49 research outputs found
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Simulating Ising and n-state planar Potts models and external fields with nonequilibrium 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 n-state planar 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.The authors acknowledge financial support from the NGP MIT-Skoltech. K.P.K. acknowledges the financial support from Cambridge Trust and EPSRC
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 threshold or to study large scale synchronization 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.This work was carried out in the framework of the joint Russian–Greek project supported by Ministry of Education and Science of The Russian Federation (project RFMEFI61617X0085). The authors acknowledge the support of the Skoltech NGP Program (Skoltech–MIT joint project), and the UK's Engineering and Physical Sciences Research Council (grant EP/M025330/1 on Hybrid Polaritonics)
Inelastic scattering of xenon atoms by quantized vortices in superfluids
We study inelastic interactions of particles with quantized vortices in superfluids by using a semiclassical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon-doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different energies and impact parameters of incident particles are considered. We show that inelastic scattering is closely linked to the generation of Kelvin waves along a quantized vortex during the interaction even if there is no capture. The capture criterion of an impurity is formulated in terms of the binding energy.The financial support from the Skoltech-MIT Next Generation Program is gratefully acknowledged
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Artificial polariton molecules
We show that geometrically coupled polariton condensates fabricated in
semiconductor devices are versatile systems capable of simulating molecules
with given characteristics. In particular, we consider oscillatory and
stationary symmetric and asymmetric states in polariton dimers, trimers, and
tetrads and their luminosity in real and Fourier space. The spectral weights of
oscillatory states are associated with discrete spectral lines. Their number
and separation can be controlled by changing the number and geometry of
condensates, reflected by the coupling strengths. We also show that asymmetric
stationary states combine discrete and continuous degrees of freedom in one
system. The continuous degree of freedom is represented by the phase while the
discrete degree of freedom is given by density asymmetry. Our work paves the
way to engineer controllable artificial molecules with a range of properties
manufactured on demand
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Toward 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
Exotic states of matter with polariton chains
We consider linear periodic chains of exciton-polariton condensates formed by pumping polaritons nonresonantly 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.The authors acknowledge the support of the Skoltech NGP
Program (Skoltech-MIT joint project). K.P.K. acknowledges
the financial support from Cambridge Trust and EPSRC
Nontrivial phase coupling in polariton multiplets
We investigate the phase coupling between spatially separated polariton condensates under nonresonant optical pulsed excitation. In the simple case of two condensates, we observe phase locking either in symmetric or antisymmetric states. We demonstrate that the coupling symmetry depends both on the separation distance and outflow velocity from the condensates. We interpret the observations through stimulated relaxation of polaritons to the phase configuration with the highest occupation. We derive an analytic criterion for the phase locking of a pair-polariton condensate and extend it to polariton multiplets. In the case of three condensates, we predict theoretically and observe experimentally either in-phase locking or the appearance of phase winding with phase differences of �2π/3 between neighbors. The latter state corresponds to a vortex of winding number �1 across the three polariton condensates..P. G. L. and A. V. K. acknowledge EPSRC through Programme Grant
on Hybrid Polaritonics EP/M025330/1 and EP/F026455/1 for co-supporting this work. N. G. B acknowledges financial support by the Ministry of Education and Science of the Russian Federation 1425320 (Project
DOI: RFMEFI58114X0006). Y. G. R. acknowledges financial support by CONACYT (Mexico) under Grant No. 251808
Nonresonant optical control of a spinor polariton condensate
We investigate the spin dynamics of polariton condensates spatially separated from and effectively confined by the pumping exciton reservoir. We obtain a strong correlation between the ellipticity of the non-resonant optical pump and the degree of circular polarisation (DCP) of the condensate at the onset of condensation. With increasing excitation density we observe a reversal of the DCP. The spin dynamics of the trapped condensate are described within the framework of the spinor complex Ginzburg-Landau equations in the Josephson regime, where the dynamics of the system are reduced to a current-driven Josephson junction. We show that the observed spin reversal is due to the interplay between an internal Josephson coupling effect and the detuning of the two projections of the spinor condensate via transition from a synchronised to a desynchronised regime. These results suggest that spinor polariton condensates can be controlled by tuning the non-resonant excitation density offering applications in electrically pumped polariton spin switches.P.G.L acknowledges support by the Engineering and Physical Sciences Research Council of UK through the Hybrid Polaritonics Programme Grant (EP/M025330/1). P.G.S. acknowledges funding from the EU Social Fund and Greek National Resources (EPEAEK II, HRAKLEITOS II), N.G.B acknowledges the financial support by Ministry of Education and Science of Russian Federation 1425320 (Project DOI: RFMEFI58114X0006). The authors acknowledge fruitful discussions with Prof. Alexey Kavokin and Dr Hamid Ohadi. The data from this paper can be obtained from the University of Southampton e-Print research repository.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by APS
Theory of Multidimensional Solitons
We review a number of topics germane to higher-dimensional solitons in
Bose-Einstein condensates. For dark solitons, we discuss dark band and planar
solitons; ring dark solitons and spherical shell solitons; solitary waves in
restricted geometries; vortex rings and rarefaction pulses; and multi-component
Bose-Einstein condensates. For bright solitons, we discuss instability,
stability, and metastability; bright soliton engineering, including pulsed atom
lasers; solitons in a thermal bath; soliton-soliton interactions; and bright
ring solitons and quantum vortices. A thorough reference list is included.Comment: review paper, to appear as Chapter 5a in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag
Beyond Gross-Pitaevskii Mean Field Theory
A large number of effects related to the phenomenon of Bose-Einstein
Condensation (BEC) can be understood in terms of lowest order mean field
theory, whereby the entire system is assumed to be condensed, with thermal and
quantum fluctuations completely ignored. Such a treatment leads to the
Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although
this theory works remarkably well for a broad range of experimental parameters,
a more complete treatment is required for understanding various experiments,
including experiments with solitons and vortices. Such treatments should
include the dynamical coupling of the condensate to the thermal cloud, the
effect of dimensionality, the role of quantum fluctuations, and should also
describe the critical regime, including the process of condensate formation.
The aim of this Chapter is to give a brief but insightful overview of various
recent theories, which extend beyond the GPE. To keep the discussion brief,
only the main notions and conclusions will be presented. This Chapter
generalizes the presentation of Chapter 1, by explicitly maintaining
fluctuations around the condensate order parameter. While the theoretical
arguments outlined here are generic, the emphasis is on approaches suitable for
describing single weakly-interacting atomic Bose gases in harmonic traps.
Interesting effects arising when condensates are trapped in double-well
potentials and optical lattices, as well as the cases of spinor condensates,
and atomic-molecular coupling, along with the modified or alternative theories
needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by
P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer
Verlag