Turning light into a liquid via atomic coherence

Self-trapping of vortex crystals via competing nonlinearities

We investigate the existence of self-trapped nonlinear waves with multiple phase singularities. Working with the cubic-quintic nonlinear Schrödinger equation, we focus on configurations with an antivortex surrounded by a triangular arrangement of vortices within a hosting soliton. We find stationary patterns that can be interpreted as stable self-trapped vortex crystals, constituting the first example of a configuration of this sort with space-independent potentials. Their stability is linked to their norm, transitioning from unstable to stable as their size increases, with an intermediate region where the structure is marginally unstable, undergoing a remarkable and puzzling self-reconstruction during its evolution.

Stability limits for modes held in alternating trapping-expulsive potentials

We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the backdrop of the critical collapse driven by the cubic self-attraction with strength g. The TEM scheme may be implemented, as spatially or temporally periodic modulations, in optics or BEC, respectively. The consideration is carried out by dint of numerical simulations and variational approximation (VA). In terms of the VA, the dynamics amounts to a nonlinear Ermakov equation, which, in turn, is tantamount to a linear Mathieu equation. Stability boundaries are found as functions of g and parameters of the periodic modulation of the trapping potential. Below the usual collapse threshold, which is known, in the numerical form, as g<g_{c}^{(num)}≈5.85 (in the standard notation), the stability is limited by the onset of the parametric resonance. This stability limit, including the setup with the self-repulsive sign of the cubic term (g<0), is accurately predicted by the VA. At g>g_{c}^{(num)}, the collapse threshold is found with the help of full numerical simulations. The relative increase of g_{c} above g_{c}^{(num)} is ≈1.5%. It is a meaningful result, even if its size is small, because the collapse threshold is a universal constant which is difficult to change.

Talbot effect of an electromagnetically induced square photonic lattice assisted by a spatial light modulator

We demonstrate the Talbot effect of an electromagnetically induced square photonic lattice formed under the electromagnetically induced transparency (EIT) condition both experimentally and theoretically in a three-level ⁸⁵Rb atomic configuration. The two-dimensional lattice patterns result from the diffraction of a Gaussian probe field traveling through the vapor cell, in which the refractive index is modulated by a coupling field with a two-dimensional periodic intensity distribution generated by a spatial light modulator. The experimental observations are consistent with the theoretical predictions. This investigation not only provides a new avenue for producing desired electromagnetically induced photonic lattices beyond the commonly adopted multi-beam interfering method but also broadens studies of electromagnetically induced Talbot effect to two-dimensional space.

Transport of light in a moving photonic lattice via atomic coherence

In this Letter, we have investigated experimentally the photonic realization of a moving lattice with an instantaneously tunable transverse velocity in a three-level Λ-type warm ⁸⁵Rb atomic medium. The dynamic photonic lattice moving along the direction of its spatial periodicity was constructed by introducing a frequency difference (determining the velocity) between two coupling beams, whose interference pattern could optically induce a (spatial) periodic refractive index change inside the atomic vapor under electromagnetically induced transparency. When a Gaussian probe field is launched into this optically induced lattice, the output diffraction patterns can shift along the transverse direction, indicating dynamical features of induced photonic structures. The realization of this effectively controllable moving photonic lattice provides a new platform for guiding the transport of light.

Localized gap modes of coherently trapped atoms in an optical lattice

We theoretically investigate one-dimensional localized gap modes in a coherent atomic gas where an optical lattice is formed by a pair of counterpropagating far-detuned Stark laser fields. The atomic ensembles under study emerge as Λ-type three-level configuration accompanying the effect of electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations and the multiple scales method, we derive a nonlinear equation governing the spatial-temporal evolution of the probe-field envelope. We then uncover the formation and properties of optical localized gap modes of two kinds, such as the fundamental gap solitons and dipole gap modes. Furthermore, we confirm the (in)stability regions of both localized gap modes in the respective band-gap spectrum with systematic numerical simulations relying on linear-stability analysis and direct perturbed propagation. The predicted results may enrich the nonlinear horizon to the realm of coherent atomic gases and open up a new door for optical communication and information processing.

Observation of edge solitons in photonic graphene

Edge states emerge in diverse areas of science, offering promising opportunities for the development of future electronic or optoelectronic devices, sound and light propagation control in acoustics and photonics. Previous experiments on edge states in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces more striking features into physics of edge states, leading to the formation of edge solitons, optical isolation, making possible stable lasing in such states, to name a few. Here we report the observation of edge solitons at the zigzag edge of a reconfigurable photonic graphene lattice created via the effect of electromagnetically induced transparency in an atomic vapor cell with controllable nonlinearity. To obtain edge solitons, Raman gain is introduced to compensate strong absorption experienced by the edge state during propagation. Our observations may open the way for future experimental exploration of topological photonics on this nonlinear, reconfigurable platform.

Observation of Photon Droplets and Their Dynamics

We present experimental evidence of photon droplets in an attractive (focusing) nonlocal nonlinear medium. Photon droplets are self-bound, finite-sized states of light that are robust to size and shape perturbations due to a balance of competing attractive and repulsive forces. It has recently been shown theoretically, via a multipole expansion of the nonlocal nonlinearity, that the self-bound state arises due to competition between the s-wave and d-wave nonlinear terms, together with diffraction. The theoretical photon droplet framework encompasses both a solitonlike stationary ground state and the nonsolitonlike dynamics that ensue when the system is displaced from equilibrium, i.e., driven into an excited state. We present numerics and experiments supporting the existence of these photon droplet states and measurements of the dynamical evolution of the photon droplet orbital angular momentum.

Nonlinear polarization instability in cubic-quintic plasmonic nanocomposites

We report a study of the nonlinear birefringence induced in a metal-dielectric nanocomposite due to the contributions of third- and fifth-order optical nonlinearities. A theoretical model describing the evolution of the light polarization state of a confined laser beam propagating through the nonlinear medium is developed with basis on a pair of coupled dissipative cubic-quintic nonlinear differential equations related to the two orthogonal polarizations of the optical field. As a proof-of-principle experiment we demonstrate the control of the light beam polarization in a silver-nanocolloid by changing the silver nanoparticles volume fraction, f, and the light intensity. A large nonlinear phase-shift (~20π) was observed using a 9 cm long capillary filled with silver nanoparticles suspended in carbon disulfide. Experiments using colloids with 1.0×10^-5≤f≤4.5×10^-5 and maximum light intensities of tens of MW/cm² are performed. In addition, we demonstrate that the modulation instability is highly sensitive to the quintic nonlinearity contribution performed showing good agreement with the experimental results.

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light

We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency

We theoretically and numerically investigate the nonparaxial self-accelerating beams in a Λ-type three-level energy system of rubidium atomic vapor in the electromagnetically induced transparency (EIT) window. In the EIT window, the absorption of the atomic vapor is small, and robust nonparaxial self-accelerating beams can be generated. The reason is that the energy of the tail transfers to the main lobe, which then maintains its shape, owing to the self-healing effect. Media with large absorption would demand large energy to compensate, and the tail would be lifted too high to maintain the profile of an accelerating beam, so that self-accelerating beams cannot be obtained any longer. An atomic vapor with small absorption is the ideal medium to produce such self-accelerating beams and, in return, self-accelerating beams may inspire new ideas in the research associated with atomic vapors and atomic-like ensembles.

Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction

We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.

Guiding and confinement of light induced by optical vortex solitons in a cubic-quintic medium

The observation of confinement and guiding of light induced by an optical vortex soliton (OVS) in a cubic-quintic (defocusing-focusing) medium is reported. The waveguide effect induced by the bright region of the vortex beam, is mainly due to the defocusing nonlinearity that allows the guiding of a probe beam propagating inside of the OVS dark region. The experimental results are corroborated by numerical simulations based on the cubic-quintic nonlinear Schrödinger equation, showing excellent agreement.

Solitons of four-wave mixing in competing cubic-quintic nonlinearity

We experimentally investigate the soliton formation and dynamics in the nonlinear propagation of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence in a three-level atomic system, under the competition between focusing and defocusing nonlinearities, as well as between gain and dissipation, due to the third- and fifth-order nonlinear susceptibilities with opposite signs. With multi-parameter controllability and nonlinear competition in the system, fundamental, dipole, and azimuthally-modulated vortex FWM solitons can transform mutually from one to the other. Such investigations have potential applications in optical pattern formation and control, and all-optical communication.

Drag force in bimodal cubic-quintic nonlinear Schrödinger equation

We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.

Coherent cavitation in the liquid of light

We study the cubic- (focusing-)quintic (defocusing) nonlinear Schrödinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortex-antivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.

Spatial domain interactions between ultraweak optical beams

We have observed spatial interactions between two ultraweak optical beams that are initially collinear and nonoverlapping. The weak beams are steered towards each other by a spatially varying cross-Kerr refractive index waveguide written by a strong laser beam in a three-level coherently prepared atomic medium. After fusing together, the combined beam shows controllable phase-dependent behaviors. This is the first observation of solitonlike interactions between weak beams and can be useful for all-optically tunable beam combining, switching, and gating for weak photonic signals.

Optical vortices induced in nonlinear multilevel atomic vapors

In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing effect. We find that the number of beads and topological charge of the incident beam, as well as its size, greatly affect the formation and evolution of vortices. To determine the number of induced vortices and the corresponding rotation direction, we give common rules associated with the initial conditions coming from various incident beams.

Bunching-induced optical nonlinearity and instability in cold atoms [Invited]

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

Pressure, surface tension, and dripping of self-trapped laser beams

We show that a laser beam which propagates through an optical medium with Kerr (focusing) and higher order (defocusing) nonlinearities displays pressure and surface-tension properties yielding capillarity and dripping effects totally analogous to usual liquid droplets. The system is reinterpreted in terms of a thermodynamic grand potential, allowing for the computation of the pressure and surface tension beyond the usual hydrodynamical approach based on Madelung transformation and the analogy with the Euler equation. We then show both analytically and numerically that the stationary soliton states of such a light system satisfy the Young-Laplace equation and that the dynamical evolution through a capillary is described by the same law that governs the growth of droplets in an ordinary liquid system.

Temporal and Spatial Interference between Four-Wave Mixing and Six-Wave Mixing Channels

Using phase control between four-wave mixing (FWM) and six-wave mixing (SWM) channels in a four-level atomic system, we demonstrate temporal and spatial interferences between these two nonlinear optical processes. Efficient and coexisting FWM and SWM signals are produced in the same electromagnetically induced transparency window via atomic coherence. The temporal interference has a femtosecond time scale corresponding to the optical transition frequency. Such studies of intermixing between different order nonlinear optical processes with a controllable phase delay can have important applications in high-precision measurements, coherence quantum control, and quantum information processing.

Spatial interference between four- and six-wave mixing signals

We experimentally demonstrate spatial interference between simultaneously generated four-wave mixing (FWM) and six-wave mixing (SWM) signals in a multilevel atomic system. By tuning the relative phase between the FWM and SWM processes the relative strengths between these two high-order nonlinear optical processes can be investigated.

Eigenvalue cutoff in the cubic-quintic nonlinear Schrödinger equation

Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic (2+1) -dimensional nonlinear Schrödinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and Hölder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrödinger equation behave similarly to those of the cubic nonlinear Schrödinger equation.

Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows

Highly efficient four-wave mixing (FWM) and six-wave mixing (SWM) processes can coexist in a four-level Y-type atomic system due to atomic coherence. The simultaneously opened dual electromagnetically induced transparency windows in this four-level atomic system allow observation of these two nonlinear optical processes at the same time, which enables detailed studies of the interplay between the FWM and SWM processes. Three-photon and five-photon destructive interferences are also observed.

Dissipative solitons that cannot be trapped

We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.

Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system

We study the formation of a nonlinear localized high-dimensional optical beam in a lifetime-broadened three-state atomic system. We show that stable high-dimensional spatial optical solitons with extremely weak-light intensity can occur in such a highly resonant medium through a mechanism of electromagnetically induced transparency. We demonstrate that the interaction between two high-dimensional spatial optical solitons displays interesting properties and these solitons can be easily controlled by manipulating the coupling optical field of the system.