Wave Modes Trapped in Rotating Nonlinear Potentials

Li, Yongyao; Pang, Wei; Malomed, Boris A.

doi:10.1007/978-3-319-02057-0_8

Cited by 5 publications

(3 citation statements)

References 126 publications

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“…We note that a finite-width barrier, as could be realized experimentally, yields very similar profiles [Fig 2(b)]. Its extension to multiple finite-width barriers is known to give rise to a wealth of nonlinear modes [24].…”

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confidence: 63%

Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

et al. 2014

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We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U (1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings. 03.75.Lm, 71.10.Pm, 73.23.Ra A quantum fluid confined on a ring and subjected to a U (1) gauge potential displays a periodicity in the particle current as a function of the flux of the corresponding classical gauge field. This persistent current phenomenon is a manifestation of the Aharonov-Bohm effect, and reflects the macroscopic coherence of the manybody wave function along the ring. Such currents were observed more than 50 years ago in bulk superconductors [1] and, more recently, in normal metallic rings, overcoming the challenges of the decoherence induced by inelastic scattering [2]. The most recent developments in the manipulation of ultracold atoms on ring traps [3, 4] have disclosed a novel platform for the study of persistent currents, which can be induced by the application of a rotating localized barrier or, alternatively, by inducing suitable artificial gauge fields [5]. Tunable localized barriers in toroidal Bose-Einstein condensates have been realized, using well-focused, repulsively tuned laser beams [4]. Also, recently the engineering of an atomic superconducting quantum interference device was demonstrated [6]. The unprecedented variety of interaction and barrier strength regimes paves the way to applications such as high-precision measurements, atom interferometry and quantum information, e.g., by the construction of macroscopic superposition of current states and flux qubits [7][8][9].The scenario becomes particularly intriguing if the transverse section of the ring is sufficiently thin to effectively confine the system in one dimension (1D): the rich interplay between interactions, quantum fluctuations, and statistics acquires a role of primary relevance. In absence of any obstacle along the ring, the persistent currents display an ideal sawtooth behavior as a function of the flux, i.e., perfect superfluidity for any interaction strength at zero temperature [10, 11]. Diamagnetic or paramagnetic response depending on the population parity is expected [12] for fermions but not for bosons. If a localized barrier is added, persistent currents are smeared-their shape taking a sinusoidal form in the case of large-barrier or small-tunneling limit-as obtained for thin superconducting rings from a Luttinger-liquid approach [13]. Beyond these limiting regimes the physics of bosonic persistent current remains unexplored.The aim of the present work is to provide a complete characterization of persistent currents for 1D bosons, in all interaction and barrier strength regimes. By combining analytical as well as numerical techniques suited fo...

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confidence: 63%

Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

et al. 2014

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“…We find that a stable quasi-2D solitary mode does exist under this circumstance. To clarify this mechanism, another objective of this work is to identify all of the solitary modes that exist in the first rotational Brillouin zone (FRBZ) [30][31][32][33][34][35], from which all solitary modes are boosted out. Three generic solitary modes are found in this zone: one belongs to the zero-harmonic (0H), and the other two belong to the first-harmonic (1H).…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal solitary modes in a twisted cylinder waveguide shell with the self-focusing Kerr nonlinearity

Huang

Lyu

Xie

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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We study the spatiotemporal solitary modes that propagate in a hollow twisted cylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three generic solitary modes, one belonging to the zero-harmonic (0H) and the other two belonging to the first-harmonic (1H), are found in the first rotational Brillouin zone. The 0H solitary modes can be termed as a quasi-1D (one-dimensional) temporal soliton. Their characteristics depend only on the energy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional) bullet, whose width is much narrower than the angular domain of the waveguide. In contrast to the 0H mode, the characteristics of the 1H solitary mode depend on both their energy flow and the rotating speed of the waveguide. We demonstrate numerically that the 1H solitary modes are stable when their energy flow is smaller than the threshold norm of the Townes soliton. The boundaries of the bistable area for these two types of solitary modes are predicted by the analyses via two-mode approximation. This prediction is in accordance with the numerical findings. We also demonstrate analytically that the 1H solitary mode of this system can be applied to emulate the nonlinear dynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics. Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, are found from this setting via the mechanism of SO coupling. Collisions between the pair of these two types of solitary modes are also discussed in the paper. The pair of the 0H solitary mode features only the elastic collision, whereas the pair of 1H solitary modes can feature both elastic and inelastic collision when the total energy flow of the two modes are smaller or close to the threshold norm of the Townes soliton. * Electronic address:

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“…Ring-shaped Bose-Einstein condensates in toroidal traps are the subject of many experimental and theoretical investigations [14][15][16][17][18][19] which study persistent currents [1,5,20], weak links [3,6], formation of matter-wave patterns by rotating potentials [21,22], solitary waves [16,23], and the decay of the persistent current via abrupt change of the rotation state (phase slips) [4,24,25]. A persistent atomic flow in a toroidal trap can be created by transferring angular momentum from optical fields [1,6] or by stirring with a rotating barrier [6,7].…”

Section: Introductionmentioning

confidence: 99%

Generation and decay of persistent current in a toroidal Bose-Einstein condensate

Yakimenko,

Vilchinskii,

Bidasyuk

et al. 2014

Preprint

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Persistent current, or "flow without friction", as well as quantum vortices are the hallmarks of superfluidity. Recently a very long-lived persistent flow of atoms has been experimentally observed in Bose-Einstein condensates trapped in a ring-shaped potential. This enables fundamental studies of superfluidity and may lead to applications in high-precision metrology and atomtronics. We overview our recent theoretical studies of the generation and decay of the persistent current in a toroidal atomic Bose-Einstein condensate, and discuss our new investigation of the hysteresis in the atomtronic circuit.

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Wave Modes Trapped in Rotating Nonlinear Potentials

Cited by 5 publications

References 126 publications

Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

Spatiotemporal solitary modes in a twisted cylinder waveguide shell with the self-focusing Kerr nonlinearity

Generation and decay of persistent current in a toroidal Bose-Einstein condensate

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