Realizing spin Hamiltonians in nanoscale active photonic lattices

Molecular Orientation-Dependent Photonic Polarization Engineering in Organic Single-Crystal-Filled Microcavities

Designing the polarization degree of freedom of light is crucial in many fields and has widespread application in, for example, all-optical circuits. In this work, we find that in an organic microcavity filled with anisotropic single crystals the cavity modes can be modulated to be elliptically polarized, i.e., partially circularly polarized and partially linearly polarized. The circular polarization component originates from the Rashba-Dresselhaus spin splitting, while the linear polarization component is due to the dislocation of linearly polarized modes. The dislocation of the linear polarizations is ascribed to the orientation of individual molecules and the molecular packing arrangement; hence, the linear polarizations can be controlled by properly structuring the molecular distributions. Our results pave the way for enriching and engineering the polarization properties of individual optical cavity modes in organic microstructures, which may favor the development of polarized lasers with various polarizations.

Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields

Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.

Improved phase-locking of laser arrays by pump shaping

We introduce a method to enhance the phase-locking quality and duration of an end-pumped laser array by precisely shaping its pump beam to overlap with the array. Shaping the pump beam results in a significant improvement in lasing efficiency and reduces the pump power required to reach the lasing threshold compared to a typical uniform pumping configuration. Our approach involves shaping a highly incoherent laser beam by addressing smaller segments of the beam with higher local spatial coherence. We demonstrate a remarkable increase in the laser array output brightness by up to a factor of 10, accompanied by a substantial extension in the phase-locking duration.

Biasing the quantum vacuum to control macroscopic probability distributions

Quantum field theory suggests that electromagnetic fields naturally fluctuate, and these fluctuations can be harnessed as a source of perfect randomness. Many potential applications of randomness rely on controllable probability distributions. We show that vacuum-level bias fields injected into multistable optical systems enable a controllable source of quantum randomness, and we demonstrated this concept in an optical parametric oscillator (OPO). By injecting bias pulses with less than one photon on average, we controlled the probabilities of the two possible OPO output states. The potential of our approach for sensing sub-photon-level fields was demonstrated by reconstructing the temporal shape of fields below the single-photon level. Our results provide a platform to study quantum dynamics in nonlinear driven-dissipative systems and point toward applications in probabilistic computing and weak field sensing.

Photonic Dirac cavities with spatially varying mass term

In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.

Improved laser phase locking with intra-cavity adaptive optics

Phase locking of coupled lasers is severely hindered by the spread in their natural lasing frequencies. We present an intra-cavity adaptive optics method that reduces the frequency spread and thereby improves phase locking. Using an intra-cavity spatial light modulator and an iterative optimization algorithm, we demonstrate a fourfold enhancement of phase locking 450 coupled lasers, as quantified by the peak intensity and the inverse participation ratio of the far-field output distributions. We further show that the improvement is long-lasting, and suitable for phase locking of weakly coupled lasers.

Modulated Rashba-Dresselhaus Spin-Orbit Coupling for Topology Control and Analog Simulations

We show theoretically that Rashba-Dresselhaus spin-orbit coupling (RDSOC) in lattices acts as a synthetic gauge field. This allows us to control both the phase and the magnitude of tunneling coefficients between sites, which is the key ingredient to implement topological Hamitonians and spin lattices useful for simulation perpectives. We use liquid crystal based microcavities in which RDSOC can be switched on and off as a model platform. We propose a realistic scheme for implementation of a Su-Schrieffer-Heeger chain in which the edge states existence can be tuned, and a Harper-Hofstadter model with a tunable contrasted flux for each (pseudo)spin component. We further show that a transverse-field Ising model and classical XY Hamiltonian with tunable parameters can be implemented, opening up prospects for analog physics, simulations, and optimization.

Droplet tilings for rapid exploration of spatially constrained many-body systems

Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet-lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.

Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine

Statistical spin dynamics plays a key role in understanding the working principle for novel optical Ising machines. Here, we propose the gauge transformation for a spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Using gauge transformation, we experimentally evaluate the phase diagram of a high-dimensional spin-glass equilibrium system with 100 fully connected spins. We observe the presence of paramagnetic, ferromagnetic, and spin-glass phases and determine the critical temperature T_{c} and the critical probability p_{c} of the phase transitions, which agree well with the mean-field theory predictions. Thus, the approximation of the mean-field model is experimentally verified in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions even when the system is associated with optical aberrations and measurement uncertainty.

Accuracy-enhanced coherent Ising machine using the quantum adiabatic theorem

The coherent Ising machine (CIM) implemented by degenerate optical parametric oscillator (DOPO) networks is a novel optical platform to accelerate computation of hard combinatorial optimization problems. Nevertheless, with the increase of the problem size, the probability of the machine being trapped by local minima increases exponentially. According to the quantum adiabatic theorem, a physical system will remain in its instantaneous ground state if the time-dependent Hamiltonian varies slowly enough. Here, we propose a method to help the machine partially avoid getting stuck in local minima by introducing quantum adiabatic evolution to the ground-state-search process of the CIM, which we call A-CIM. Numerical simulation results demonstrate that A-CIM can obtain improved solution accuracy in solving MAXCUT problems of vertices ranging from 10 to 2000 than CIM. The proposed machine that is based on quantum adiabatic theorem is expected to solve optimization problems more correctly.

Non-reciprocal phase transitions

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter^1-6, non-equilibrium systems^7-9, networks of neurons^10,11, social groups with conformist and contrarian members¹², directional interface growth phenomena^13-15 and metamaterials^16-20. Although wave propagation in non-reciprocal media has recently been closely studied^1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points²¹. We describe the emergence of these phases using insights from bifurcation theory^22,23 and non-Hermitian quantum mechanics^24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.