The coupling of two macroscopic quantum states through a tunnel barrier gives rise to Josephson phenomena 1 such as Rabi oscillations 2 , the a.c. and d.c. effects 3 , or macroscopic self-trapping, depending on whether tunnelling or interactions dominate 4 . Nonlinear Josephson physics was first observed in superfluid helium 5 and atomic condensates 6,7 , but it has remained inaccessible in photonic systems because it requires large photon-photon interactions. Here we report on the observation of nonlinear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule formed by two overlapping micropillars etched in a semiconductor microcavity 8 . At low densities we observe coherent oscillations of particles tunnelling between the two sites. At high densities, interactions quench the transfer of particles, inducing the macroscopic self-trapping of polaritons in one of the micropillars 9,10 . The finite lifetime results in a dynamical transition from self-trapping to oscillations with π phase. Our results open the way to the experimental study of highly nonlinear regimes in photonic systems, such as chaos 11-13 or symmetry-breaking bifurcations 14,15 .A bosonic Josephson junction is a device in which two macroscopic ensembles of bosons, each of them occupying a single quantum state, are coupled by a tunnel barrier. The system can be described by the following coupled nonlinear Schrödinger equations 1 :where ψ L,R are the bosonic wavefunctions with particle densities |ψ L,R | 2 localized to the left (L) and to the right (R) of the barrier, E 0 L,R is the single particle energy of the quantum states, U is the particle-particle interaction strength and J is the tunnel coupling constant. In the absence of interactions, equations (1a) and (1b) can be diagonalized in a basis of bonding (). An initial state prepared in a linear combination of these two (for instance, all particles in the left site) will result in density oscillations between the two sites. This is the main principle of the bosonic Josephson effect, which manifests in an ensemble of oscillatory regimes. In the absence of interactions, sinusoidal oscillations take place 4,7 with a frequencȳ Josephson physics shows the most spectacular phenomena in the nonlinear regime, when the interaction energy (U |ψ| 2 ) is greater than the coupling J . The transfer of particles from one site to the other gives rise to a dynamical renormalization of the energy in each site, resulting in anharmonic oscillations. If interactions are strong enough (U |ψ| 2 J ), the self-induced energy renormalization quenches the tunnelling, and most of the particles remain localized in one of the sites. This out of equilibrium metastable regime is called macroscopic quantum self-trapping.A number of bosonic systems have demonstrated Josephson physics. Harmonic oscillations in the linear regime have been observed in superconductor junctions 2 or in nanoscale apertures connecting superfluid helium vessels 5 . Bose-Einstein condensates of ultracold atoms in cou...

Manipulation of nonlinear waves in artificial periodic structures leads to spectacular spatial features, such as generation of gap solitons or onset of the Mott insulator phase transition. Cavity exciton–polaritons are strongly interacting quasiparticles offering large possibilities for potential optical technologies. Here we report their condensation in a one-dimensional microcavity with a periodic modulation. The resulting mini-band structure dramatically influences the condensation process. Contrary to non-modulated cavities, where condensates expand, here, we observe spontaneous condensation in localized gap soliton states. Depending on excitation conditions, we access different dynamical regimes: we demonstrate the formation of gap solitons either moving along the ridge or bound to the potential created by the reservoir of uncondensed excitons. We also find Josephson oscillations of gap solitons triggered between the two sides of the reservoir. This system is foreseen as a building block for polaritonic circuits, where propagation and localization are optically controlled and reconfigurable.

We review the unconventional photon blockade mechanism. This quantum effect remarkably enables a strongly sub-Poissonian light statistics, even from a system characterized by a weak single-photon nonlinearity. We revisit the past results, which can be interpreted in terms of quantum interferences or optimal squeezing, and show how recent developments on input-output field mixing can overcome the limitations of the original schemes towards passive and integrable single-photon sources. We finally present some valuable alternative schemes for which the unconventional blockade can be directly adapted.

Monopoles are magnetic charges, point-like sources of magnetic field. Contrary to electric charges they are absent in Maxwell's equations and have never been observed as fundamental particles. Quantum fluids such as spinor Bose-Einstein condensates have been predicted to show monopoles in the form of excitations combining phase and spin topologies. Thanks to its unique spin structure and the direct optical control of the fluid wavefunction, an ideal system to experimentally explore this phenomenon is a condensate of exciton-polaritons in a semiconductor microcavity. We use this system to create half-solitons, non-linear excitations with mixed spin-phase geometry. By tracking their trajectory, we demonstrate that half-solitons behave as monopoles, magnetic charges accelerated along an effective magnetic field present in the microcavity. The field-induced spatial separation of half-solitons of opposite charges opens the way to the generation of magnetic currents in a quantum fluid.

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Quantum fluids based on light is a highly developing research field, since they provide a nonlinear platform for developing optical functionalities and quantum simulators. An important issue in this context is the ability to coherently control the properties of the fluid. Here we propose an all-optical approach for controlling the phase of a flow of cavity-polaritons, making use of their strong interactions with localized excitons. Here we illustrate the potential of this method by implementing a compact exciton–polariton interferometer, which output intensity and polarization can be optically controlled. This interferometer is cascadable with already reported polariton devices and is promising for future polaritonic quantum optic experiments. Complex phase patterns could be also engineered using this optical method, providing a key tool to build photonic artificial gauge fields.

We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to the conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is observed. We find a minimum second-order correlation g ð2Þ ð0Þ ≈ 0.37, which corresponds to g ð2Þ ð0Þ ≈ 0.005 when corrected for detector jitter, and observe the expected polarization dependency and photon bunching and antibunching; close by in parameter space, which indicates the abrupt change from phase to amplitude squeezing. DOI: 10.1103/PhysRevLett.121.043601 A two-level system strongly coupled to a cavity results in polaritonic dressed states with a photon-number dependent energy. This dressing gives rise to the photon blockade effect [1,2] resulting in photon-number dependent transmission and reflection, enabling the transformation of incident coherent light into specific photon number states such as single photons. Single photon sources are a crucial ingredient for various photonic quantum technologies ranging from quantum key distribution to optical quantum computing. Such sources are characterized by a vanishing second-order autocorrelation g ð2Þ ð0Þ ≈ 0 [3]. In the strong coupling regime, where the coupling between the two-level system and the cavity is larger than the cavity decay rate ðg > κÞ [4], photon blockade has been demonstrated in atomic systems [5], quantum dots in photonic crystal cavities [6], and circuit QED [7,8]. At the onset of the weak coupling regime (g ≈ κ), it has been shown that by detuning the dipole transition frequency with respect to the cavity resonance, photon blockade can still be observed [9]. However, moving further into the weak coupling regime (g < κ), which is much easier to achieve [10,11] (in particular if one aims for a small polarization mode splitting), the conventional photon blockade is no longer possible because the energy gap between the polariton states vanishes. Nevertheless, also in the weak coupling regime, the two-level system enables photon number sensitivity, which has recently enabled high-quality single photon sources using polarization postselection [12][13][14] or optimized cavity in-coupling [15,16].In 2010, Liew and Savona introduced the concept of the unconventional photon blockade (UPB) [17,18]

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