We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatiallytrapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two ellipticallypolarized (up to 95% circularly-polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100-fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.Condensation of exciton-polaritons (polaritons) spontaneously breaks the global phase symmetry [1][2][3][4][5]. Owing to their easy optical interrogation, high-speed (ps) interactions, and macroscopic coherence (over hundreds of microns) [6], polariton condensates are excellent candidates to probe and exploit for sensing [7,8], spinoptronics [9][10][11], new optoelectronic devices [12][13][14], and quantum simulators [15]. The driven-dissipative multicomponent polariton system can undergo additional bifurcations and condense into states which are not eigenstates of the single-particle Hamiltonian, but many-body states with reduced symmetry [16,17]. Thus, we should expect that two-component exciton-polariton condensates can also show spontaneous symmetry breaking bifurcations in their polarization state. Spin studies of microcavity polaritons have been of great interest in recent years [18][19][20][21][22][23][24][25][26][27][28][29]. However, spontaneous symmetry-breaking bifurcation of spin has not been observed before.Here, we demonstrate spontaneous magnetization in an exciton-polariton condensate, as a direct result of bifurcations in the spin degree of freedom. Utilizing an optically trapped geometry, condensates spontaneously emerge in either of two discrete spin-polarized states that are stable for many seconds, > 10 10 longer than their formation time. These states emit highly circularly-polarized coherent light (up to 95%) and have opposite circular polarizations. The condensate stochastically condenses in a left-or right-circularly polarized state, with an occurrence likelihood that can be controlled by the ellipticity * ho278@cam.ac.uk † jjb12@cam.ac.uk of the nonresonant pump. The two spin-polarized states can be initialized and switched from one state to another with weak resonant optical pulses. Our system has potential applications in sensing, optical spin memories and spin switches, and it can be implemented for studying long-range spin interactions in polariton condensate lattices. This article is structured as follows: in Section I we review trapped polariton condensates and the current understanding of polarization in untrapped polariton condensates. In Section ...

Polariton condensates are macroscopic quantum states formed by half-matter half-light quasiparticles, thus connecting the phenomena of atomic Bose-Einstein condensation, superfluidity, and photon lasing. Here we report the spontaneous formation of such condensates in programmable potential landscapes generated by two concentric circles of light. The imposed geometry supports the emergence of annular states that extend up to 100 μm, yet are fully coherent and exhibit a spatial structure that remains stable for minutes at a time. These states exhibit a petal-like intensity distribution arising due to the interaction of two superfluids counterpropagating in the circular waveguide defined by the optical potential. In stark contrast to annular modes in conventional lasing systems, the resulting standing wave patterns exhibit only minimal overlap with the pump laser itself. We theoretically describe the system using a complex Ginzburg-Landau equation, which indicates why the condensate wants to rotate. Experimentally, we demonstrate the ability to precisely control the structure of the petal condensates both by carefully modifying the excitation geometry as well as perturbing the system on ultrafast timescales to reveal unexpected superfluid dynamics.interferometer | rings | BEC | SQUID C ircular loops are a key geometry for superfluid and superconducting devices because rotation around a closed ring is coupled to the phase of a quantum wavefunction; so far, however, they have not been optically accessible, although this would enable a new class of quantum devices, particularly if room temperature condensate operation is achieved.In lasing systems with an imposed circular symmetry, an annulus of lasing spots can sometimes form along the perimeter of the structure (1-6). Such transverse modes are often referred to as "petal states" (1) or "daisy modes" (2) and are interpreted as annular standing waves (3), whispering gallery modes (4), or coherent superpositions of Laguerre-Gauss (LG) modes with zero radial index (5, 6). Their circular symmetry makes them interesting for numerous applications such as free space communication or fiber coupling (7), and their LG-type structure suggests implementations using the orbital angular momentum of light (8), such as optical trapping (9) or quantum information processing (10). Petal states have been reported for various conventional lasing systems, including electrically and optically pumped vertical cavity surface-emitting lasers (VCSELs) (2, 4), as well as microchip (6) and rod lasers (1).A fundamentally different type of lasing system is the polariton laser (11,12). Polaritons are bosonic quasiparticles, resulting from the strong coupling between microcavity photons and semiconductor excitons (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Their small effective mass (bestowed by their photonic component) and strong interactions (arising from their excitonic component) favor Bose-stimulated condensation into a single quantum state, called a polariton condensate (14,15). These full...

We theoretically demonstrate the generation of dark soliton trains in a one-dimensional excitonpolariton condensate within an experimentally trivial scheme. In particular we show that the frequency of the train can be finely tuned fully optically or electrically to provide a stable and efficient output signal modulation. Taking the polarization degree of freedom into account we elucidate the possibility to form on-demand half-soliton trains.PACS numbers: 67.85.Hj, 03.75.Kk Introduction.-The first unambiguous observation of Bose-Einstein condensation in dilute Bose gases at low temperature [1] set off an avalanche of research on this new state of matter. The lowest energy fraction of a degenerated Bose gas occupying low energy modes obeys the property of vanishing viscosity and does not take part in the dissipation of momentum, a phenomenon referred to as superfluidity [2]. This holds true as long as the condensate is only slightly disturbed [3]. As soon as strong dynamical density modulations occur, e.g. when the condensate is abruptly brought out of its equilibrium through an external perturbation, it responds in a unique way by generating robust elementary excitations such as solitons in 1D and vortices in 2D settings [4].More recently the concept of macroscopically populated single particle states [5,6] was transposed to a variety of mesoscopic systems such as cavity photons [7,8] In the proper regime all those systems can be described by complex-valued order parameters -the condensate wave functions -with dynamics governed by nonlinear Schrödinger-type equations (NSE) such as the GrossPitaevskii (GP) [13] and the complex Ginzburg-Landau equation (cGLE) [14]. Here the nonlinearity associated with self-interactions plays an essential role on the possible states with or without excitations, their dynamics and in particular their stability [15]. Similarly in the slowly varying envelope approximation light waves can be approximated by complex-valued wave functions governed by NSE's that are formally comparable to those of BECs and thus show analog dynamical behavior such as stationary and moving optical dark or bright solitons in quasi 1D settings [16,17]. For several decades light waves have been utilized in a wide range of applications such as in nonlinear fibre optic communication [16,[18][19][20] while research on new technologies is thriving in particular on elementary circuit components such as optical diodes [21], transistors [22] or realizations of analog devices involving exciton-polariton condensates [23,24] and conceptually on optical computing schemes [25].Polaritons are half-light half-matter quasi-particles

We present an asymptotic analysis of the effects of rapid rotation on the ground state properties of a superfluid confined in a two-dimensional trap. The trapping potential is assumed to be radial and homogeneous of degree larger than two in addition to a quadratic term. Three critical rotational velocities are identified, marking respectively the first appearance of vortices, the creation of a 'hole' of low density within a vortex lattice, and the emergence of a giant vortex state free of vortices in the bulk. These phenomena have previously been established rigorously for a 'flat' trap with fixed boundary but the 'soft' traps considered in the present paper exhibit some significant differences, in particular the giant vortex regime, that necessitate a new approach. These differences concern both the shape of the bulk profile and the size of vortices relative to the width of the annulus where the bulk of the superfluid resides. Close to the giant vortex transition the profile is of Thomas-Fermi type in 'flat' traps, whereas it is gaussian for soft traps, and the 'last' vortices to survive in the bulk before the giant vortex transition are small relative to the width of the annulus in the former case but of comparable size in the latter.MSC: 35Q55,47J30,76M23. PACS: 03.75.Hh, 47.37.+q.

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range | log ε| ≪ Ω ε −2 | log ε| −1 where Ω is the rotational velocity and the coupling parameter is written as ε −2 with ε ≪ 1. Three critical speeds can be identified. At Ω = Ωc 1 ∼ | log ε| vortices start to appear and for | log ε| ≪ Ω < Ωc 2 ∼ ε −1 the vorticity is uniformly distributed over the disc. For Ω ≥ Ωc 2 the centrifugal forces create a hole around the center with strongly depleted density. For Ω ≪ ε −2 | log ε| −1 vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at Ω = Ωc 3 ∼ ε −2 | log ε| −1 there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.MSC: 35Q55,47J30,76M23. PACS: 03.75.Hh, 47.37.+q.

We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limiting speed determined by the interaction strength. The transition is characterized by the disappearance of the vortices from the annulus where the bulk of the superfluid is concentrated due to centrifugal forces while a macroscopic phase circulation remains. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and reveals significant differences between 'soft' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary: In the latter case the transition takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus whereas in 'soft' traps the vortex lattice persists until the width of the annulus becomes comparable to the vortex cores. Moreover, the density profile in the annulus where the bulk is concentrated is, in the 'soft' case, approximately gaussian with long tails and not of the Thomas-Fermi type like in a trap with a fixed boundary.

We introduce and analyze a novel mean-field model for polariton condensates with velocity dependence of the effective polariton mass due the photon and exciton components. The effective mass depends on the in-plane wave vector k, which at the inflection point of the lower polariton energy branch becomes infinite and above negative. The polariton condensate modes of the new mean-field theory are now sensitive to mass variations and for certain points of the energy dispersion the polariton condensate mode represents fractional quantum mechanics. The impact of the generalized kinetic energy term is elucidated by numerical studies in 1D and 2D showing significant differences for large velocities. Analytical expressions for plane wave solutions as well as a linear waves analysis show the significance of this new model.

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 threedimensional 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.