Snake Instability Research Articles

Dynamic instabilities and turbulence of merged rotating Bose–Einstein condensates

We present the simulation results of merging harmonically confined rotating Bose–Einstein condensates in two dimensions. Merging of the condensate is triggered by positioning the rotation axis at the trap minima and moving both condensates toward each other while slowly ramping their rotation frequency. We analyze the dynamics of the merged condensate by letting them evolve under a single harmonic trap. We systematically investigate the formation of solitonic and vortex structures in the final, unified condensate, considering both nonrotating and rotating initial states. In both cases, merging leads to the formation of solitons that decay into vortex pairs through snake instability, and subsequently, these pairs annihilate. Soliton formation and decay-induced phase excitations generate sound waves, more pronounced when the merging time is short. We witness no sound wave generation at sufficiently longer merging times that finally leads to the condensate reaching its ground state. With rotation, we notice off-axis merging (where the rotation axes are not aligned), leading to the distortion and weakening of soliton formation. The incompressible kinetic energy spectrum exhibits a Kolmogorov-like cascade [E(k)∼k−5/3] in the initial stage for merging condensates rotating above a critical frequency and a Vinen-like cascade [E(k)∼k−1] at a later time for all cases. Our findings hold potential significance for atomic interferometry, continuous atomic lasers, and quantum sensing applications.

Assessment of a space and energy resolved diagnostic based on GEM technology on MAST-U

Abstract A Gas Electron Multiplier (GEM)-based detector was utilized for the first
time on a spherical tokamak, MAST-U, during the 2023 campaign to investigate Soft
X-Ray (SXR) radiation (1-20 keV) emitted from the plasma. GEM detectors, chosen
for their resilience to harsh fusion environments and their ability to provide energy-
resolved SXR emission images with sub-millisecond time resolution, are a relatively
new diagnostic compared to standard semiconductor diodes. In this study, the GEM
detector features a pinhole geometry outside the vacuum chamber and observes the
plasma through a beryllium window. Filled with an ArCO2 mixture, the detector
consists of an Aluminized Mylar cathode, three Aluminum-coated GEM foils, and an
anode made of a 16x16 matrix of 6mm2 pads for 2D readout. It employs custom
GEMINI ASICs (Application Specific Integrated Circuits) for signal readout, enabling
photon-counting techniques with Time over Threshold (ToT) analysis on each detector
channel, reaching a total maximum rate of 256 MHz.
Preliminary findings from the 2023 campaign demonstrate the effectiveness of the
GEM detector in complementing existing SXR camera data in terms of spatial and
temporal resolution. Case studies include the identification of Magnetohydrodynamic
(MHD) instabilities, such as the Snake instability, and the exploitation of energy
capabilities for plasma event energy characterization, as shown in the case of Internal
Reconnection Events. Additionally, the GEM detector allows for estimation of the
Electron Temperature of Maxwellian plasmas. These results underscore the potential
of the GEM-based diagnostic system in advancing tokamak research for comprehensive
plasma characterization and control.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose–Einstein condensate

Manipulating nonlinear excitations, including solitons and vortices, is an essential topic in quantum many-body physics. A new progress in this direction is a protocol proposed in [Phys. Rev. Res. 2 043256 (2020)] to produce dark solitons in a one-dimensional atomic Bose–Einstein condensate (BEC) by quenching inter-atomic interaction. Motivated by this work, we generalize the protocol to a two-dimensional BEC and investigate the generic scenario of its post-quench dynamics. For an isotropic disk trap with a hard-wall boundary, we find that successive inward-moving ring dark solitons (RDSs) can be induced from the edge, and the number of RDSs can be controlled by tuning the ratio of the after- and before-quench interaction strength across different critical values. The role of the quench played on the profiles of the density, phase, and sound velocity is also investigated. Due to the snake instability, the RDSs then become vortex–antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction. By tuning the geometry of the box traps, demonstrated as polygonal ones, more subtle dynamics of solitons and vortices are enabled. Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in near future cold-atom experiments.

Photonic snake states in two-dimensional frequency combs

Taming the instabilities inherent to many nonlinear optical phenomena is of paramount importance for modern photonics. In particular, the so-called snake instability is universally known to severely distort localized wave stripes, leading to the occurrence of transient, short-lived dynamical states that eventually decay. This phenomenon is ubiquitous in nonlinear science—from river meandering to superfluids—and so far it apparently remains uncontrollable; however, here we show that optical snake instabilities can be harnessed by a process that leads to the formation of stationary and robust two-dimensional zigzag states. We find that such a new type of nonlinear waves exists in the hyperbolic regime of cylindrical microresonators, and that it naturally corresponds to two-dimensional frequency combs featuring spectral heterogeneity and intrinsic synchronization. We uncover the conditions of the existence of such spatiotemporal photonic snakes and confirm their remarkable robustness against perturbations. Our findings represent a new paradigm for frequency comb generation, thus opening the door to a whole range of applications in communications, metrology and spectroscopy. By tuning the spatial width, the strength and the frequency of a pump beam in two-dimensional cylindrical microcavities supporting stable, robust photonic snake states, a set of broadband and perfectly synchronized two-dimensional frequency combs can be realized.

Dynamics of phase defects trapped in optically imprinted orbits in dissipative binary polariton condensates

We study the dynamics of phase defects trapped in a finite optically imprinted ring lattice in binary polariton condensates, under the influence of the cross interaction (CI) between the condensate fractions in different spin components and the spin-orbit interaction (SOI). In this configuration, we find that a vortex circulates unidirectionally in optically induced orbits because of the Magnus force acting in the polariton fluid and the vortex' angular velocity is influenced by the SOI and CI. Interestingly, in our system, these two interactions can also lead to elongated and frozen phase defects, forming a frozen dark solution with similarity to a dark soliton but with finite size in both spin components. When the dark solution is stretched further to occupy the entire orbit of a condensate ring, the phase defect triggers a snake instability and induces the decay of the dark ring solution. The circulation direction of a single vortex is determined by the Magnus force. This situation is more complex for the group motion of multiple vortices because of significant vortex-antivortex interaction. The collective motion of such vortex constellations, however, is determined by the SOI.

Overcoming the snaking instability and nucleation of dark solitons in nonlinear Kerr media by spatially inhomogeneous defocusing nonlinearity

Dark solitons, localized nonlinear waves with center notch standing on a stable uniform background, own rich formation and dynamics for physics and applications in diverse fields, and have thus recently attracted many theoretical and experimental studies. Transverse modulational instability is an impeditive factor for dark solitons in multidimensional space, to stabilize them various methods have been proposed. We here take use of a purely nonlinear strategy by introducing quasi-one-dimensional Gaussian like trap, and its combination with the external linear harmonic trap, in the framework of the (2 + 1)-dimensional Gross-Pitaveski/nonlinear Schrödinger equation, to realize the stabilization mechanism of dark-soliton stripes. Variational approximation analytical method, linear-stability analysis and direct perturbed numerical simulations are adopted to carry out the study, and agreement is reached. We demonstrate that the dark-soliton stripes can be stabilized completely, and the associated modulational instability wave number band is reduced greatly. Particularly, in the case of linear harmonic trap, the nucleation of dark solitons, subjected to snaking instability, can be overcome by the nonlinear trap with both defocusing and focusing strengths. The predicted results may be realized in Bose-Einstein condensates and nonlinear optics.

Modelling and Stability Analysis of Articulated Vehicles

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

Dark-soliton-like magnetic domain walls in a two-dimensional ferromagnetic superfluid

We report a stable magnetic domain wall in a uniform ferromagnetic spin-1 condensate, characterized by the magnetization having a dark soliton profile with nonvanishing superfluid density. We find exact stationary solutions for a particular ratio of interaction parameters with and without magnetic fields, and develop an accurate analytic solution applicable to the whole ferromagnetic phase. In the absence of magnetic fields, this domain wall relates various distinct solitary excitations in binary condensates through $\textrm{SO}(3)$ spin rotations, which otherwise are unconnected. Remarkably, studying the dynamics of a quasi-two-dimensional (quasi-2D) system we show that standing wave excitations of the domain wall oscillate without decay, being stable against the snake instability. The domain wall is dynamically unstable to modes that cause the magnetization to grow perpendicularly while leaving the domain wall unchanged. Real time dynamics in the presence of white noise reveals that this "spin twist" instability does not destroy the topological structure of the magnetic domain wall.

Stability analysis and attractor dynamics of three-dimensional dark solitons with localized dissipation

We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate with dark or grey kink solitons in the presence of localized dissipation. To this end, the 3D Gross-Pitaevskii equation with an additional imaginary potential is solved numerically. We analyze the suppression of the snaking instability in dependence of the dissipation strength and extract the threshold value for the stabilization of the dark soliton for experimentally realistic parameters. Below the threshold value, we observe the decay into a solitonic vortex. Above the stabilization threshold, we observe the attractor dynamics towards the dark soliton when initially starting from a grey soliton. We find that for all initial conditions the dark soliton is the unique steady-state of the system - even when starting from the BEC ground state.

Bogoliubov–de Gennes theory of the snake instability of gray solitons in higher dimensions

Gray solitons are a one-parameter family of solutions to the one-dimensional non-linear Schr\"odinger equation (NLSE) with positive cubic nonlinearity, as found in repulsively interacting dilute Bose-Einstein condensates or electromagnetic waves in the visible spectrum in waveguides described by Gross-Pitaevskii mean field theory. In two dimensions these solutions to the NLSE appear as a line or plane of depressed condensate density or light intensity, but numerical solutions show that this line is dynamically unstable to `snaking': the initially straight line of density or intensity minimum undulates with exponentially growing amplitude. To assist future studies of quantum mechanical instability beyond mean field theory, we here pursue an approximate analytical description of the snake instability within Bogoliubov-de Gennes perturbation theory. Within this linear approximation the two-dimensional result applies trivially to three dimensions as well, describing buckling modes of the low-density plane. We extend the analytical results of Kuznetsov and Turitsyn [Sov. Phys. JETP \textbf{67}, 1583 (1988)] to shorter wavelengths of the `snake' modulation and show to what extent the snake mode can be described accurately as a parametric instability, in which the position and grayness parameter of the initial soliton simply become dependent on the transverse dimension(s). We find that the parametric picture remains accurate up to second order in the snaking wave number, if the snaking soliton is also dressed by an outward-propagating sound wave, but that beyond second order in the snaking wave number the parametric description breaks down.

Parallel dark-soliton pair in a bistable two-dimensional exciton-polariton superfluid

Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, 2D dark solitons are unstable and collapse into vortices due to snake instabilities. Making use of the optical bistability in exciton-polariton microcavities, we demonstrate that a pair of dark solitons can be formed in the wake of an obstacle in a polariton flow resonantly supported by a homogeneous laser beam. Unlike the purely dissipative case where the solitons are grey and spatially separate, here the two solitons are fully dark, rapidly align at a specific separation distance and propagate parallel as long as the flow is in the bistable regime. Remarkably, the use of this regime allows to avoid the phase fixing arising in resonant pumping regime and to circumvent the polariton decay. Our work opens very wide perspectives of studying new classes of phase-density defects which can form in driven-dissipative quantum fluids of light.

Taming the snake instabilities in a polariton superfluid

The dark solitons observed in a large variety of nonlinear media are unstable against the modulational (snake) instabilities and can break in vortex streets. This behavior has been investigated in nonlinear optical crystals and ultra-cold atomic gases. However, a deep characterization of this phenomenon is still missing. In a resonantly pumped two-dimensional polariton superfluid, we use an all-optical imprinting technique together with the bistability of the polariton system to create dark solitons in confined channels. Due to the snake instabilities, the solitons are unstable and break into arrays of vortex streets whose dynamical evolution is frozen by the pump-induced confining potential, allowing their direct observation in our system. A deep quantitative study shows that the vortex street period is proportional to the quantum fluid healing length, in agreement with the theoretical predictions. Finally, the full control achieved on the soliton patterns is exploited to give proof of principle of an efficient, ultra-fast, analog, all-optical maze solving machine in this photonic platform.

Snake—Modulation Dynamics of an Optical—Terahertz Soliton in a Graded-Index Waveguide

A nonlinear stage of the effect of snake and modulation instabilities on the dynamics of an optical—terahertz soliton in a quadratically nonlinear graded-index waveguide has been studied theoretically. It has been shown that both instabilities are of fundamental importance and cannot be separated from each other. If the carrier frequency of the optical component is in the region of an anomalous dispersion of the group velocity, these instabilities are developed in a blow-up regime, leading to the self-focusing of the soliton. In the case of the normal dispersion of the group velocity, the mutual effect of the waveguide and snake—modulation dynamics results in the formation of a stable spatiotemporal soliton.

Long Josephson junctions with exciton-polariton condensates

We demonstrate the possibility to build stable Josephson $\pi$-junction stripes with exciton-polariton condensates. The stability of the $\pi$-junction between arbitrary long polariton stripes is achieved at low pumping by balancing the snaking instability with counter-propagating flows towards the junction. Not dissimilar from a dark soliton, the instability becomes relevant at high pumping leading to formation of vortex dipoles. The resulting structures can be stabilised to produce static lattices of Josephson vortices in straight and ring geometries. Our results build towards realization of quantum technological applications based on the Josephson effect at room temperature.

Holographic superfluid solitons with backreaction

Solitons are important nonperturbative excitations in superfluids. For holographic superfluids, we numerically construct dark solitons that have the symmetry-restored phase at their core. A central point is that we include the gravitational back-reaction of the matter fields, which becomes important at low temperatures. We study in detail the properties of these solitons under variation of the back-reaction strength via tuning the gravitational constant. In particular, the depletion fraction of the particle number density at the core of the solitons is carefully investigated. In agreement with the probe-limit analysis, the depletion fraction shows the same qualitative behavior as in Bogoliubov-de Gennes (BdG) theory, even if the back-reaction is included. We find that the depletion decreases with increasing back-reaction strength. Moreover, the inclusion of back-reaction enables us to obtain the effective energy density of solitons within holography, which together with an evaluation of the surface tension leads to a simple physical explanation for the snake instability of dark solitons.

Crossover between snake instability and Josephson instability of dark solitons in superfluid Fermi gases

Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC- and BCS-regimes. On the BEC-side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS-side, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents. The latter mechanism is qualitatively different from the snaking instability and this difference should be experimentally detectable.

Decay of the relative phase domain wall into confined vortex pairs: The case of a coherently coupled bosonic mixture

A domain wall of relative phase in a flattened harmonically-trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity $\Omega$, is predicted to decay through two different mechanisms. For small values of $\Omega$ the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, whose motion inside the trap causes the emergence of magnetization, the bending of the domain wall and its consequent fragmentation. For large values of $\Omega$ the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.

Magnetic solitons in binary mixtures of Bose–Einstein condensates

Solitons, that is stable localized perturbations of a medium, are the topological excitations of nonlinear systems. They can be stable and live for a long time and may have promising applications for telecommunication. The basic one is the Tsuzuki dark soliton, which can be described by an analytical solution of the Gross–Pitaevskii equation (GPE). Ultracold Bose–Einstein condensed (BEC) gases are an important example for the investigation of solitons which can be created by phase and density imprinting. New possibilities arise in mixtures of different hyperspin states of ultra-cold gases, where the so-called magnetic solitons (MS), that is localized magnetized regions, can exist. We will see that these MS permit an analytical description. New peculiar phenomena can take place in the presence of a coherent Rabi coupling between the spin states, where two different type of solitons exist—so-called $$2\pi $$ and $$0\pi $$ solitons. $$2\pi $$ solitons, unlike the usual Tsuzuki solitons, have at small velocity a positive effective mass and consequently do not undergo the snake instability. Solitary waves can oscillate in BEC gases along elongated traps. The theoretical description of this motion requires the knowledge of the effective soliton mass and the effective number of particles in the soliton. These quantities are calculated.

Decay of Phase-Imprinted Dark Soliton in Bose–Einstein Condensate at Nonzero Temperature

We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose-Einstein condensate at non-zero temperatures by using the projected Gross-Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At non-zero temperature, as we expected, we find that this snake instability cannot be clearly seen as in the absolute zero temperature case because of the presence of thermal fluctuations. However, we find that the decay rate, the half width of the overlap integral with respect to the phase-imprinted initial state, shows a power low decay as a function of the energy and finally remains a non-zero value.

Observation of Wall-Vortex Composite Defects in a Spinor Bose-Einstein Condensate.

We report the observation of spin domain walls bounded by half-quantum vortices (HQVs) in a spin-1 Bose-Einstein condensate with antiferromagnetic interactions. A spinor condensate is initially prepared in the easy-plane polar phase, and then, suddenly quenched into the easy-axis polar phase. Domain walls are created via the spontaneous Z_{2} symmetry breaking in the phase transition and the walls dynamically split into composite defects due to snake instability. The end points of the defects are identified as HQVs for the polar order parameter and the mass supercurrent in their proximity is demonstrated using Bragg scattering. In a strong quench regime, we observe that singly charged quantum vortices are formed with the relaxation of free wall-vortex composite defects. Our results demonstrate a nucleation mechanism for composite defects via phase transition dynamics.