arXiv subjects

Hayder Salman

Publications and source records attributed to Hayder Salman.

14 recordsLinked to original sources

arXiv2025

Simulating Quantum Turbulence with Matrix Product States

Quantum turbulence spans length scales from the system size $L$ to the healing length $\xi$, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when $L \gg \xi$. We present a matrix product state (MPS) solver for the GP equation that efficiently compresses the wavefunction by truncating weak interlength-scale correlations. This approach reduces memory usage by factors ranging from 10x to over 10,000x compared to DNS. We benchmark our approach on nonlinear excitations, namely dark solitons (1D) and quantized vortices (2D, 3D), capturing key dynamics such as Kelvin wave propagation and vortex ring emission in the case of vortex line reconnection. For turbulent states composed of multiple nonlinear excitations, we find that the memory compression of the MPS representation is directly proportional to the soliton or vortex densities. We also accurately reproduce established results from two-point correlation functions and energy spectra, where we recover the incompressible kinetic energy spectrum with little memory overhead. These results demonstrate the representative capabilities of the MPS ansatz for quantum turbulence and pave the way for studying this nonequilibrium state using previously-prohibited system sizes to uncover novel physics.

quant-ph↗

arXiv2024

Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas

We simulate interaction quenches crossing from a superfluid to a supersolid state in a dipolar quantum gas of ${}^{164}\mathrm{Dy}$ atoms, trapped in an elongated tube with periodic boundary conditions, via the extended Gross-Pitaevskii equation. A freeze-out time is observed through a delay in supersolid formation after crossing the critical point. We compute the density-density correlations at the freeze-out time and extract the frozen correlation length for the solid order. An analysis of the freeze-out time and correlation length versus the interaction quench rate allows us to extract universal exponents corresponding to the relaxation time and correlation length based on predictions of the Kibble-Zurek mechanism. Over several orders of magnitude, clear power-law scaling is observed for both the freeze-out time and the correlation length, and the corresponding exponents are compatible with predictions based on the excitation spectrum calculated via Bogoliubov theory. Defects due to independent local breaking of translational symmetry, contributing to globally incommensurate supersolid order, are identified, and their number at the freeze-out time is found to also scale as a power law. Our results support the hypothesis of a continuous transition whose universality class remains to be determined but appears to differ from that of the (1+1)D XY model.

cond-mat.quant-gas↗

arXiv2023

Dynamics of a Nonequilibrium Discontinuous Quantum Phase Transition in a Spinor Bose-Einstein Condensate

Symmetry-breaking quantum phase transitions lead to the production of topological defects or domain walls in a wide range of physical systems. In second-order transitions, these exhibit universal scaling laws described by the Kibble-Zurek mechanism, but for first-order transitions a similarly universal approach is still lacking. Here we propose a spinor Bose-Einstein condensate as a testbed system where critical scaling behavior in a first-order quantum phase transition can be understood from generic properties. We demonstrate the applicability of the Kibble-Zurek mechanism for this transition to determine the critical exponents for: (1) the onset of the decay of the metastable state on short times scales, and (2) the number of resulting phase-separated ferromagnetic domains at longer times, as a one-dimensional spin-1 condensate is ramped across a first-order quantum phase transition. The predictions are in excellent agreement with mean-field numerical simulations and provide a paradigm for studying the decay of metastable states in experimentally accessible systems.

cond-mat.quant-gas↗

arXiv2023

Ising Hamiltonian Minimization: Gain-Based Computing with Manifold Reduction of Soft-Spins vs Quantum Annealing

We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semi-classical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a Mobius graph evolves with increased annealing parameters. Our findings indicate that these semi-classical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the `manifold reduction' method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian's energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from combining classical and quantum annealing techniques.

quant-ph↗

arXiv2022

Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas

We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the meanfield Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\cal{H}$ and angular momentum $\cal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\hatβ$ and rotation frequency $\hatω$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.

cond-mat.quant-gas↗

arXiv2018

Vortex Nucleation Limited Mobility of Free Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid

We study the motion of an electron bubble in the zero temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupled to a Schrödinger equation for the electron wavefunction, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^4$He at a pressure of one bar. By performing fully 3D spatio-temporal simulations of the superfluid coupled to an electron, that is modelled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data.

cond-mat.other↗

arXiv2017

Helicity Conservation, and Twisted Seifert Surfaces for Superfluid Vortices

Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterise the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times. It follows that the Gauss-linking number is a more appropriate definition of helicity for superfluids. Despite this, we explain how a quasiclassical limit can arise in a superfluid in which the continuum definition for helicity can be used. This provides a clear connection between a microscopic and a macroscopic description of a superfluid as provided by the Hall-Vinen-Bekarevich-Khalatnikov equations. This leads to consistency with the definition of helicity used for classical vortices.

math-ph↗

arXiv2016

Long-range Ordering of Topological Excitations in a Two-Dimensional Superfluid Far From Equilibrium

We study the relaxation of a 2D ultracold Bose-gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a non-zero coarse-grained vorticity field. The streamfunction of this emergent quasi-classical 2D flow is governed by a Boltzmann-Poisson equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Boltzmann-Poisson equation. The results allow us to characterise the spectral energy condensate in a 2D quantum fluid that bears striking similarity with similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.

cond-mat.quant-gas↗

arXiv2016

A Vortex Filament Tracking Method for the Gross-Pitaevskii Model of a Superfluid

We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.

physics.flu-dyn↗

arXiv2014

Scattering of Line-Ring Vortices in a Superfluid

We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. Using this, we show that the scattering of the vortex ring in our Gross-Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter.

physics.flu-dyn↗

arXiv2013

Breathers on Quantized Superfluid Vortices

We consider the propagation of breathers along a quantised superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localised in both space and time. The emergent structures on the vortex filament are analogous to loop solitons. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the cross-over range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings.

physics.flu-dyn↗

arXiv2012

Approximating Steady States in Equilibrium and Nonequilibrium Condensates

We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly valid approximation for the condensate density of an ultracold Bose gas confined in a harmonic trap that extends into the classically forbidden region. This provides an accurate approximation of the condensate density that includes healing effects at leading order that are missing in the widely adopted Thomas-Fermi approximation. The results presented herein allow us to formulate useful approximations to a range of experimental systems including the equilibrium properties of a finite temperature Bose gas and the steady-state properties of a 2D nonequilibrium condensate. Comparisons between our asymptotic and numerical results for the conservative and forced-dissipative forms of the GP equations as applied to these systems show excellent agreement between the two sets of solutions thereby illustrating the accuracy of these approximations.

cond-mat.quant-gas↗

arXiv2011

From Classical Fields to Two-Fluid Model of Superfluidity: Emergent Kinetics and Local Gauge Transformations

The first successful macroscopic theory for the motion of superfluid helium was that of Lev Landau (1941) in which the fluid is modelled phenomenologically as an interpenetrating mixture of a superfluid and a normal fluid. It has later been shown that Landau's two-fluid model can be rigorously derived from a one-fluid model within the classical fields approximation. Assuming a separation of scales exists between the slowly varying, large-scale, background (condensate) field, and the short rapidly evolving excitations, a full description of the kinetics between the condensate and the thermal cloud can be obtained. The kinetics describes three-wave and four-wave interactions that resemble the C_{12} and C_{22} terms, respectively, in the collision integral of the ZNG theory. The scale separation assumption precludes analysis of the healing layer and thus does not include the dynamics of quantised vortices. Whilst the analysis required the use of small parameters arising from the scale separation assumption and the assumption of a weakly depleted condensate, we expect the results to hold true over a wider range of parameters. This belief is motivated by the validity of Landau's two-fluid model which can be derived from a one-fluid model using nothing more than Galilean invariance principles. Indeed, we argue that similar arguments can be used to recover a two-fluid model directly from a classical field simply by invoking a local gauge transformation. This derivation does not require any small parameters to be introduced suggesting that the results that lead to the kinetic equations may turn out to be more general.

cond-mat.quant-gas↗

arXiv2008

Condensation of Classical Nonlinear Waves in a Two-Component System

We study the formation of large-scale coherent structures (a condensate) for a system of two weakly interacting classical waves. Using the coupled defocusing nonlinear Schrödinger (NLS) equations as a representative model, we focus on condensation in the phase mixing regime. We employ weak turbulence theory to provide a complete thermodynamic description of the classical condensation process. We show that the temperature and the condensate mass fractions are fully determined by the total number of particles in each component and the initial total energy. Moreover, we find that, at higher energies, condensation can occur in only one component. The theory presented provides excellent agreement with results of numerical simulations obtained by directly integrating the dynamical model.

cond-mat.stat-mech↗