Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration.

Higher-order topological insulators and superconductors are topological phases that exhibit novel boundary states on corners or hinges. Recent experimental advances in controlling dissipation such as gain/loss in atomic and optical systems provide a powerful tool for exploring non-Hermitian topological phases. Here we show that higher-order topological corner states can emerge by introducing staggered on-site gain/loss to a Hermitian system in a trivial phase. For such a non-Hermitian system, we establish a general bulk-corner correspondence by developing a biorthogonal nested-Wilson-loop and edge-polarization theory, which can be applied to a wide class of non-Hermitian systems with higher-order topological orders. The theory gives rise to topological invariants characterizing the non-Hermitian topological multipole moments (i.e., corner states) that are protected by reflection or chiral symmetry. Such gain/loss induced higher-order topological corner states can be experimentally realized using photons in coupled cavities or cold atoms in optical lattices. arXiv:1903.02448v3 [cond-mat.mes-hall]

If neutrinos are Dirac particles the existence of light right-handed neutrinos νR is implied. Those would contribute to the effective number of relativistic neutrino species Neff in the early Universe. With pure standard model interactions, the contribution is negligibly small. In the presence of new interactions, however, the contribution could be significantly enhanced. We consider the most general effective four-fermion interactions for neutrinos (scalar, pseudo-scalar, vector, axial-vector and tensor), and compute the contribution of right-handed neutrinos to Neff. Taking the Planck 2018 measurement of Neff, strong constraints on the effective four-fermion coupling are obtained, corresponding to interaction strengths of 10−5∼10−3 in units of the Fermi constant. This translates in new physics scales of up to 43 TeV and higher. Future experiments such as CMB-S4 can probe or exclude the existence of effective 4-neutrino operators for Dirac neutrinos. Ways to avoid this conclusion are discussed.

Second-order topological superconductors host Majorana corner and hinge modes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions/layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an s-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses between adjacent boundaries, leading to one Majorana mode at each corner. Similar paradigm also applies to 3D topological insulators with the emergence of Majorana hinge states. Avoiding complex superconductor pairing and material structure, our scheme provides an experimentally realistic platform for implementing Majorana corner and hinge states.

Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chiral symmetric lattice with disordered gain and loss. The increasing disorder strength can drive a transition from trivial to topological insulators, characterizing by the change of topological winding number defined by localized states in the gapless and complex bulk spectra. The non-Hermitian critical behaviors are characterized by the biorthogonal localization length of zero energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement C, which converges to the winding number through time-averaging and can be extracted from proper Ramsey-interference sequences. We propose a scheme to implement and probe such non-Hermitian disorder driven topological insulators using photons in coupled micro-cavities.

We propose a scheme to simulate topological physics within a single degenerate cavity, whose modes are mapped to lattice sites. A crucial ingredient of the scheme is to construct a sharp boundary so that open boundary condition can be implemented for this effective lattice system. In doing so, the topological properties of the system can manifest themselves on the edge states, which can be probed from the spectrum of output cavity field. We demonstrate this with two examples: a static Su-Schrieffer-Heeger chain and a periodically driven Floquet topological insulator. Our work opens up new avenues to explore exotic photonic topological phases inside a single optical cavity.

All-optical photonic devices are crucial for many important photonic technologies and applications, ranging from optical communication to quantum information processing. Conventional design of all-optical devices is based on photon propagation and interference in real space, which may rely on large numbers of optical elements, and the requirement of precise control makes this approach challenging. Here we propose an unconventional route for engineering all-optical devices using the photon’s internal degrees of freedom, which form photonic crystals in such synthetic dimensions for photon propagation and interference. We demonstrate this design concept by showing how important optical devices such as quantum memory and optical filters can be realized using synthetic orbital angular momentum (OAM) lattices in degenerate cavities. The design route utilizing synthetic photonic lattices may significantly reduce the requirement for numerous optical elements and their fine tuning in conventional design, paving the way for realistic all-optical photonic devices with novel functionalities.

The recent experimental realization of spin-orbit coupling for ultracold atomic gases provides a powerful platform for exploring many interesting quantum phenomena. In these studies, spin represents spin vector (spin-1/2 or spin-1) and orbit represents linear momentum. Here we propose a scheme to realize a new type of spin-tensor-momentum coupling (STMC) in spin-1 ultracold atomic gases. We study the ground state properties of interacting Bose-Einstein condensates (BECs) with STMC and find interesting new types of stripe superfluid phases and multicritical points for phase transitions. Furthermore, STMC makes it possible to study quantum states with dynamical stripe orders that display density modulation with a long tunable period and high visibility, paving the way for direct experimental observation of a new dynamical supersolid-like state.. Our scheme for generating STMC can be generalized to other systems and may open the door for exploring novel quantum physics and device applications.Introduction.-The coupling between matter and gauge field plays a crucial role for many fundamental quantum phenomena and practical device applications in condensed matter [1][2][3] and atomic physics [4]. A prominent example is the spin-orbit coupling, the coupling between a particle's spin and orbit (e.g., momentum) degrees of freedom, which is responsible for important physics such as topological insulators and superconductors [2,3]. In this context, recent experimental realization of spin-orbit coupling in ultracold atomic gases [5][6][7][8][9][10][11][12][13] opens a completely new avenue for investigating quantum many-body physics under gauge field [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].So far in most works on spin-orbit coupling in solid state and cold atomic systems, the spin degrees of freedom are taken as rank-1 spin vectors F i (i = x, y, z), such as electron spin-1/2 or pseudospins formed by atomic hyperfine states that can be large (e.g., spin-1 or 3/2). Experimentally, spin-orbit coupling for spin-1 Bose-Einstein condensates (BECs) has been realized recently [29,30] and interesting magnetism physics has been observed [31][32][33][34][35]. Mathematically, it is well known that there exist not only spin vectors, but also spin tensors [e.g., irreducible rank-2 spin-quadrupole tensorin a large spin (≥ 1) system. Therefore two natural questions are: i ) Can the coupling between spin tensors of particles and their linear momenta be realized in experiments? ii ) What new physics may emerge from such spin-tensor-momentum coupling (STMC)?In this Letter, we address these two questions by proposing a simple experimental scheme for realizing STMC for spin-1 ultracold atomic gases. Our scheme is based on slight modification of previous experimental setup [29] and is experimentally feasible. The STMC changes the band structure dramatically, leading to interesting new physics in the presence of many-body interactions between atoms. Although both bosons and fermions can be studied, here we only consider spi...