We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases. DOI: 10.1103/PhysRevLett.114.225301 PACS numbers: 67.85.-d, 03.65.Vf, 03.75.Lm In relativistic quantum field theory there are three types of fermions: Dirac, Majorana, and Weyl fermions [1]. The latter two have never been observed. It was conjectured that neutrinos could be Weyl fermions before the discovery of neutrino oscillations ruled out such a possibility. Nowadays, there is a great excitement on Weyl semimetals: gapless topological states of matter with bulk low-energy electrons behaving as Weyl fermions, and intriguing "Fermi arc" topological surface states [2][3][4]. Besides the fundamental importance of Weyl fermions and related phenomena such as the Adler-Bell-Jackiw chiral anomaly, the topological surface states of Weyl semimetals also hold great potential for applications [3]. These systems followed the development of topological insulators [5,6], emphasizing the role of band topology in describing exotic phases of matter. However, experiments on Weyl fermions are highly elusive.Recent experiments on synthetic magnetic fields in ultracold atomic gases [7][8][9][10][11][12][13][14][15][16][17], alongside advances in photonics [18][19][20][21][22][23][24], have propelled these systems as promising platforms for investigating topological effects and novel states of matter (see for reviews). However, Weyl points have been scarcely addressed in these fields [24,[30][31][32][33]. In photonics, a double gyroid photonic crystal with broken time reversal and/or parity symmetry was predicted to have Weyl points [24]. Theoretical lattice models possessing Weyl points [30,32,33], and Weyl spin-orbit coupling [31], were studied in the context of ultracold atomic gases. Because of the elusive nature of Weyl fermions, a viable and possibly simple scheme for their experimental realization in ultracold atomic gases would be of great importance, exploiting advantages of atomic systems to contribute to Weyl physics research across disciplines.Here, we propose the realization of the Weyl Hamiltonian for ultracold atoms in a straightforward modification of the experimental system that was recently employed to obtain the Harper Hamiltonian [12]. As an example of phenomena inherent to Weyl points, but most suitable for observing in ultracold systems, we discuss the unique spherical-shell expansion ...

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort toward developing application-specific hardware across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the potential of such architectures requires the development of algorithms which optimally exploit their fundamental properties. Here, we present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures allowing fast and efficient sampling from distributions of arbitrary Ising problems. Since the PRIS relies on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of Ising models, by converging in probability to their associated Gibbs distribution. The PRIS also relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS.

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The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort recently toward developing photonic networks which exploit fundamental properties enshrined in the wave nature of light and of its interaction with matter: high-speed, low-power, optical passivity, and parallelization. However, unleashing the true potential of photonic architectures requires the development of featured algorithms which optimally exploit these fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for photonic parallel networks that allows for fast and efficient sampling from distributions of combinatorially hard Ising problems. The PRIS provides sample solutions which converge in probability to the ground state of arbitrary Ising models. By running the PRIS at various noise levels, we probe the critical behavior of universality classes and their critical exponents. In addition to the attractive features of photonic networks, the PRIS relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work paves the way to orders-of-magnitude speedups in heuristic methods via photonic implementations of the PRIS. We also hint at a broader class of (meta)heuristic algorithms derived from the PRIS, such as combined simulated annealing on the noise and eigenvalue dropout levels.

We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one-and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

We theoretically predict a novel type of synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fairly spatially uniform and strong force can be constructed for gases in macroscopic volumes of several cubic millimeters and more. This opens the possibility to mimic classical charged gases in magnetic fields in cold atom experiments.

Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting electrons in two-dimensions (2D), in a uniform magnetic field, where the probes are external solenoids with a magnetic flux that is a fraction of the flux quantum. The Hamiltonian could also be implemented in an ultracold (fermionic) atomic gas in 2D, in a uniform synthetic magnetic field, where the probes are lasers giving rise to synthetic solenoid gauge potentials. We find analytically and numerically the ground state of this system when only the lowest Landau level states are occupied. It is shown that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules of synthetic anyons are discussed for different microscopic realizations of the fusion process.

Synthetic magnetism in cold atomic gases opened the doors to many exciting novel physical systems and phenomena. Ubiquitous are the methods used for the creation of synthetic magnetic fields. They include rapidly rotating Bose-Einstein condensates employing the analogy between the Coriolis and the Lorentz force, and laser-atom interactions employing the analogy between the Berry phase and the Aharonov-Bohm phase. Interestingly, radiation pressure - being one of the most common forces induced by light - has not yet been used for synthetic magnetism. We experimentally demonstrate a synthetic Lorentz force, based on the radiation pressure and the Doppler effect, by observing the centre-of-mass motion of a cold atomic cloud. The force is perpendicular to the velocity of the cold atomic cloud, and zero for the cloud at rest. Our novel concept is straightforward to implement in a large volume, for a broad range of velocities, and can be extended to different geometries.