Quantized vortices appear in quantum gases at the breakdown of superfluidity. In liquid helium and cold atomic gases, they have been indentified as the quantum counterpart of turbulence in classical fluids. In the solid state, composite light-matter bosons known as exciton polaritons have enabled studies of non-equilibrium quantum gases and superfluidity. However, there has been no experimental evidence of hydrodynamic nucleation of polariton vortices so far. Here we report the experimental study of a polariton fluid flowing past an obstacle and the observation of nucleation of quantized vortex pairs in the wake of the obstacle. We image the nucleation mechanism and track the motion of the vortices along the flow. The nucleation conditions are established in terms of local fluid density and velocity measured on the obstacle perimeter. The experimental results are successfully reproduced by numerical simulations based on the resolution of the Gross-Pitaevskii equation.H ydrodynamic instabilities in classical fluids were studied in the pioneering experiments of Bénard in the 1910's. Convective Bénard-Rayleigh flows and Bénard-Von Kár-mán streets are now well known examples in nonlinear and chaos sciences 1 . In conventional fluids, the flow around an obstacle is characterized by the dimensionless Reynolds number Re = vR/ν, with v and ν the fluid velocity and dynamical viscosity, respectively, and R the diameter of the obstacle. When increasing the Reynolds number, laminar flow, stationary vortices, Bénard-Von Kármán streets of moving vortices and fully turbulent regimes are successively observed in the wake of the obstacle 1 .In quantum fluids, such as liquid helium or atomic BoseEinstein condensates, quantum turbulence has long been predicted to appear at the breakdown of superfluidity 2-8 . In superfluid systems, the Reynolds number cannot be defined owing to the absence of viscosity. However, quantum turbulence, in the form of quantized vortices, appears simultaneously with dissipation and drag on the obstacle once a critical velocity is exceeded. This critical velocity is predicted to be lower than the Landau criterion for superfluidity far from the obstacle, because of a local increase of the fluid velocity in the vicinity of the impenetrable obstacle 2,4,5 .Experimental evidence has been given for the appearance of a drag force or heat above some critical velocity in superfluid helium 5 and atomic Bose-Einstein condensates 9,10 . In stirred atomic gases, vortex lattices appear above a critical stirring frequency 11-13 , analogously to the rotating bucket experiments originally performed with superfluid helium 14 . Irregular vortex tangle patterns were also observed under an external oscillating perturbation, indicating the presence of turbulence in the atomic cloud 15 . Finally, vortex nucleation has been reported in the wake of a blue-detuned laser moving above a critical velocity through the condensate 16,17 . However, no experiment has yet allowed the imaging of the hydrodynamic nucleation mechanism with ...

Multidimensional Coherent Optical Photocurrent Spectroscopy (MD-COPS) is implemented using unstabilized interferometers. Photocurrent from a semiconductor sample is generated using a sequence of four excitation pulses in a collinear geometry. Each pulse is frequency shifted by a unique radio frequency through acousto-optical modulation; the Four-Wave Mixing (FWM) signal is then selected in the frequency domain. The interference of an auxiliary continuous wave laser, which is sent through the same interferometers as the excitation pulses, is used to synthesize reference frequencies for lock-in detection of the photocurrent FWM signal. This scheme enables the partial compensation of mechanical fluctuations in the setup, achieving sufficient phase stability without the need for active stabilization. The method intrinsically provides both the real and imaginary parts of the FWM signal as a function of inter-pulse delays. This signal is subsequently Fourier transformed to create a multi-dimensional spectrum. Measurements made on the excitonic resonance in a double InGaAs quantum well embedded in a p-i-n diode demonstrate the technique.

Exciton polaritons have been shown to be an optimal system in order to investigate the properties of bosonic quantum fluids. We report here on the observation of dark solitons in the wake of engineered circular obstacles and their decay into streets of quantized vortices. Our experiments provide a timeresolved access to the polariton phase and density, which allows for a quantitative study of instabilities of freely evolving polaritons. The decay of solitons is quantified and identified as an effect of disorderinduced transverse perturbations in the dissipative polariton gas. DOI: 10.1103/PhysRevLett.107.245301 PACS numbers: 67.10.Jn, 03.75.Lm, 71.36.+c, 78.67.Àn Perturbations of quantum fluids can lead to the creation of solitary waves called solitons resulting from the compensation between dispersion and particle interaction. In the particular case of repulsive interaction, dark solitons are created. These density depressions move in the fluid while keeping a constant shape and they are characterized by a phase jump across the density minimum. Since the first theoretical prediction [1], dark solitons have been studied and then observed in a variety of systems such as nonlinear lattices [2], thin magnetic films [3], and complex plasma [4]. They have attracted considerable interest especially in the field of nonlinear optics [5], because of their consequent use in communication devices (i.e., optical fibers [6]), and in atomic Bose-Einstein condensation (BEC) [7]. As quantized vortices [8][9][10], dark solitons are BEC excitations, which arise spontaneously upon the phase transition. As such, they are clear evidences for the onset of a quantum behavior and powerful tools to understand BEC instabilities. Controlling these instabilities is of crucial importance for the development of optoelectronic devices based on quantum fluids in which stable regimes and structures are required. Dark solitons are considered as the dispersive and nonlinear analog of shock waves of supersonic motion [11]. The creation of solitons by phase imprinting in BEC has been reported [12,13], triggering a growing interest in their hydrodynamic formation and stability of solitons.In this Letter we report on the observation of hydrodynamic oblique dark solitons in a 2D polariton fluid and the formation of quantized vortex streets. Polaritons are bosonic quasiparticles arising from the strong coupling between quantum well excitons and photons in semiconductor microcavities. Because of their small effective mass and their strong nonlinearity, they have turned out to be an optimal system in order to investigate the properties of a bosonic quantum fluid. Polaritons can undergo BEC [14] and, by virtue of their nonequilibrium nature, they are accompanied with the spontaneous appearance of quantized vortices [15]. With the demonstration of polariton superfluidity [16,17] much effort has been performed to better understand the nature of different turbulences arising from the breakdown of this fascinating state of matter. Recently, the hydrodynam...

Polariton fluids have revealed huge potentialities in order to investigate the properties of bosonic fluids at the quantum scale. Among those properties, the opportunity to create dark as well as bright solitons has been demonstrated recently. In the present experiments, we image the formation dynamics of oblique dark solitons. They nucleate in the wake of an engineered attractive potential that perturbs the polariton quantum fluid. Thanks to time and phase measurements, we assess quantitatively the formation process. The formation velocity is observed to increase with increasing distance between the flow injection point and the obstacle which modulates the density distribution of the polariton fluid. We propose an explanation in terms of the increased resistance to the flow and of the conditions for the convective instability of dark solitons. By using an iterative solution of the generalized Gross-Pitaevskii equation, we are able to reproduce qualitatively our experimental results. In the recent past much effort has been devoted to characterizing the properties of quantum fluids, with particular attention given to phase transitions such as the Bose-Einstein condensate (BEC) and superfluidity. As in everyday fluids, waves and turbulence are also expected at the quantum scale. Quantized vortices 1,2 and spin texture, 3 for example, have been topics of major discussion. Presently, there is growing interest around solitons, especially in condensed matter systems. 4,5 Solitons are solitary waves which propagate in the medium while maintaining their shape. The stability of their shape is the result of the exact compensation of the dispersion by the interparticle interactions. For attractive interactions, bright solitons (BSs) are formed.5 For the opposite case of repulsion, dark solitons (DSs) may appear, having the shape of density depressions in the fluid.Originally predicted in the 1970s, 6 DSs have been experimentally observed only 20 years later in the field of nonlinear optics 7 and then in cold atom BECs by phase and density imprinting. 8,9 DSs are indeed characterized by both a density minimum and an associated phase shift. 10 However, imprinting is not the only possible way to create a DS. More recently, the growing attention to quantum hydrodynamics has triggered a clear interest towards the nucleation of DSs in the wake of an obstacle. Similar to a boat sailing across calm waters, an obstacle flowing in a quantum fluid can leave turbulence in its wake 1 and generate waves. Under particular conditions, solitons can form in the condensate.2 Such conditions are basically set out by the density and the velocity of the fluid, together with the nature of the obstacle. Recently, condensed matter systems, and in particular exciton-polaritons, have turned out to be a very accessible means to study quantum hydrodynamics. Polaritons are half-matter half-light particles arising from the strong coupling between excitons and cavity photons in a semiconductor microcavity. They have evidenced BEC 11 as well as superfluid...

We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the double well coherent optical response. Coherent and incoherent contributions to the coupling between the two quantum well excitons are clearly separated. An excellent agreement with density matrix calculations reveals that coherent inter-well coupling originates from many-body interactions.Coupled quantum wells (QWs) are one of the most fundamental topics of quantum mechanics. They can be realized in epitaxially-grown semiconductor materials, where the coupling can be exploited in optoelectronic devices such as quantum cascade lasers [1]. Furthermore, since QW and barrier sizes can be tailored, coupled semiconductor QWs can serve as a model for other systems. For example, the absence of vibrational coupling in semiconductor QWs allows isolation of electronic coupling; this distinctive feature may help understanding extremely efficient energy transfer in light harvesting complexes, where the roles played by electronic and vibrational coupling are under debate [2][3][4][5]. Semiconductor double QWs (DQWs) have attracted theoretical and experimental attention for more than twenty years. The roles of resonant transfer and wavefunction hybridization [6][7][8], phonon-assisted tunneling [9,10], dipole-dipole coupling [11], percolation of carriers through imperfect barriers [12], and thermally activated charge transfer [13] have been studied and discussed, as well as the formation of indirect excitons [14,15]. However, the role played by many-body effects-which have been shown to dominate the coherent response of semiconductor excitons [16,17]-in the coupling mechanism has been neglected so far.We use optical two-dimensional coherent spectroscopy (2DCS) to characterize coupling between the QW excitons, which are electron-hole pairs bound together by their Coulomb attraction. 2DCS is an extension of transient four-wave-mixing (FWM) spectroscopy, with the addition of interferometric stabilization of inter-pulse delays and measurement of the signal field. It is an ideal technique to study coupling between resonances, since unfolding one-dimensional spectra onto a second dimension distinguishes quantum beats from polarization interferences [18]. Additionally, 2DCS has been demonstrated as a powerful tool for revealing many-body effects in semiconductor nanostructures [16,17]. Several types of 2D spectra-isolating zero-, one-, and two-quantum coherences-have been shown in previous work to reveal information that one-dimensional techniques cannot access [19][20][21][22][23][24][25][26], but these different types of spectra have never been recorded and analyzed together for a single system so far. Previously, multidimensional spectroscopy showed electronic coherences between excitonic transitions of a GaAs/AlGaAs DQW [27][28][29]. However, the presence of heavy and light holes in each GaAs/Al...