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Register a new userStable circulation modes in a dual-core matter-wave soliton laser
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We consider a model of a matter-wave laser generating a periodic array of solitary-wave pulses. The system, a general version of which was recently proposed in Ref. [5], is composed of two parallel tunnel-coupled cigar-shaped traps (a reservoir and a lasing cavity), solitons being released through a valve at one edge of the cavity. We report a stable lasing mode accounted for by circulations of a narrow soliton in the cavity, which generates an array of strong pulses (with 1,000 - 10,000 atoms in each, the arrays duty cycle ~ 30%) when the soliton periodically hits the valve.
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We present a novel compact dual-comb source based on a monolithic optical crystalline MgF$_2$ multi-resonator stack. The coherent soliton combs generated in two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio-frequency comb. Analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications and massively parallel optical communications.
We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the cubic self-repulsive terms and quadratic attractive ones,which represent the Lee-Huang-Yang corrections to the mean-field theory in this geometry. The main subject is spontaneous symmetry breaking (SSB) of quantum droplets (QDs), followed by restoration of the symmetry, with respect to the symmetric parallel-coupled trapping cores, following the increase of the QDs total norm. The SSB transition and inverse symmetry-restoring one form a bifurcation loop, whose shape in concave at small values of the inter-core coupling constant, $kappa$, and convex at larger $kappa $. The loop does not exist above a critical value of $kappa $. At very large values of the norm, QDs do not break their symmetry, featuring a flat-top shape. Some results are obtained in an analytical form, including an exact front solution connecting constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.
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Shrinidhi S. Pandurangi
, Ryan S. Elliott
, Timothy J. Healey andn Nicolas Triantafyllidis
2020
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in many applications in mechanics. Instead of a numerical search for such solutions using arbitrary imperfections, we propose a systematic search using branch-following and bifurcation techniques along with group-theoretic methods to find all the bifurcated solution orbits (primary, secondary, etc.) of the system and to examine their stability and hence their observability. Unlike previously proposed methods that use multi-scale perturbation techniques near the critical load, we show that to obtain a spatially localized deformation equilibrium path for the perfect structure, one has to consider the secondary bifurcating path with the longest wavelength and follow it far away from the critical load. The novel use of group-theoretic methods here illustrates a general methodology for the systematic analysis of structures with a high degree of symmetry.
We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, as a result of the effective potential created by a stable vortex in the other component. The resulting vortex-bright solitary waves, which naturally generalize the recently experimentally observed dark-bright solitons, are examined both in the homogeneous medium and in the presence of parabolic and periodic external confinement and are found to be very robust.
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