Effective Gauge Potential Research Articles

Dirac Theory in Noncommutative Phase Spaces

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a (0,2)-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation.

Programmable photonic system for quantum simulation in arbitrary topologies

Synthetic dimensions have generated great interest for studying many types of topological, quantum, and many-body physics, and they offer a flexible platform for simulation of interesting physical systems, especially in high dimensions. In this paper, we describe a programmable photonic device capable of emulating the dynamics of a broad class of Hamiltonians in lattices with arbitrary topologies and dimensions. We derive a correspondence between the physics of the device and the Hamiltonians of interest, and we simulate the physics of the device to observe a wide variety of physical phenomena, including chiral states in a Hall ladder, effective gauge potentials, and oscillations in high-dimensional lattices. Our proposed device opens new possibilities for studying topological and many-body physics in near-term experimental platforms.

Geometry-induced monopole magnetic field and quantum spin Hall effects

For a relativistic particle confined to a M\"obius strip, the effective Dirac equation is first given in the thin-layer quantization formalism. We find that an effective gauge potential results from the rotation transformation of the adapted frame moving on the M\"obius strip, and that an effective mass results from the rescaling transformation determined by the metric tensor of the M\"obius strip. It is intriguing that the geometry-induced gauge potential can provide an effective monopole magnetic field for the particle with spin, and can induce quantum spin Hall effects. As potential applications, an effective monopole magnetic field and spin Hall effects can be generated and manipulated by designing the geometry of a two-dimensional nanodevice.

Technologically feasible quasi-edge states and topological Bloch oscillation in the synthetic space.

The dimensionality of a physical system is one of the major parameters defining its physical properties. The recently introduced concept of synthetic dimension has made it possible to arbitrarily manipulate the system of interest and harness light propagation in different ways. It also facilitates the transformative architecture of system-on-a-chip devices enabling far reaching applications such as optical isolation. In this report, a novel architecture based on dynamically-modulated waveguide arrays with the Su-Schrieffer-Heeger configuration in the spatial dimension is proposed and investigated with an eye on a practical implementation. The propagation of light through the one-dimensional waveguide arrays mimics time evolution of the field in a synthetic two-dimensional lattice. The addition of the effective gauge potential leads to an exotic topologically protected one-way transmission along adjacent boundary. A cosine-shape isolated band, which supports the topological Bloch oscillation in the frequency dimension under the effective constant force, appears and is localized at the spatial boundary being robust against small perturbations. This work paves the way to improved light transmission capabilities under topological protections in both spatial and spectral regimes and provides a novel platform based on a technologically feasible lithium niobate platform for optical computing and communication.

Optical excitations of Skyrmions, knotted solitons, and defects in atoms

Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band structures. Three-dimensional topological objects of localised particle-like nature attract broad interest across discipline boundaries from elementary particle physics and cosmology to condensed matter physics. Here we propose how simple structured light beams can be transformed into optical excitations of atoms with considerably more complex topologies representing three-dimensional particle-like Skyrmions. This construction can also be described in terms of linked Hopf maps, analogous to knotted solitons of the Skyrme-Faddeev model. We identify the transverse polarisation density current as the effective magnetic gauge potential for the Chern-Simons helicity term. While we prepare simpler two-dimensional baby-Skyrmions and singular defects using the traditional Stokes vectors on the Poincaré sphere for light, particle-like topologies can only be achieved in the full optical hypersphere description that no longer discards the variation of the total electromagnetic phase of vibration.

Reduction of the twisted bilayer graphene chiral Hamiltonian into a 2×2 matrix operator and physical origin of flat bands at magic angles

The chiral Hamiltonian for twisted graphene bilayers is written as a $2\times2$ matrix operator by a renormalization of the Hamiltonian that takes into account the particle-hole symmetry. This results in an effective Hamiltonian with an average field plus and effective non-Abelian gauge potential. The action of the proposed renormalization maps the zero-mode region into the ground state. Modes near zero energy have an antibonding nature in a triangular lattice. This leads to a phase-frustration effect associated with massive degeneration, and makes flat-bands modes similar to confined modes observed in other bipartite lattices. Suprisingly, the proposed Hamiltonian renormalization suggests that flat-bands at magic angles are akin to floppy-mode bands in flexible crystals or glasses, making an unexpected connection between rigidity topological theory and magic angle twisted two-dimensional heterostructures physics.

Topological behavior of a neutral spin-1/2 particle in a background magnetic field

We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double-slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a non-Abelian Aharonov-Bohm effect due to the emergence of an effective Wu-Yang (WY)flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilzcek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy can be lifted by higher order gauge corrections that alter the semi-classical, non-Abelian, WZ phase. Models that allow analytic description offer a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this study concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that posses electric charge. In that case, we explore interference between fundamental gauge fields (i.e. electromagnetism) with effective gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.

Broadband frequency control of light using synthetic frequency lattices formed by four-wave-mixing Bragg scatterings

Recent exploration in synthetic frequency lattices has re-formed the methods of manipulating the light spectrum by analogizing the diffraction management in real space, which can be created by employing electro-optic modulation (EOM) in dielectric waveguides or ring resonators. In the presence of effective gauge potential, that is, the accumulated phase of mode transfer between adjacent lattice sites, the frequency spectrum of incident light can be flexibly tailored. However, the finite bandwidth and modulation depth of EOM vastly restrain the frequency shift and efficiency of mode transfer. Here we experimentally demonstrate that the synthetic frequency lattice can be created with the nonlinear process of four-wave-mixing Bragg scattering. The bandwidth of frequency manipulation is expanded up to terahertz and the frequency shift can be larger than 200 GHz. Furthermore, we can realize effects such as negative refraction and perfect imaging in frequency dimension by changing the effective gauge potentials. The study provides a powerful and promising approach to precisely control light frequency in broadband and may benefit all-optical modulation in optical telecommunication systems.

Optically contorting into new dimensions

Topological Optics Creating synthetic dimensions has generated interest in many branches of science, ranging from ultracold atomic physics to photonics. The ability to do so provides a versatile platform for realizing effective gauge potentials and novel topological physics that might be difficult or impossible to realize in real systems. Dutt et al. show that a structured optical ring cavity can sustain more than one synthetic dimension. Under modulation, coupling the different degrees of freedom within the resonator is used synthesize two additional dimensions. The authors are then able to emulate many complex physical phenomena usually associated with condensed matter systems. Science , this issue p. [59][1] [1]: /lookup/doi/10.1126/science.aaz3071

A single photonic cavity with two independent physical synthetic dimensions.

The concept of synthetic dimensions has generated interest in many branches of science, ranging from ultracold atomic physics to photonics, as it provides a versatile platform for realizing effective gauge potentials and topological physics. Previous experiments have augmented the real-space dimensionality by one additional physical synthetic dimension. In this study, we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We observe a wide variety of physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and signatures of topological chiral one-way edge currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.

Efficient Spectrum Reshaping with Photonic Gauge Potentials in Resonantly Modulated Fiber-Loop Circuits

An efficient way of controlling frequency relies on the strong phase modulation of propagating waves. The authors design a fiber-loop circuit with two phase modulators (PMs) to remarkably enhance phase modulation. Effective gauge potentials can also be introduced by changing the modulation phases of the PMs; varying these potentials shifts the incident frequency spectrum as much as 50 GHz, and yields threefold band expansion. This work is sure to boost applications in spectrum management for optical communication and signal processing.

Creating lattice gauge potentials in circuit QED: The bosonic Creutz ladder

In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The schemes consist of coupled transmons whose flux are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the fixed phase offset of each site on the complex coupling rate between coupled qubits. These configurations can be directly realised in a superconducting circuit and is easily extendable to a scalable lattice. Due to the intrinsic non-linearity of the transmon qubits such lattices would be an ideal platform for simulating Bose-Hubbard Hamiltonians with non-trivial gauge fields.

Photonic Gauge Potential in One Cavity with Synthetic Frequency and Orbital Angular Momentum Dimensions.

We explore a single degenerate optical cavity supporting a synthetic two-dimensional space, which includes the frequency and the orbital angular momentum (OAM) axes of light. We create the effective gauge potential inside this synthetic space and show that the system exhibits topologically protected one-way edge states along the OAM axis at the boundaries of the frequency dimension. In this synthetic space, we present a robust generation and manipulation of entanglement between the frequency and OAM of photons. Our Letter shows that a higher-dimensional synthetic space involving multiple degrees of freedom of light can be achieved in a "zero-dimensional" spatial structure, pointing towards a unique platform to explore topological photonics and to realize potential applications in optical communications and quantum information processing.

Nonreciprocal Photonics Without Magneto-Optics

Optical isolators, which break the Lorentz reciprocity, are fundamental building blocks for regulating the flow of light. Here, we provide a brief perspective on the developments in nonmagnetic approaches to constructing optical isolators. We show that nonlinear optical isolators are fundamentally constrained by dynamic reciprocity and cannot completely reproduce functionalities of standard magneto-optical devices. We also show that complete optical isolation is achievable with dynamic modulation of refractive index. Moreover, the reciprocity-breaking in modulated systems is closely related to the concept of an effective gauge potential for photons. The use of such gauge potential points to a route toward novel nonreciprocal topological photonics physics as well as new capabilities for controlling the propagation of electromagnetic waves.

Synthetic gauge potential and effective magnetic field in a Raman medium undergoing molecular modulation

We theoretically demonstrate non-trivial topological effects for a probe field in a Raman medium undergoing molecular modulation processes. The medium is driven by two non-collinear pump beams. We show that the angle between the pumps is related to an effective gauge potential and an effective magnetic field for the probe field in the synthetic space consisting of a synthetic frequency dimension and a spatial dimension. As a result of such effective magnetic field, the probe field can exhibit topologically-protected one-way edge state in the synthetic space, as well as Landau levels which manifests as suppression of both diffraction and sideband generation. Our work identifies a previously unexplored route towards creating topological photonics effects, and highlights an important connection between topological photonics and nonlinear optics.

Time reversal of a wave packet with temporal modulation of gauge potential

We show that time reversal can be achieved with a spatially uniform temporal modulation of the gauge potential. The method can be applied to the quantum wave function of electrons where there are natural gauge potentials, and to classical waves such as the acoustic and optical waves where effective gauge potentials have been demonstrated recently. This time-reversal process can provide a compensation of higher-order dispersion effects. Moreover, our approach can be used to time reverse the propagation of a wave packet in three dimensions, as well as a topologically protected one-way edge state where the underlying Hamiltonian does not have time-reversal symmetry. Our work shows that modulation of gauge potentials provides a versatile approach for dynamically controlling wave propagation.

Haldane quantum Hall effect for light in a dynamically modulated array of resonators

Topological insulators have attracted abundant attention for a variety of reasons -- notably, the possibility for lossless energy transport through edge states `protected' against disorder. Topological effects like the Quantum Hall state can be induced through a gauge field, which is however hard to create in practice, especially for charge-neutral particles. One way to induce an effective gauge potential is through a dynamic, time-periodic modulation of the lattice confining such particles. In this way, the Haldane Quantum Hall effect was recently observed in a cold atom system. Here, we show how this same effect can be induced for light confined to a lattice of identical optical resonators, using an on-site modulation of the resonant frequencies. We further demonstrate the existence of one-directional edge states immune to back-scattering losses, and discuss the possibilities for a practical implementation, which would enable slow-light devices of unprecedented quality.

The Average Field Approximation for Almost Bosonic Extended Anyons

Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter $$\alpha $$ is proportional to $$N ^{-1}$$ when $$N\rightarrow \infty $$ . This means that the statistics is seen as a “perturbation from the bosonic end”. We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of radius R (extended anyons). Our method allows to take $$R\rightarrow 0$$ not too fast at the same time as $$N\rightarrow \infty $$ . In this limit we rigorously justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

Three-Dimensional Dynamic Localization of Light from a Time-Dependent Effective Gauge Field for Photons.

We introduce a method to achieve the three-dimensional dynamic localization of light. We consider a dynamically modulated resonator lattice that has been previously shown to exhibit an effective gauge potential for photons. When such an effective gauge potential varies sinusoidally in time, dynamic localization of light can be achieved. Moreover, while previous works on such an effective gauge potential for photons were carried out in the regime where the rotating wave approximation is valid, the effect of dynamic localization persists even when the counterrotating term is taken into count.

Vortex Dynamics in a Spin-Orbit-Coupled Bose-Einstein Condensate

Vortices in a one-component dilute atomic ultracold Bose-Einstein condensate (BEC) usually arise as a response to externally driven rotation. Apart from a few special situations, these vortices are singly quantized with unit circulation. Recently, the NIST group has constructed a two-component BEC with a spin-orbit coupled Hamiltonian involving Pauli matrices, and I here study the dynamics of a two-component vortex in such a spin-orbit coupled condensate. These spin-orbit coupled BECs use an applied magnetic field to split the hyperfine levels. Hence they rely on a focused laser beam to trap the atoms. In addition, two Raman laser beams create an effective (or synthetic) gauge potential. The resulting spin-orbit Hamiltonian is discussed in some detail. The various laser beams are fixed in the laboratory, so that it is not feasible to nucleate a vortex by an applied rotation that would need to rotate all the laser beams and the magnetic field. In a one-component BEC, a vortex can also be created by a thermal quench, starting from the normal state and suddenly cooling deep into the condensed state. I propose that a similar method would work for a vortex in a spin-orbit coupled BEC. Such a vortex has two components, and each has its own circulation quantum number. If both components have the same circulation, I find that the composite vortex should execute uniform precession, like that observed in a single-component BEC. In contrast, if one component has unit circulation and the other has zero circulation, then some fraction of the dynamical vortex trajectories should eventually leave the condensate, providing clear experimental evidence for this unusual vortex structure. In the context of exciton-polariton condensates, such a vortex is known as a "half-quantum vortex".