New effects of polarization multistability and polarization hysteresis in a coherently driven polariton condensate in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is of 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.

We report on the two-dimensional gap-soliton nature of exciton-polariton macroscopic coherent phases (PMCP) in a square lattice with a tunable amplitude. The resonantly excited PMCP forms close to the negative mass M point of the lattice band structure with energy within the lattice band gap and its wave function localized within a few lattice periods. The PMCPs are well described as gap solitons resulting from the interplay between repulsive polariton-polariton interactions and effective attractive forces due to the negative mass. The solitonic nature accounts for the reduction of the PMCP coherence length and optical excitation threshold with increasing lattice amplitude. DOI: 10.1103/PhysRevLett.111.146401 PACS numbers: 71.36.+c, 42.65.Yj, 63.20.kk, 73.21.Cd The periodic spatial modulation of a medium creates an artificial band structure with energy gaps and anomalous (i.e., negative) dispersion. In the presence of nonlinearity, spatially self-localized states may appear within the energy gaps as the result of the interplay between the anomalous dispersion and interparticle interactions. This takes place when the kinetic energy contribution [E K ¼ À 2 @ 2 =ð2m b 2 Þ] due to localization of particles with a negative mass Àm b within a radius compensates the repulsive interparticle interaction energy E I . These states, known as gap solitons (GSs), are metastable solutions of the Gross-Pitaevskii equation [1]. GSs have been explored in optical fibers [2], nonlinear photonic crystals [3-6], atomic Bose Einstein condensates (BECs) in optical lattices [7,8], and, very recently, also in the hybrid lightmatter polariton system [9]. Polaritons result from the strong coupling of photons and quantum well (QW) excitons in a semiconductor microcavity (MC). Being bosonic light-matter quasiparticles, they advantageously combine features from both species. Namely, the small mass arising from the photonic component allows them to form polariton macroscopic coherent phases (PMCPs) at low densities and high temperatures, while the interexcitonic interactions provide a nonlinearity several orders of magnitude stronger than in purely photonic systems [10]. While GSs in one-dimensional (1D) potentials have been extensively studied [2,3,5,[7][8][9], GSs in 2D lattices have so far only been reported for purely photonic systems [4,6]. GSs in 2D potentials are qualitatively different from their 1D counterparts, for example, opening the way to the realization of novel topological phases [6,11].In this Letter, we demonstrate the formation and manipulation of GSs of PMCPs in a 2D tunable lattice. The studies were carried out in PMCPs resonantly excited in a tunable square lattice created by surface acoustic waves (SAWs). While PMCPs in a homogeneous MC normally appear at the lowest energy state with zero in-plane momentum, PMCPs in a shallow (i.e., low amplitude) lattice have a GS character and are excited via the accumulation of particles at critical points of negative mass and energy above the ground state [12]. The PMCP forms clo...

The transmission of a pump laser resonant with the lower polariton branch of a semiconductor microcavity is shown to be highly dependent on the degree of circular polarization of the pump. Spin dependent anisotropy of polariton-polariton interactions allows the internal polarization to be controlled by varying the pump power. The formation of spatial patterns, spin rings with high degree of circular polarization, arising as a result of polarization bistability, is observed. A phenomenological model based on spin dependent Gross-Pitaevskii equations provides a good description of the experimental results. Inclusion of interactions with the incoherent exciton reservoir, which provides spin-independent blueshifts of the polariton modes, is found to be essential. Nonlinear interactions in optical systems result in a variety of important phenomena such as frequency conversion, parametric oscillation, bistability, pattern formation and self-organization. In this context hybrid lightmatter particles, polaritons, which form due to strong exciton-photon coupling in semiconductor microcavities (MCs), attract much attention [1]. In this case strong nonlinear interactions due to the excitonic component of polaritons lead to stimulated polariton-polariton scattering and optical parametric oscillation [2,3], bistability [4,5] and superfluidity [6,7]. Bose-Einstein condensation of polariton quasi-particles has also been reported [8]. It is notable that compared to weakly coupled light/matter microcavity systems, polariton nonlinear interactions are several orders of magnitude stronger [1].A further distinguishing feature of polariton systems arises from their spin properties. In particular, polaritons with parallel spins repel, whereas polaritons with opposite spins attract. Such interactions provide blueshifts and redshifts respectively of the energies of coherent polariton modes. This anisotropy in spin properties results in polarization bistability and multistability predicted recently [9]. Polariton polarization bistability has also been predicted to lead to the formation of spatial spin rings of high degree of circular polarization (DCP) [11]. These non-linear spin properties and spatial patterns may lead to novel optical/spin-based devices such as fast optical modulators, spin switches [11,12] and polariton logic elements (polariton neurons) [10], operating at high picosecond speeds and very low pump powers.In the present work we investigate bistability of spin-up and spin-down polariton fields as a function of the intensity and polarization of an external pump beam. As a result of spin dependent polariton-polariton interactions [9] we are able to switch abruptly the internal polariton DCP by 40-50% by tuning the pump power. Despite strong photonic disorder we demonstrate the formation of spatial ring patterns of high DCP, a result of the bistable threshold-like behavior of the DCP for spatially nonuniform excitation [11]. The pump power behavior and the similar bistability thresholds for spin-up and spindown coherent po...

We report on the spin properties of bright polariton solitons supported by an external pump to compensate losses. We observe robust circularly polarized solitons when a circularly polarized pump is applied, a result attributed to phase synchronization between nondegenerate TE and TM polarized polariton modes at high momenta. For the case of a linearly polarized pump, either σ þ or σ − circularly polarized bright solitons can be switched on in a controlled way by a σ þ or σ − writing beam, respectively. This feature arises directly from the widely differing interaction strengths between co-and cross-circularly polarized polaritons. In the case of orthogonally linearly polarized pump and writing beams, the soliton emission on average is found to be unpolarized, suggesting strong spatial evolution of the soliton polarization. The observed results are in agreement with theory, which predicts stable circularly polarized solitons and unstable linearly polarized solitons.

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Basing on the Gross-Pitaevskii equations, it is predicted that a repulsive (defocusing) interaction makes a 2D polariton condensate able to accumulate its energy under above-resonance optical pumping. The energy can be accumulated during a lot of polariton lifetimes, resulting in the state in which the mismatch of the pump frequency is compensated by the blueshift of the polariton resonance. The process begins when the field density reaches the parametric scattering threshold that is inversely proportional to the polariton lifetime. Although the increase in energy may be arbitrarily slow in its beginning, it is followed by a blowup. This scenario applies to the case of the transitions between steady states in multistable cavity-polariton systems. There is a tradeoff between the latency of the transitions and the pump power involving them.Comment: 8 pages, 2 figure

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