Collective excitations of a degenerate Fermi vapour in a magnetic trap

Amoruso, M.; Meccoli, I.; Minguzzi, Anna; Tosi, M. P.

doi:10.1007/s100530050588

Cited by 96 publications

(166 citation statements)

References 16 publications

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“…It may also be possible to consider the spontaneous symmetry breaking in a degenerate fermion gas filling a dual-core trap, using a relatively simple description of the fermion gas based on the Thomas-Fermi (alias mean-field-hydrodynamic) approximation, which was developed, for various settings, in Refs. [35].…”

Section: Discussionmentioning

confidence: 99%

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Gubeskys

Malomed

2007

Phys. Rev. A

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We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, ∆, between the OLs in the two cores is also studied. It is concluded that ∆ = π/2 only mildly deforms the picture, while ∆ = π changes it drastically, replacing the symmetry-breaking bifurcations by pseudo-bifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.

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Section: Discussionmentioning

confidence: 99%

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Gubeskys

Malomed

2007

Phys. Rev. A

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“…The nonlinear coupling results from inter-atomic collisions while the linear coupling accounts for spin state interconversion usually induced by a spinflipping resonant electromagnetic wave [296]. In the case of fermionic mixtures one needs to replace the self-interacting nonlinear terms by g n,n |ψ n | 4/3 ψ n [297][298][299]. In the absence of losses (σ n = 0), the total number of atoms is conserved:…”

Section: Spinor/multicomponent Condensatesmentioning

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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“…The dynamical behaviour that we shall discuss in Sect.3 will therefore correspond to a collisional regime [20].…”

Section: Equilibrium Density Profiles and Phase Diagrammentioning

confidence: 99%

Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

Minguzzi

Tosi

2000

Physics Letters A

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We discuss the ground state and the small-amplitude excitations of dilute bosonfermion mixtures confined in spherical harmonic traps at T = 0, assuming repulsive boson-boson interactions and with each component being in a single hyperfine state. From previous studies of the equilibrium density profiles we propose a schematic phase diagram in a plane defined by the variables a bf /a bb and a bb k (0) f , where a bb and a bf are the boson-boson and boson-fermion scattering lengths and k (0) f is the Fermi wave number at the centre of the trap. With this background we turn to the equations of motion for density fluctuations in the collisional regime and discuss some general features of the eigenmodes. We display analytic solutions for sound waves in a quasi-homogeneous mixture and for surface modes at weak fermion-boson coupling.

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Collective excitations of a degenerate Fermi vapour in a magnetic trap

Cited by 96 publications

References 16 publications

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

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

Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

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