Formation of dispersive shock waves by merging and splitting Bose-Einstein condensates

Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas

We numerically study the transport properties of a two-dimensional Fermi gas in a weakly and strongly interacting regimes, in the range of temperatures close to the transition to a superfluid phase. For that we excite sound waves in a fermionic mixture by using the phase imprinting technique, follow their evolution, and finally determine both their speed and attenuation. Our formalism, originated from a density-functional theory, incorporates thermal fluctuations via the grand canonical ensemble description and with the help of Metropolis algoritm. From numerical simulations we extract temperature dependence of the sound velocity and diffusivity as well as the dependence on the interaction strength. We emphasize the role of virtual vortex-antivortex pairs creation in the process of sound dissipation.

Fast particles overtaking shock front in two-dimensional Yukawa solids

High-speed particles overtaking the shock front during the propagation of compressional shocks in two-dimensional (2D) Yukawa solids are investigated using molecular dynamical simulations. When the compressional speed is lower, all particles around the shock front are almost accelerated synchronously. However, when the compressional speed is much higher, some particles penetrate the shock front to enter the preshock region. Around the shock front, it is found that the particle velocity profile at the first peak of the dispersive shock wave (DSW) is able to be described using the Gaussian distribution, so that the amplitudes of the DSW can be well characterized. As the compressional speed increases, the particle velocity corresponding to these DSW's amplitudes increase more substantially than the shock front speed. These amplitudes of the DSW are found to be able to predict the occurrence of the fast particles. Combined with the previous study of the DSW's period, it is demonstrated that the properties of the DSW are nearly not affected by the conditions of the 2D Yukawa systems, but only related to the compressional speed.

Pattern Formation in One-Dimensional Polaron Systems and Temporal Orthogonality Catastrophe

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.

Berezinskii-Kosterlitz-Thouless phase induced by dissipating quasisolitons

We theoretically study the sound propagation in a two-dimensional weakly interacting uniform Bose gas. Using the classical fields approximation we analyze in detail the properties of density waves generated both in a weak and strong perturbation regimes. While in the former case density excitations can be described in terms of hydrodynamic or collisionless sound, the strong disturbance of the system results in a qualitatively different response. We identify observed structures as quasisolitons and uncover their internal complexity for strong perturbation case. For this regime quasisolitons break into vortex pairs as time progresses, eventually reaching an equilibrium state. We find this state, characterized by only fluctuating in time averaged number of pairs of opposite charge vortices and by appearance of a quasi-long-range order, as the Berezinskii-Kosterlitz-Thouless (BKT) phase.

Head-on collision of compressional shocks in two-dimensional Yukawa systems

The head-on collision of compressional shocks in two-dimensional dusty plasmas is investigated using both molecular dynamical and Langevin simulations. Two compressional shocks are generated from the inward compressional boundaries in simulations. It is found that, during the collision of shocks, there is a generally existing time delay of shocks τ, which diminishes monotonically with the increasing compressional speed of boundaries, corresponding to the time resolution of the studied system. Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks τ. When the inward compressional speed of boundaries increases further, the DSWs gradually vanish. We speculate that, for these high compressional speeds of boundaries, the period of the DSW might be reduced to a comparable timescale of the time delay of shocks τ, i.e., the time resolution of our studied system, or even shorter, thus the DSW reasonably vanishes.

Anisotropic Optical Shock Waves in Isotropic Media with Giant Nonlocal Nonlinearity

Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point. The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.

What is a Quantum Shock Wave?

Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.

Balancing long-range interactions and quantum pressure: Solitons in the Hamiltonian mean-field model

The Hamiltonian mean-field (HMF) model describes particles on a ring interacting via a cosine interaction, or equivalently, rotors coupled by infinite-range XY interactions. Conceived as a generic statistical mechanical model for long-range interactions such as gravity (of which the cosine is the first Fourier component), it has recently been used to account for self-organization in experiments on cold atoms with long-range optically mediated interactions. The significance of the HMF model lies in its ability to capture the universal effects of long-range interactions and yet be exactly solvable in the canonical ensemble. In this work we consider the quantum version of the HMF model in one dimension and provide a classification of all possible stationary solutions of its generalized Gross-Pitaevskii equation (GGPE), which is both nonlinear and nonlocal. The exact solutions are Mathieu functions that obey a nonlinear relation between the wave function and the depth of the mean-field potential, and we identify them as bright solitons. Using a Galilean transformation these solutions can be boosted to finite velocity and are increasingly localized as the mean-field potential becomes deeper. In contrast to the usual local GPE, the HMF case features a tower of solitons, each with a different number of nodes. Our results suggest that long-range interactions support solitary waves in a novel manner relative to the short-range case.

Dispersive shock wave theory for nonintegrable equations

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham's "number of waves conservation law" as well as on the conjecture of applicability of its soliton counterpart to the above mentioned class of initial conditions which is substantiated by comparison with similar situations in the case of completely integrable wave equations. This allows one to calculate the limiting characteristic velocities of the Whitham modulation equations at the boundary with the smooth part of the pulse whose evolution obeys the dispersionless approximation equations. We show that explicit analytic expressions can be obtained for laws of motion of the edges. The validity of the method is confirmed by its application to similar situations described by the integrable Korteweg-de Vries (KdV) and nonlinear Schrödinger (NLS) equations and by comparison with the results of numerical simulations for the generalized KdV and NLS equations.

Dissipative shock waves generated by a quantum-mechanical piston

The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes. Here we investigate this problem for a nominally dissipationless, superfluid Bose-Einstein condensate and observe rich dynamics including the formation of a plateau region, a non-expanding shock front, and rarefaction waves. Many aspects of the observed dynamics follow predictions of classical dissipative-rather than superfluid dispersive-shock theory. The emergence of dissipative-like dynamics is attributed to the decay of large amplitude excitations at the shock front into turbulent vortex excitations, which allow us to invoke an eddy viscosity hypothesis. Our experimental observations are accompanied by numerical simulations of the mean-field, Gross-Pitaevskii equation that exhibit quantitative agreement with no fitting parameters. This work provides an avenue for the investigation of quantum shock waves and turbulence in channel geometries, which are currently the focus of intense research efforts.

Relaxation Dynamics in the Merging of N Independent Condensates

Controlled quantum systems such as ultracold atoms can provide powerful platforms to study nonequilibrium dynamics of closed many-body quantum systems, especially since a complete theoretical description is generally challenging. In this Letter, we present a detailed study of the rich out-of-equilibrium dynamics of an adjustable number N of uncorrelated condensates after connecting them in a ring-shaped optical trap. We observe the formation of long-lived supercurrents and confirm the scaling of their winding number with N in agreement with the geodesic rule. Moreover, we provide insight into the microscopic mechanism that underlies the smoothening of the phase profile.

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic Y_{3}Fe_{5}O_{12} thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Real-space collapse of a polariton condensate

Microcavity polaritons are two-dimensional bosonic fluids with strong nonlinearities, composed of coupled photonic and electronic excitations. In their condensed form, they display quantum hydrodynamic features similar to atomic Bose-Einstein condensates, such as long-range coherence, superfluidity and quantized vorticity. Here we report the unique phenomenology that is observed when a pulse of light impacts the polariton vacuum: the fluid which is suddenly created does not splash but instead coheres into a very bright spot. The real-space collapse into a sharp peak is at odd with the repulsive interactions of polaritons and their positive mass, suggesting that an unconventional mechanism is at play. Our modelling devises a possible explanation in the self-trapping due to a local heating of the crystal lattice, that can be described as a collective polaron formed by a polariton condensate. These observations hint at the polariton fluid dynamics in conditions of extreme intensities and ultrafast times.

From coherent shocklets to giant collective incoherent shock waves in nonlocal turbulent flows

Understanding turbulent flows arising from random dispersive waves that interact strongly through nonlinearities is a challenging issue in physics. Here we report the observation of a characteristic transition: strengthening the nonlocal character of the nonlinear response drives the system from a fully turbulent regime, featuring a sea of coherent small-scale dispersive shock waves (shocklets) towards the unexpected emergence of a giant collective incoherent shock wave. The front of such global incoherent shock carries most of the stochastic fluctuations and is responsible for a peculiar folding of the local spectrum. Nonlinear optics experiments performed in a solution of graphene nano-flakes clearly highlight this remarkable transition. Our observations shed new light on the role of long-range interactions in strongly nonlinear wave systems operating far from thermodynamic equilibrium, which reveals analogies with, for example, gravitational systems, and establishes a new scenario that can be common to many turbulent flows in photonic quantum fluids, hydrodynamics and Bose–Einstein condensates.

Understanding turbulent flows arising from random dispersive waves that interact through nonlinearities is a challenging issue in physics. Here, the authors model and observe experimentally in a nonlinear optics set-up the transition between a sea of small-scale shocklets and a giant collective shock wave.

Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation

We study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking occurs at a finite critical time. In particular, both Riemann invariants experience a simultaneous breaking at the origin. Although the initial vacuum point is no longer preserved in the presence of a finite dispersion, the critical behavior manifests itself through an abrupt transition occurring around the breaking time.

Incoherent dispersive shocks in the spectral evolution of random waves

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.

Dispersive shock wave interactions and asymptotics

Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time.

Spontaneous solitons in the thermal equilibrium of a quasi-1D Bose gas

We show that solitons occur generically in the thermal equilibrium state of a weakly interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state, usually thought of as primarily phase-fluctuating. Thermal solitons are seen in uniform 1D, trapped 1D, and elongated 3D gases, appearing as shallow solitons at low quasicondensate temperatures, becoming widespread and deep as temperature rises. This behavior can be understood via thermal occupation of the type II excitations in the Lieb-Liniger model of a uniform 1D gas. Furthermore, we find that the quasicondensate phase includes very appreciable density fluctuations while leaving phase fluctuations largely unaltered from the standard picture derived from a density-fluctuation-free treatment.

Quantum shock waves and domain walls in the real-time dynamics of a superfluid unitary Fermi gas

We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by π and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase jumps appear to collide elastically.

Observation of shock waves in a strongly interacting Fermi gas

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.

Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly. A collision of sodium BECs with 1.5 x 10;{5} atoms is simulated, in a regime that is difficult to describe semiclassically. The uncertainty of physical quantities depends on the statistics of the full quantum prediction. Cutoffs are minimized to a discretization of the Hamiltonian. The technique presented is quite general and extension to other systems is considered.

Soliton generation and multiple phases in dispersive shock and rarefaction wave interaction

Interactions of dispersive shock waves (DSWs) and rarefaction waves (RWs) associated with the Korteweg-de Vries equation are shown to exhibit multiphase dynamics and isolated solitons. There are six canonical cases: one is the interaction of two DSWs that exhibit a transient two-phase solution but evolve to a single-phase DSW for large time; two tend to a DSW with either a small amplitude wave train or a finite number of solitons, which can be determined analytically; two tend to a RW with either a small wave train or a finite number of solitons; finally, one tends to a pure RW.

Dissipation-induced coherent structures in Bose-Einstein condensates

We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.