Geometrically locked vortex lattices in semiconductor quantum fluids

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional nonlinear Schrödinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates. DOI: 10.1103/PhysRevB.93.020502 Introduction. The quantum Hall effect is one of the most celebrated results of modern condensed matter physics [1]. The robustness of the Hall conductance can be traced back to the nontrivial topology of the underlying electronic band structure [2], which ensures the existence of chiral edge states and thus eliminates backscattering. Recently there was a surge of interest in the possibility to exploit such topology to create chiral bosonic modes in driven-dissipative systemswith possible applications to one-way transport of photons [3][4][5][6][7][8][9][10][11][12][13], polaritons [14][15][16], excitons [16,17], magnons [18,19], and phonons [20,21]. A common thread through these seemingly diverse ideas has been to induce topology by external manipulations of a single-particle band structure, with interactions playing a negligible role. Exceptions from this noninteracting paradigm are proposals that combine strong interactions with externally induced artificial gauge fields to create nonequilibrium analogs of bosonic fractional quantum Hall states [22][23][24][25].Here, we take a new perspective and consider (bosonic) Bogoliubov excitations ("Bogoliubons") where weak interactions induce a nontrivial topology [26]. We demonstrate that topological Bogoliubons naturally occur on top of a condensate that exhibits a lattice of vortex-antivortex pairs, with no net flux required. Interactions are key to harness the time-reversal (TR) symmetry breaking induced by the condensate vortices. From the viewpoint of Bogoliubov excitations, they generate nontrivial "hopping" phases which lead to an analog of the Haldane lattice model [27]. The corresponding lattice can be defined by a periodic potential introduced either externally or via interactions with the condensate.Although our scheme can be applied to any system described by a two-dimensional (2D) nonlinear Schrödinger equation (Gross-Pitaevskii equation or analog thereof), our analysis focuses on systems of weakly interacting bosons that have a light component, where the required vortex lattice can readily be obtained from the interference of several coherent optical fields (see Fig. 1). In this setting, the phase-imprinting mechanism allowing for nontrivial topology is analogous to that proposed a few years ago in the context of optomech...

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“…[33]). The required pumping field is readily obtainable with a spatial light modulator [34] or by passing light through a mask [35].…”

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Chiral Bogoliubov excitations in nonlinear bosonic systems

et al. 2016

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“…In view of our observations, care should be taken when describing oscillations in small potential wells, when the total population is not conserved but constantly fed from an exciton reservoir. In this case, relaxation and decay cannot be disregarded, being intrinsic to the condensation process.The experiments have been carried in an Al 0.15 Ga 0.85 As/AlAs microcavity with four sets of 3 GaAs quantum wells (QWs) placed at the antinodes of the electric field [21]. A pulsed laser of 100 fs excites non-resonantly the polariton population of the lower branch (LPB).…”

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Relaxation Oscillations in the Formation of a Polariton Condensate

et al. 2014

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We report observation of oscillations in the dynamics of a microcavity polariton condensate formed under pulsed non resonant excitation. While oscillations in a condensate have always been attributed to Josephson mechanisms due to a chemical potential unbalance, here we show that under some localisation conditions of the condensate, they may arise from relaxation oscillations, a pervasive classical dynamics that repeatedly provokes the sudden decay of a reservoir, shutting off relaxation as the reservoir is replenished. Using non-resonant excitation, it is thus possible to obtain condensate injection pulses with a record frequency of 0.1 THz. Light-matter particles-that arise from the strong interaction between the photonic field in a semiconductor microcavity and the exciton dipole in quantum wells (QWs)-have recently shown a variety of interesting phenomena related to non-equilibrium condensation. These particles, polaritons, have striking similarities with BoseEinstein condensates (BECs) of atomic gases, and, in other aspects, with photon lasers. Nonetheless, polaritons have demonstrated peculiarities of their own that set them apart from both quantum condensates and lasers. Recently many observation in fluid dynamics have shown such peculiar behaviors, related to the polaritonic dispersion on the one hand and its dissipative character on the other hand. Fundamental phenomena like condensation [1, 2], superfluidity [3][4][5], quantised vorticity [6,7], quantum turbulence [8,9] and phase transitions [10] have shown to deviate from conventional BEC, stimulating new models for the quantum dynamics of polariton condensates. These models consider some of the many parameters that are typical of polaritons, including the upper and lower dispersions, pumping, dissipation, spin, non-linearities, etc. One component that is seldom considered in details is the exciton reservoir. This, however, often plays an important role, even under resonant excitation [11,12], and in particular when it comes to polariton relaxation and condensation.We will show here how a polariton condensate formed by non-resonant excitation, in a confined region of space of a few micron squared, can exhibit marked oscillations of its population. While many oscillatory behaviours have been observed [13,14] or predicted [15] in the polariton literature, relating them to coherent and/or quantum phenomena, we report semi-classical oscillations due to the interplay between reservoir feeding and Bose stimulation. These oscillations fall in the class of so-called "relaxation oscillations" [16], that are well known in class B lasers [17], typically solid-state ones with a small active volume and slow-inversion decay [18], where they lead to the phenomenon of spiking [19]. The effect is an important class of self-oscillations [20]. In this form, it is analogous to the Tantalus cup oscillations, used by the Romans to measure time, or in natural phenomena such as rhythmic springs. The underlying principle is the following: passed a threshold, a siphon triggers...

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“…Recently stable solitons bifurcating from gain-guided modes were predicted in defocusing cubic media [14]. Similar effects can be encountered in other physical systems, such as nonconservative polariton condensates, whose evolution is governed by a similar mathematical model [15]. Up to now, only soliton formation in static gain profiles has been studied.…”

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Rotation-managed dissipative solitons

Kartashov

Torner

2013

Opt. Lett.

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We show that when spatially localized gain landscape performs accelerated motion in the transverse plane, i.e., when it rotates or oscillates around the light propagation axis, the effective gain experienced by the light beam considerably reduces with increase of the amplitude of oscillations or frequency of rotation of the localized gain. In the presence of uniform background losses and defocusing nonlinearity, such gain landscapes may support dynamically oscillating gain-managed solitons, but if the amplitude of oscillations or the frequency of rotation of the localized gain exceeds a threshold, stable attractors disappear and any input beam decays.Comment: 4 pages, 5 figures, to appear in Optics Letter

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Geometrically locked vortex lattices in semiconductor quantum fluids

Cited by 137 publications

References 31 publications

Chiral Bogoliubov excitations in nonlinear bosonic systems

Chiral Bogoliubov excitations in nonlinear bosonic systems

Relaxation Oscillations in the Formation of a Polariton Condensate

Rotation-managed dissipative solitons

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