimental investigations, including, among others, the formation of bright matter-wave solitons [40][41][42][43].…”

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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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“…This is due to the Pauli blocking of the atom-atom collisions, which prolongs the cooling into time scales at which technical losses become dominant [7]. Alternative cooling mechanisms [8,9] combined with the external modification of the scattering length [10], have been proposed as possible mechanisms to achieve BCS.…”

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