Dynamics of dark-soliton formation in a polariton quantum fluid

Abstract

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...

Linear Wave Dynamics Explains Observations Attributed to Dark Solitons in a Polariton Quantum Fluid

“…In the microcavity polariton literature, the observation of dark solitons has been claimed using both a Gaussian excitation beam [15,17] and half-Gaussian excitation beam [15,19]. We have used both excitation shapes and find that they do not affect the observed structure significantly.…”

“…As in the atomic BECs, also in the case of polariton condensates equation 3 has been used to identify dark solitons [15][16][17][18]. However, in all the previous works the healing length condition which is related to the width of the soliton has been neglected.…”

“…In the case of a polariton quantum fluid it has been shown that different hydrodynamic regimes are connected to the Mach number (M ), which is the ratio between the local flow velocity v f low and the local speed of sound c s [15][16][17][18]:…”

“…In particular, the nucleation of solitary waves in the wake of an obstacle (i.e. defect) has been claimed recently [15][16][17][18][19]. Here, the source of nonlinearity, essential for the formation of such a solitary wave, has been identified in the repulsive polariton-polariton interactions.…”

“…Moreover, we show that the appearance or disappearance of these features for different in-plane kinetic energies is found also in the linear regime and, thus, does not provide evidence of an interacting quantum fluid. Therefore, the previous reports of the observation of dark solitons [15][16][17][18] and half-dark-solitons [19], which were based on these features, have to be reconsidered. The investigated sample is a bulk λ GaAs microcavity surrounded by 27 (top) and 24 (bottom) distributed GaAs/AlAs Bragg reflector pairs.…”