arXiv subjects

Natalia G. Berloff

Publications and source records attributed to Natalia G. Berloff.

At least 55 records · Page 3Linked to original sources

arXiv2019

Towards Arbitrary Control of Lattice Interactions in Nonequilibrium Condensates

There is a growing interest in investigating new states of matter using out-of-equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. Here we suggest how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions. Representing spin by condensate phase, the effective two spin interactions are created with nonresonant pumping, are directed with dissipative channels, and are further controlled with dissipative gates. The dissipative barriers are used to block unwanted interactions between condensates. Together, spatial anisotropy of dissipation and pump profiles allow an effective control of sign and intensity of the coupling strength between any two neighboring sites independent of the rest of the spins, which we demonstrate with a two dimensional square lattice of polariton condensates. Experimental realisation of such fully-controllable networks offers great potential for an efficient analog Hamiltonian optimizer and for reservoir computing.

cond-mat.mes-hall↗

arXiv2019

Formation and Dynamics of Quantum Hydrodynamical Breathing Ring Solitons

We show that exciton-polariton condensates may exhibit a new fundamental, self-localized nonlinear excitation not seen in other quantum hydrodynamical systems, which takes the form of a dark ring shaped breather. We predict that these structures form spontaneously and remain stable under a combination of uniform resonant and nonresonant forcing. We study single ring dynamics, ring interactions and ring turbulence, and explain how direct experimental observations might be made. We discuss the statistics of ring formation and propose an experimental scheme by which these structures may be exploited to study the smooth cross-over between equilibrium and non-equilibrium critical phase transitions. Finally, we present an alternative mechanism of formation for these topological breathers, in which they circumscribe Gaussian resonant pumps. The observation of a breathing ring soliton would represent the first fundamental breathing soliton within the broad field of quantum hydrodynamics.

nlin.PS↗

arXiv2019

Polaritonic network as a paradigm for dynamics of coupled oscillators

Photonic and polaritonic lattices have been recently theoretically proposed and experimentally realised as many-body simulators due to the rich behaviors exhibited by such systems at the macroscale. We show that the networks of polariton condensates encapsulate a large variety of behaviours of systems of coupled oscillators. By eliminating spatial degrees of freedom in nonresonantly pumped polariton network, we establish that depending on the values of experimentally tunable parameters the networks of polariton condensates may represent Kuramoto, Sakaguchi-Kuramoto, Stuart-Landau, Lang-Kobayashi oscillators and beyond. The networks of polariton condensates are therefore capable of implementing various regimes acting as analogue spin Hamiltonian minimizers, producing complete and cluster synchronization, exotic spin glasses and large scale secondary synchronization of oscillations. We suggest that the recently implemented control of the system parameters for individual sites in polariton lattices allows addressing for the first time the interaction of sublattices that belong to different oscillatory classes.

cond-mat.mes-hall↗

arXiv2018

Networks of non-equilibrium condensates for global optimization

Recently several gain-dissipative platforms based on the networks of optical parametric oscillators, lasers, and various non-equilibrium Bose-Einstein condensates have been proposed and realised as analogue Hamiltonian simulators for solving large-scale hard optimisation problems. However, in these realisations the parameters of the problem depend on the node occupancies that are not known a priori, which limits the applicability of the gain-dissipative simulators to the classes of problems easily solvable by classical computations. We show how to overcome this difficulty and formulate the principles of operation of such simulators for solving the NP-hard large-scale optimisation problems such as constant modulus continuous quadratic optimisation and quadratic binary optimisation for any general matrix. To solve such problems any gain-dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain and coupling strengths.

physics.class-ph↗

arXiv2018

Global optimization of spin Hamiltonians with gain-dissipative systems

Recently, several platforms were proposed and demonstrated a proof-of-principle for finding the global minimum of the spin Hamiltonians such as the Ising and XY models using gain-dissipative quantum and classical systems. The implementation of dynamical adjustment of the gain and coupling strengths has been established as a vital feedback mechanism for analog Hamiltonian physical systems that aim to simulate spin Hamiltonians. Based on the principle of operation of such simulators we develop a novel class of gain-dissipative algorithms for global optimisation of NP-hard problems and show its performance in comparison with the classical global optimisation algorithms. These systems can be used to study the ground state and statistical properties of spin systems and as a direct benchmark for the performance testing of the gain-dissipative physical simulators. The estimates of the time operation of the physical implementation of the gain-dissipative simulators for large matrices show a possible speed-up of the several orders of magnitude in comparison with classical computations.

cs.ET↗

arXiv2018

Simulating Ising and Potts models and external fields with non-equilibrium condensates

Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we show how to simulate the discrete Ising and Potts models with or without external fields using the physical gain-dissipative platforms with continuous phases such as lasers and various non-equilibrium Bose-Einstein condensates. The underlying operational principle originates from a combination of resonant and non-resonant pumping. Our results lay grounds for the physical simulations of a broad range of Hamiltonians with complex interactions that can vary in time and space and with combined symmetries.

cond-mat.dis-nn↗

arXiv2018

Blockchain platform with proof-of-work based on analog Hamiltonian optimisers

The development of quantum information platforms such as quantum computers and quantum simulators that will rival classical Turing computations are typically viewed as a threat to secure data transmissions and therefore to crypto-systems and financial markets in general. We propose to use such platforms as a proof-of-work protocol for blockchain technology, which underlies cryptocurrencies providing a way to document the transactions in a permanent decentralised public record and to be further securely and transparently monitored. We reconsider the basis of blockchain encryption and suggest to move from currently used proof-of-work schemes to the proof-of-work performed by analog Hamiltonian optimisers. This approach has a potential to significantly increase decentralisation of the existing blockchains and to help achieve faster transaction times, therefore, removing the main obstacles for blockchain implementation. We discuss the proof-of-work protocols for a few most promising optimiser platforms: quantum annealing hardware based on D-wave simulators and a new class of gain-dissipative simulators.

quant-ph↗

arXiv2017

Matter wave coupling of spatially separated and unequally pumped polariton condensates

Spatial quantum coherence between two separated driven-dissipative polariton condensates created non-resonantly and with a different occupation is studied. We identify the regions where the condensates remain coherent with the phase difference continuously changing with the pumping imbalance and the regions where each condensate acquires its own chemical potential with phase differences exhibiting time-dependent oscillations. We show that in the mutual coherence limit the coupling consists of two competing contributions: a symmetric Heisenberg exchange and the Dzyloshinskii-Moriya asymmetric interactions that enable a continuous tuning of the phase relation across the dyad and derive analytic expressions for these types of interactions. The introduction of non-equal pumping increases the complexity of the type of the problems that can be solved by polariton condensates arranged in a graph configuration. If equally pumped polaritons condensates arrange their phases to solve the constrained quadratic minimisation problem with a real symmetric matrix, the non-equally pumped condensates solve that problem for a general Hermitian matrix.

cond-mat.mes-hall↗

arXiv2017

Exotic states of matter with polariton chains

We consider linear periodic chains of exciton-polariton condensates formed by pumping polaritons non-resonantly into a linear network. To the leading order, such a sequence of condensates establishes relative phases as to minimize a classical one-dimensional XY Hamiltonian with nearest and next to nearest neighbors. We show that the low energy states of polaritonic linear chains demonstrate various classical regimes: ferromagnetic, antiferromagnetic and frustrated spiral phases, where quantum or thermal fluctuations are expected to give rise to a spin liquid state. At the same time nonlinear interactions at higher pumping intensities bring about phase chaos and novel exotic phases.

cond-mat.mes-hall↗

arXiv2017

A Polariton Graph Simulator

We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to the threshold or to study large-scale synchronisation phenomena and dynamical phase transitions when operating above the threshold. We consider the modelling of polariton graphs using the complex Ginzburg-Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.

cond-mat.other↗

arXiv2017

Simulating the spectral gap with polariton graphs

We recently proposed polariton graphs as a novel platform for solving hard optimization problems that can be mapped into the $XY$ model. Here, we elucidate a relationship between the energy spectrum of the $XY$ Hamiltonian and the total number of condensed polariton particles. Using as a test-bed the hexagonal unit lattice we show that the lower energy states of the $XY$ Hamiltonian are faithfully reproduced by mean-field numerical simulations utilising the Ginzburg--Landau equation coupled to an exciton reservoir. Our study paves the way to simulating the spectral gap of the XY model using polariton graphs.

cond-mat.other↗

arXiv2016

Realizing the $XY$ Hamiltonian in polariton simulators

Several platforms are currently being explored for simulating physical systems whose complexity increases faster than polynomially with the number of particles or degrees of freedom in the system. Defects and vacancies in semiconductors or dielectric materials, magnetic impurities embedded in solid helium \cite{lemeshko13}, atoms in optical lattices, photons, trapped ions and superconducting q-bits are among the candidates for predicting the behaviour of spin glasses, spin-liquids, and classical magnetism among other phenomena with practical technological applications. Here we investigate the potential of polariton graphs as an efficient simulator for finding the global minimum of the $XY$ Hamiltonian. By imprinting polariton condensate lattices of bespoke geometries we show that we can simulate a large variety of systems undergoing the U(1) symmetry breaking transitions. We realise various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on unit cells of various lattices: square, triangular, linear and a disordered graph. Our results provide a route to study unconventional superfluids, spin-liquids, Berezinskii-Kosterlitz-Thouless phase transition, classical magnetism among the many systems that are described by the $XY$ Hamiltonian.

cond-mat.mes-hall↗

arXiv2014

Transitions and excitations in a superfluid stream passing small impurities

We analyse asymptotically and numerically the motion around a single impurity and a network of impurities inserted in a two-dimensional superfluid. The criticality for the break down of superfluidity is shown to occur when it becomes energetically favourable to create a doublet - the limiting case between a vortex pair and a rarefaction pulse on the surface of the impurity. Depending on the characteristics of the potential representing the impurity different excitation scenarios are shown to exist for a single impurity as well as for a lattice of impurities. Depending on the lattice characteristics it is shown that several regimes are possible: dissipationless flow, excitations emitted by the lattice boundary, excitations created in the bulk and the formation of large scale structures.

cond-mat.supr-con↗

arXiv2013

Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains

We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analogue of a classical piston the condensed atoms are pushed through the trap generating vortex rings in a fully three- dimensional condensates or soliton trains in quasi-one dimensional scenarios. The vortex rings form due to transverse instability of the shock wave train enhanced and supported by the energy transfer between waves. We elucidate in which sense the self-interactions within the atom cloud define the properties of generated vortex rings and soliton trains. Based on the quantum piston scheme we study the behavior of two component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component and vice versa. Finally, we show the dynamical emergence of skyrmions within two component systems in the immiscible regime.

cond-mat.quant-gas↗

arXiv2012

Exploiting quantum coherence of polaritons for ultra sensitive detectors

Besides being superfluids, microcavity exciton-polariton condensates are capable of spontaneous pattern formation due to their forced-dissipative dynamics. Their macroscopic and easily detectable response to small perturbations can be exploited to create sensitive devices. We show how controlled pumping in the presence of a peak-dip shaped potential can be used to detect small externally applied velocities which lead to the formation of traveling holes in one dimension and vortex pairs in two dimensions. Combining an annulus geometry with a weak link, the set up that we describe can be used to create a sensitive polariton gyroscope.

cond-mat.quant-gas↗

arXiv2012

Robustness and observability of rotating vortex-lattices in an exciton-polariton condensate

Exciton-polariton condensates display a variety of intriguing pattern-forming behaviors, particularly when confined in potential traps. It has previously been predicted that triangular lattices of vortices of the same sign will form spontaneously as the result of surface instabilities in a harmonic trap. However, natural disorder, deviation of the external potential from circular symmetry, or higher-order terms modifying the dynamical equations may all have detrimental effects and destabilize the circular trajectories of vortices. Here we address these issues, by characterizing the robustness of the vortex lattice against disorder and deformations of the trapping potential. Since most experiments use time integrated measurements it would be hard to observe directly the rotating vortex lattices or distinguish them from vortex-free states. We suggest how these difficulties can be overcome and present an experimentally viable interference-imaging scheme that would allow the detection of rotating vortex lattices.

cond-mat.quant-gas↗

arXiv2012

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.

cond-mat.mes-hall↗

arXiv2011

Controllable half-vortex lattices in an incoherently pumped polariton condensate

We show how the transition between synchronized and desynchronized states of a spinor polariton condensate can be used to drive a transition between stationary vortex lattices and half-vortex lattices. This provides a way to control polariton spin textures by a combination of pump spot profile and applied magnetic fields. To do this, we extend the model of non-equilibrium spinor condensates to include relaxation, and study how this affects the desynchronization transition. We discuss how the pattern formation can be explained by behavior of the homogeneous system.

cond-mat.quant-gas↗