Creation and Manipulation of Stable Dark Solitons and Vortices in Microcavity Polariton Condensates

Controllable bistability and squeezing of confined polariton dark solitons

The generation of squeezed light in semiconductor materials opens opportunities for building on-chip devices that are operated at the quantum level. Here we study theoretically a squeezed light source of polariton dark solitons confined in a geometric potential well of semiconductor microcavities in the strong coupling regime. We show that polariton dark solitons of odd and even parities can be created by tuning the potential depth. When driving the potential depth linearly, a bistability of solitons with the two different parities can be induced. Strong intensity squeezing is obtained near the turning point of the bistability due to the large nonlinear interaction, which can be controlled by the cavity detuning. The phase diagram of the bistability and squeezing of the dark solitons is obtained through large scale numerical calculations. Our study contributes to the current efforts in realizing topological excitations and squeezed light sources with solid-state devices.

Unidirectional vortex waveguides and multistable vortex pairs in polariton condensates

Vortices carrying quantized topological charges have potential applications in information processing. In this work, we investigate vortex carriers and waveguides in microcavity polariton condensates, nonresonantly excited by a homogeneous pump with intensity grooves. An intensity groove with a ring shape in the pump gives rise to dark-ring states of the condensate with a π-phase jump, akin to dark solitons. The dark-ring states can be destroyed by a stronger density of the surrounding condensate and reduce into vortex-antivortex pairs. Multiple vortex-pair states are found to be stable in the same dark ring of the pump. When the pump ring is broader, higher-order dark states with multiple π-phase jumps can be obtained, and interestingly they can be used to construct vortex waveguides. If a single vortex is imprinted in such waveguides, it can travel in a particular direction, showing one-way transportation. In other words, an imprinted vortex with a certain charge in a specifically designed higher-order dark state is only allowed to propagate unidirectionally.

Classification of dark solitons via topological vector potentials

Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.

Nonreciprocal Transport of Exciton Polaritons in a Non-Hermitian Chain

We consider exciton polaritons in a zigzag chain of coupled elliptical micropillars subjected to incoherent excitation. The driven-dissipative nature of the system along with the naturally present polarization splitting inside the pillars gives rise to nonreciprocal dynamics, which eventually leads to the non-Hermitian skin effect, where all the modes of the system collapse to one edge. As a result, the polaritons propagate only in one direction along the chain, independent of the excitation position, and the propagation in the opposite direction is suppressed. The system shows robustness against disorder and, using the bistable nature of polaritons to encode information, we show one-way information transfer. This paves the way for compact and robust feedback-free one-dimensional polariton transmission channels without the need for external magnetic field, which are compatible with proposals for polaritonic circuits.

Pattern Formation and Exotic Order in Driven-Dissipative Bose-Hubbard Systems

Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a "Bose surface," a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.

Multistable circular currents of polariton condensates trapped in ring potentials

We demonstrate the formation and trapping of different stationary solutions, oscillatory solutions, and rotating solutions of a polariton condensate in a planar semiconductor microcavity with a built-in ring-shaped potential well. Multistable ring-shaped solutions are trapped in shallow potential wells. These solutions have the same ring-shaped density distribution but different topological charges, corresponding to different orbital angular momentum (OAM) of the emitted light. For stronger confinement potentials, besides the fundamental modes, higher excited (dipole) modes can also be trapped. If two modes are excited simultaneously, their beating produces a complex oscillation or rotation dynamics. When the two modes have the same OAM, a double-ring solution forms for which the density oscillates between the inner and the outer ring. When the two modes have different OAM, a rotating solution with fractional OAM is created.

Spontaneous and engineered transformations of topological structures in nonlinear media with gain and loss

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures exhibit many unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen potential carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.

Dynamics of rotating Laguerre-Gaussian soliton arrays

Trajectory control of spatial solitons is an important subject in optical transmission field. Here we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters, which we refer to as initial tangential velocity and displacement, to control the propagation path. The general analytical expression for the evolution of the soliton array is derived and the propagation properties, such as the intensity distribution, the propagation trajectory, the center distance, and the angular velocity are analyzed. It is found that the initial tangential velocity and displacement make the solitons sinusoidally oscillate in the x and y directions, and each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation. A series of numerical examples is exhibited to graphically illustrate these typical propagation properties. Our results may provide a new perspective and stimulate further active investigations of multisoliton interaction and may be applied in optical communication and particle control.

Manipulation of a stable dark soliton train in polariton condensate

With a potential trap to mimic the finite-size effect, we predict the generation of dark soliton train in a nonresonant polariton condensate excited with the spatially homogeneous continuous wave (cw) field by exploiting the quantum interference in spatial domain. The number of solitons in the train is demonstrated to be controllable on demand in the domain of material parameters. We show that, similar to dark solitons in conservative systems, these nonlinear excitations have infinite lifetime and remain spatially localized even for the periodically oscillating and colliding state of dark soliton train, which do not depend on the parameters of the condensate. Especially, a final state of anti-dark soliton is observed for all kinds of dark soliton trains with the increase of pump power.

Bloch oscillations of multidimensional dark soliton wave packets and light bullets

The robust propagation of dark solitonic waves featuring Bloch oscillations (BOs) in media with a Kerr nonlinearity is demonstrated. The models considered have a discrete refractive index gradient in one dimension and are continuous in the orthogonal direction or directions. Such systems can be realized in photonic settings, where temporal dispersion of a normal type is able to support dark solitons. The demonstrated effects may also appear in the dynamics of Bose-Einstein condensates (BECs), where dark solitons appear due to the joint action of diffraction and a self-defocusing nonlinearity. Furthermore, our analysis shows that a periodic variation of the refractive index gradient in the propagation direction allows us to realize the spatial analog of dynamical localization. In addition, we demonstrate that dark solitons serve as excellent supporters for light bullets of a peculiar dark-bright type that can also feature robust BOs.

Vortex Multistability and Bessel Vortices in Polariton Condensates

Vortices are topological objects formed in coherent nonlinear systems. As such they are studied in a wide number of physical systems and promise applications in information storage, processing, and communication. In semiconductor microcavities, vortices in polariton condensates can be conveniently created, studied, and manipulated using solely optical means. For nonresonant excitation with a ring-shaped pump a stable vortex can be formed, leading to bistability with left- and right-handed vorticity. In the present work we report on a much richer vortex multistability, with optically addressable vortices with topological charges m=±1, ±2, and ±3, all stable for the same system and excitation parameters. This unusual multistable behavior is rooted in the inherent nonlinear feedback between reservoir excitations and condensate in the microcavity. For larger radius of the ring-shaped pump we also find a Bessel vortex with its characteristic spiralling phase in the high density region and pronounced self-stabilization ability. Our theoretical results open up exciting possibilities for optical manipulation of vortex multiplets in a compact semiconductor system.

Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke-type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of vorticity-free, weakly (algebraically) localized two-dimensional dark-lump solitons. We find that, in the presence of dissipation, dark lumps exhibit a lifetime three times larger than that of planar dark solitons. Direct numerical simulations show that dark lumps do exist, and their dissipative dynamics is well captured by our analytical approximation. It is also shown that lumplike and vortexlike structures can spontaneously be formed as a result of the transverse "snaking" instability of dark soliton stripes.

Controllable Gaussian-shaped soliton clusters in strongly nonlocal media

In this paper, we discuss the evolution of the Gaussian-shaped soliton clusters in strongly nonlocal nonlinear media, which is modeled by the nonlinear Schrödinger equation. The influences of three initial incident parameters (the initial transverse velocity, the initial position, the input power) on propagation dynamics of the soliton clusters are all discussed in detail. The results show that the intensity distribution, the trajectory, the center distance, and the angular velocity of the clusters can be controlled by adjusting the initial incident parameters. A series of analytical solutions on the propagation dynamics of the clusters are derived by borrowing ideas from classical physics. The results in this paper may have potential applications in the beam controlling and all-optical interconnection with the interacting characteristics of (2+1)-dimensional soliton clusters.

Dark gap solitons in exciton-polariton condensates in a periodic potential

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.