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)

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

Tuning the Energy of a Polariton Condensate via Bias-Controlled Rabi Splitting

We introduce an electrically driven scheme to tune the polariton condensate energy in a high-finesse GaAs microcavity. In contrast to the conventional redshift observed in semiconductor quantum wells (QWs) under applied electrical bias arising from the quantum-confined Stark effect (QCSE), we report here the blueshift of a polariton condensate caused by controlled reduction of the Rabi splitting due to tunneling-induced charge buildup and fractional bleaching of QWs. At larger electrical bias, the QCSE becomes dominant, leading to a redshift in the linear regime, while in the nonlinear regime to the eventual quenching of the condensate emission. This ability to tune the polariton condensate energy brings within reach the realization of voltage-controlled polariton condensate devices and variable-wavelength sources of coherent light

Vortices in polariton OPO superfluids

This chapter reviews the occurrence of quantised vortices in polariton fluids, primarily when polaritons are driven in the optical parametric oscillator (OPO) regime. We first review the OPO physics, together with both its analytical and numerical modelling, the latter being necessary for the description of finite size systems. Pattern formation is typical in systems driven away from equilibrium. Similarly, we find that uniform OPO solutions can be unstable to the spontaneous formation of quantised vortices. However, metastable vortices can only be injected externally into an otherwise stable symmetric state, and their persistence is due to the OPO superfluid properties. We discuss how the currents charactering an OPO play a crucial role in the occurrence and dynamics of both metastable and spontaneous vortices.Comment: 40 pages, 16 figure

Disorder Effects on Exciton-Polariton Condensates

The impact of a random disorder potential on the dynamical properties of Bose Einstein condensates is a very wide research field. In microcavities, these studies are even more crucial than in the condensates of cold atoms, since random disorder is naturally present in the semiconductor structures. In this chapter, we consider a stable condensate, defined by a chemical potential, propagating in a random disorder potential, like a liquid flowing through a capillary. We analyze the interplay between the kinetic energy, the localization energy, and the interaction between particles in 1D and 2D polariton condensates. The finite life time of polaritons is taken into account as well. In the first part, we remind the results of [G. Malpuech et al. Phys. Rev. Lett. 98, 206402 (2007).] where we considered the case of a static condensate. In that case, the condensate forms either a glassy insulating phase at low polariton density (strong localization), or a superfluid phase above the percolation threshold. We also show the calculation of the first order spatial coherence of the condensate versus the condensate density. In the second part, we consider the case of a propagating non-interacting condensate which is always localized because of Anderson localization. The localization length is calculated in the Born approximation. The impact of the finite polariton life time is taken into account as well. In the last section we consider the case of a propagating interacting condensate where the three regimes of strong localization, Anderson localization, and superfluid behavior are accessible. The localization length is calculated versus the system parameters. The localization length is strongly modified with respect to the non-interacting case. It is infinite in the superfluid regime whereas it is strongly reduced if the fluid flows with a supersonic velocity.Comment: chapter for a book "Exciton Polaritons in Microcavities: New Frontiers" by Springer (2012), the original publication is available at http://www.springerlink.co

Observation of bright polariton solitons in a semiconductor microcavity

Microcavity polaritons are composite half-light half-matter quasi-particles, which have recently been demonstrated to exhibit rich physical properties, such as non-equilibrium Bose-Einstein condensation, parametric scattering and superfluidity. At the same time, polaritons have some important advantages over photons for information processing applications, since their excitonic component leads to weaker diffraction and stronger inter-particle interactions, implying, respectively, tighter localization and lower powers for nonlinear functionality. Here we present the first experimental observations of bright polariton solitons in a strongly coupled semiconductor microcavity. The polariton solitons are shown to be non-diffracting high density wavepackets, that are strongly localised in real space with a corresponding broad spectrum in momentum space. Unlike solitons known in other matter-wave systems such as Bose condensed ultracold atomic gases, they are non-equilibrium and rely on a balance between losses and external pumping. Microcavity polariton solitons are excited on picosecond timescales, and thus have significant benefits for ultrafast switching and transfer of information over their light only counterparts, semiconductor cavity lasers (VCSELs), which have only nanosecond response time

Sculpting oscillators with light within a nonlinear quantum fluid

Seeing macroscopic quantum states directly remains an elusive goal. Particles with boson symmetry can condense into such quantum fluids producing rich physical phenomena as well as proven potential for interferometric devices [1-10]. However direct imaging of such quantum states is only fleetingly possible in high-vacuum ultracold atomic condensates, and not in superconductors. Recent condensation of solid state polariton quasiparticles, built from mixing semiconductor excitons with microcavity photons, offers monolithic devices capable of supporting room temperature quantum states [11-14] that exhibit superfluid behaviour [15,16]. Here we use microcavities on a semiconductor chip supporting two-dimensional polariton condensates to directly visualise the formation of a spontaneously oscillating quantum fluid. This system is created on the fly by injecting polaritons at two or more spatially-separated pump spots. Although oscillating at tuneable THz-scale frequencies, a simple optical microscope can be used to directly image their stable archetypal quantum oscillator wavefunctions in real space. The self-repulsion of polaritons provides a solid state quasiparticle that is so nonlinear as to modify its own potential. Interference in time and space reveals the condensate wavepackets arise from non-equilibrium solitons. Control of such polariton condensate wavepackets demonstrates great potential for integrated semiconductor-based condensate devices.Comment: accepted in Nature Physic

Polaritonic Feshbach resonance

A Feshbach resonance occurs when the energy of two interacting free particles comes into resonance with a molecular bound state. When approaching this resonance, marked changes in the interaction strength between the particles can arise. Feshbach resonances provide a powerful tool for controlling the interactions in ultracold atomic gases, which can be switched from repulsive to attractive and have allowed a range of many-body quantum physics effects to be explored. Here we demonstrate a Feshbach resonance based on the polariton spinor interactions in a semiconductor microcavity. By tuning the energy of two polaritons with anti-parallel spins across the biexciton bound state energy, we show an enhancement of attractive interactions and a prompt change to repulsive interactions. A mean-field two-channel model quantitatively reproduces the experimental results. This observation paves the way for a new tool for tuning polariton interactions and to move forward into quantum correlated polariton physics