Natalia G. Berloff

Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate

Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behavior. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyze the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.

Sculpting oscillators with light within a nonlinear quantum fluid

Polaritons—quasiparticles made up of a photon and exciton strongly coupled together—can form macroscopic quantum states even at room temperature. Now these so-called condensates are imaged directly. This achievement could aid the development of semiconductor-based polariton-condensate devices.

Solitary and Periodic Solutions of Nonlinear Nonintegrable Equations

The singular manifold method and partial fraction decomposition allow one to find some special solutions of nonintegrable partial differential equations (PDE) in the form of solitary waves, traveling wave fronts, and periodic pulse trains. The truncated Painleve expansion is used to reduce a nonlinear PDE to a multilinear form. Some special solutions of the latter equation represent solitary waves and traveling wave fronts of the original PDE. The partial fraction decomposition is used to obtain a periodic wave train solution as an infinite superposition of the “corrected” solitary waves.

Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate

Quasiparticles in semiconductors—such as microcavity polaritons—can form condensates in which the steady-state density profile is set by the balance of pumping and decay. By taking account of the polarization degree of freedom for a polariton condensate, and considering the effects of an applied magnetic field, we theoretically discuss the interplay between polarization dynamics, and the spatial structure of the pumped decaying condensate. If spatial structure is neglected, this dynamics has attractors that are linearly polarized condensates (fixed points), and desynchronized solutions (limit cycles), with a range of bistability. Considering spatial fluctuations about the fixed point, the collective spin modes can either be diffusive, linearly dispersing, or gapped. Including spatial structure, interactions between the spin components can influence the dynamics of vortices; produce stable complexes of vortices and rarefaction pulses with both co- and counter-rotating polarizations; and increase the range of possible limit cycles for the polarization dynamics, with different attractors displaying different spatial structures.

The Nonlinear Schrödinger Equation as a Model of Superfluidity

The results of theoretical and numerical studies of the Gross-Pitaevskii (GP) model are reviewed. This model is used to elucidate different aspects of superfluid behaviour: the motion, interactions, annihilations, nucleation and reconnections of vortex lines, vortex rings, and vortex loops; the motion of impurities; flow through apertures; superfluid turbulence and the capture of impurities by vortex lines. The review also considers some generalizations of the model.

Geometrically locked vortex lattices in semiconductor quantum fluids

Macroscopic quantum states can be easily created and manipulated within semiconductor microcavity chips using exciton-photon quasiparticles called polaritons. Besides being a new platform for technology, polaritons have proven to be ideal systems to study out-of-equilibrium condensates. Here we harness the photonic component of such a semiconductor quantum fluid to measure its coherent wavefunction on macroscopic scales. Polaritons originating from separated and independent incoherently pumped spots are shown to phase-lock only in high-quality microcavities, producing up to 100 vortices and antivortices that extend over tens of microns across the sample and remain locked for many minutes. The resultant regular vortex lattices are highly sensitive to the optically imposed geometry, with modulational instabilities present only in square and not triangular lattices. Such systems describe the optical equivalents to one- and two-dimensional spin systems with (anti)-ferromagnetic interactions controlled by their symmetry, which can be reconfigured on the fly, paving the way to widespread applications in the control of quantum fluidic circuits.

Realizing the classical XY Hamiltonian in polariton simulators

The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.

Unpinning triggers for superfluid vortex avalanches

The pinning and collective unpinning of superfluid vortices in a decelerating container is a key element of the canonical model of neutron star glitches and laboratory spin-down experiments with helium II. Here the dynamics of vortex (un)pinning is explored using numerical Gross-Pitaevskii calculations, with a view to understanding the triggers for catastrophic unpinning events (vortex avalanches) that lead to rotational glitches. We explicitly identify three triggers: rotational shear between the bulk condensate and the pinned vortices, a vortex proximity effect driven by the repulsive vortex-vortex interaction, and sound waves emitted by moving and repinning vortices. So long as dissipation is low, sound waves emitted by a repinning vortex are found to be sufficiently strong to unpin a nearby vortex. For both ballistic and forced vortex motion, the maximum inter-vortex separation required to unpin scales inversely with pinning strength.

Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

The stability of the axisymmetric solitary waves of the Gross–Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones–Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory.

Polariton ring condensates and sunflower ripples in an expanding quantum liquid

Optically pumping high quality semiconductor microcavities allows for the spontaneous formation of polariton condensates, which can propagate over distances of many microns. Tightly focussed pump spots here are found to produce expanding incoherent bottleneck polaritons which coherently amplify the ballistic polaritons and lead to the formation of unusual ring condensates. This quantum liquid is found to form a remarkable sunflower-like spatial ripple pattern which arises from self interference with Rayleigh-scattered coherent polariton waves in the Cerenkov regime.