Creation and Characterization of Matter-Wave Breathers

Bright traveling breathers in media with long-range nonconvex dispersion

The existence and properties of envelope solitary waves on a periodic traveling-wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed-point computational scheme, a space-time boundary-value problem for bright traveling breather solutions is solved for the weakly nonlinear Benjamin-Bona-Mahony equation, a nonlocal, regularized shallow water wave model, and the strongly nonlinear conduit equation, a nonlocal model of viscous core-annular flows. Curves of unit-mean traveling breather solutions within a three-dimensional parameter space are obtained. Resonance due to nonconvex, rational linear dispersion leads to a nonzero oscillatory background upon which traveling breathers propagate. These solutions exhibit a topological phase jump and so act as defects within the periodic background. For small amplitudes, traveling breathers are well approximated by bright soliton solutions of the nonlinear Schrödinger equation with a negligibly small periodic background. These solutions are numerically continued into the large-amplitude regime as elevation defects on cnoidal or cnoidal-like periodic traveling-wave backgrounds. This study of bright traveling breathers provides insight into systems with nonconvex, nonlocal dispersion that occur in a variety of media such as internal oceanic waves subject to rotation and short, intense optical pulses.

Shortcuts to adiabatic soliton compression in active nonlinear Kerr media

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

Density Dependent Gauge Field Inducing Emergent Su-Schrieffer-Heeger Physics, Solitons, and Condensates in a Discrete Nonlinear Schrödinger Equation

We investigate a discrete nonlinear Schrödinger equation with dynamical, density-difference-dependent gauge fields. We find a ground-state transition from a plane wave condensate to a localized soliton state as the gauge coupling is varied. Interestingly we find a regime in which the condensate and soliton are both stable. We identify an emergent chiral symmetry, which leads to the existence of a symmetry-protected zero-energy edge mode. The emergent chiral symmetry relates low and high energy solitons. These states indicate that the interaction acts both repulsively and attractively.

Integrator for general spin-s Gross-Pitaevskii systems

We provide an algorithm, i-SPin 2, for evolving general spin-s Gross-Pitaevskii or nonlinear Schrödinger systems carrying a variety of interactions, where the 2s+1 components of the "spinor" field represent the different spin-multiplicity states. We consider many nonrelativistic interactions up to quartic order in the Schrödinger field (both short and long range, and spin-dependent and spin-independent interactions), including explicit spin-orbit couplings. The algorithm allows for spatially varying external and/or self-generated vector potentials that couple to the spin density of the field. Our work can be used for scenarios ranging from laboratory systems such as spinor Bose-Einstein condensates (BECs), to cosmological or astrophysical systems such as self-interacting bosonic dark matter. As examples, we provide results for two different setups of spin-1 BECs that employ a varying magnetic field and spin-orbit coupling, respectively, and also collisions of spin-1 solitons in dark matter. Our symplectic algorithm is second-order accurate in time, and is extensible to the known higher-order-accurate methods.

Observation of Traveling Breathers and Their Scattering in a Two-Fluid System

The observation of traveling breathers (TBs) with large-amplitude oscillatory tails realizes an almost 50-year-old theoretical prediction [E. A. Kuznetsov and A. V. Mikhailov, Stability of stationary waves in nonlinear weakly dispersive media, Zh. Eksp. Teor. Fiz. 67, 1717 (1974) ZETFA70044-4510[E. A. Kuznetsov and A. V. MikhailovSov. Phys. JETP 40, 855 (1975)] SPHJAR0038-5646] and generalizes the notion of a breather. Two strongly nonlinear TB families are created in a core-annular flow by interacting a soliton and a nonlinear periodic (cnoidal) carrier. Bright and dark TBs are observed to move faster or slower, respectively, than the carrier while imparting a phase shift. Agreement with model equations is achieved. Scattering of the TBs is observed to be physically elastic. The observed TBs generalize to many continuum and discrete systems.

Generation of higher harmonics in dipolar Bose-Einstein condensates trapped in periodically modulated potentials

We consider a quasi-one-dimensional Bose-Einstein condensate with contact and long-range dipolar interactions, under the action of the time-periodic modulation applied to the harmonic-oscillator and optical-lattice trapping potentials. The modulation results in generation of a variety of harmonics in oscillations of the condensate's width and centre-of-mass coordinate. These include multiple and combinational harmonics, represented by sharp peaks in the system's spectra. Approximate analytical results are produced by the variational method, which are verified by systematic simulations of the underlying Gross-Pitaevskii equation. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Exploring Integrability-Chaos Transition with a Sequence of Independent Perturbations

A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that, even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by the number of principal components (NPC)-the number of integrable system eigenstates involved into the nonintegrable one, which increases linearly with the number of strong scatterers. This rule is a particular case of the general effect of an additional perturbation on the system chaotic properties. The perturbation independence criteria supposing the system chaoticity increase are derived here as well. The effect can be observed in experiments with photons or cold atoms as the decay of observable fluctuation variance, which is inversely proportional to NPC and, therefore, to the number of scatterers. This decay indicates that the eigenstate thermalization is approached. The results are confirmed by numerical calculations for a harmonic waveguide with zero-range scatterers along its axis.

New trends in quantum integrability: recent experiments with ultracold atoms

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.

Extreme wave excitation from localized phase-shift perturbations

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of sidebands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this Letter, we show that phase-shift localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers, and thus by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such a focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitaevskii Breather

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

We numerically realize a breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial" generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207].

Scattering of Matter Wave Solitons on Localized Potentials

We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate, we find different reflection and transmission properties of the dark and the bright components.