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.
We explore topological properties of a modulated Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor terms is made unequal and the three-fold rotational symmetry $\mathcal{C}_3$ is broken by introducing a trimerization term ($|t_{1w(2w)}|< t_{1s(2s)}$) in the Hamiltonian. Using the parameter $η={t_{1w}}/{t_{1s}}= t_{2w}/t_{2s}$, we show that the MHM supports a transition from the quantum anomalous Hall insulator (QAHI) to a HOTI phase at $η=\pm 0.5$. The MHM also hosts a zero-energy corner mode on a nano-disk that can transition to a trivial insulator wi…
We study nonreciprocity in spatiotemporally modulated 1D resonator chains from the perspective of equivalent 2D resonator arrays with a synthetic dimension and transverse synthetic electric and magnetic fields. The synthetic fields are respectively related to temporal and spatial modulation of the resonator chain, and we show that their combination can break transmission reciprocity without additional elements. This nonreciprocal effect is analogous to the Hall effect for charged particles. We experimentally implement chains of 2 and 3 spatiotemporally modulated resonators and measure over 58 …
We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, and the nontrivial topology is a result of next-nearest couplings with non-zero staggered phases. The system exhibits a topological phase transition between trivial and spin Chern insulator phases when the sublattices are frequency detuned. Such topol…
A MEMS Duffing resonator is driven by two adjacent frequency tones into the nonlinear regime. We show that if the two-tone drive is applied at a frequency where a bistable response of the nonlinear oscillator exists, then the system output will be modulated by a relaxation cycle caused by periodically jumping between the two solution-branches of the bistable response. Although the jumps are caused by the beating of the drives, the existence and period of this relaxation or hysteresis cycle is not solely dictated by the beat frequency between the two driving tones, but also by their amplitude a…
Synchronization has been reported for a wide range of self-oscillating systems. However, even though it has been predicted theoretically for several decades, the experimental realization of phase self-oscillation, sometimes called phase trapping, in the high driving regime has been studied only recently. We explored in detail the phase dynamics in a synchronized field emission SiC nanoelectromechanical system with intrinsic feedback. A richer variety of phase behavior has been unambiguously identified, implying phase modulation and inertia. This synchronization regime is expected to have impli…
We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (< 1 kHz). This additional parametric modulation leads to prominent antiresonance lineshapes in the sideband spectra, which can be controlled through the vibration state of the driven mode. We also establish a direct connection between the antiresonance frequency and the squeezing of thermal fluctuation in the system. Our work not only provides a simple and robust method for squeezing characterization but also opens a new possibility toward sideband applications.
We investigate the dynamics and topology of metastructures with quasiperiodically modulated local resonances. The concept is implemented on a LEGO beam featuring an array of tunable pillar-cone resonators. The versatility of the platform allows the experimental mapping of the beam's Hofstadter-like resonant spectrum, which is the first reported observation for an elastic medium. The non-trivial spectral gaps are classified by evaluating the integrated density of states of the bulk bands, which is experimentally verified through the observation of topological edge states localized at the bounda…
We propose and analyze the detector of modulated terahertz (THz) radiation based on the graphene field-effect transistor with mechanically floating gate made of graphene as well. The THz component of incoming radiation induces resonant excitation of plasma oscillations in graphene layers (GLs). The rectified component of the ponderomotive force between GLs invokes resonant mechanical swinging of top GL, resulting in the drain current oscillations. To estimate the device responsivity, we solve the hydrodynamic equations for the electrons and holes in graphene governing the plasma-wave response,…
We study the extended Su-Schrieffer-Heeger model with both the nearest-neighbor and next-nearest-neighbor hopping strengths being cyclically modulated and find the family of the model system exhibiting topologically nontrivial phases, which can be characterized by a nonzero Chern number defined in a two-dimensional space spanned by the momentum and modulation parameter. It is interesting that the model has a similar phase diagram as the well-known Haldane's model. We propose to use photonic crystal systems as the idea systems to fabricate our model systems and probe their topological propertie…
We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a gate voltage variation. For a two-qubit ($n$-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal $σ_z$-coupling, offering gate times of 10s of ns even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse $σ_x$-coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron…
We propose a quantum non-demolition Majorana qubit readout protocol based on parametricmodulation of a longitudinal interaction between a pair of Majorana bound states and a resonator. The interaction can be modulated through microwave frequency gate-voltage or flux control of a tunable tunnel barrier. The qubit-resonator coupling is quantum non-demolition to exponential accuracy, a property inherited from the topological nature of the Majorana zero modes. The same mechanism as used for single-qubit readout can also be extended to perform multi-qubit measurements and be used to enact long rang…
We demonstrate mechanical modulations of the exciton lifetime by using vibrational strain of a gallium arsenide (GaAs) resonator. The strain-induced modulations have anisotropic dependences on the crystal orientation, which reveals the origin of these modulations to be the piezoelectric effect. Numerical analyses based on the tunneling model clarify that the mechanical strain modulates the internal electric field and spatially separates the electrons and holes, leading to non-radiative exciton decomposition. This carrier separation also generates an optomechanical back-action force from the ph…
When one of the parameters in the Euler-Lagrange equations of motion of a system is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir effect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveguides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir effects, consisting of an LC resonator, with the indu…
We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8 superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification i…
We study theoretically the spatial distribution of the polarizations in the array of resonant electromagnetic dipole emitters coupled to a one-dimensional waveguide. The ratchet effect manifests itself in the spatial asymmetry of the distribution of the emitter occupations along the array under symmetrical pumping from both sides. The occupation asymmetry is driven by the periodic modulation in time of the emitter resonance frequencies. We find numerically and analytically the optimal conditions for maximal asymmetry. We also demonstrate that the ratchet effect can be enhanced due to the forma…
We report on a giant enhancement in the thermal responsivity of the doubly-clamped GaAs microelectromechanical (MEMS) beam resonators by using the internal mode coupling effect. This is achieved by coupling the fundamental bending mode with the fundamental torsional mode of the MEMS beam resonators through the cubic Duffing nonlinearity. In the mode coupling regime, we have found that, when the input heat to the MEMS resonators is modulated at a particular frequency, the resonance frequency shift caused by heating can be enhanced by almost two orders of magnitude. The observed effect is promis…
Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous qu…
We consider a model of a quantum-mechanical resonator capacitively coupled to a single electron transistor (SET). The tunnel current in the SET is modulated by the vibrations of the resonator, and thus the system operates as a displacement detector. We analyze the effect of the back-action noise of charge fluctuations in the SET onto the dynamics of the resonator and evaluate the displacement sensitivity of the system. The relation between the "classical" and "quantum" parts of the SET charge noise and their effect on the measured system are also discussed.
Recent observation of quantum emitters in monolayers of hexagonal boron nitride (h-BN) has provided a novel platform for optomechanical experiments where the single-photon emitters can couple to the motion of freely suspended h-BN membrane. Here, we propose a scheme where the electronic degree of freedom of an embedded color center is coupled to the motion of the hosting h-BN resonator via dispersive forces. We show that the coupling of membrane vibrations to the electronic degree of freedom of the emitter can reach the strong regime. By suitable driving of a three-level $Λ$-system composed of…
Based on the recently proposed concept of effective gauge potential and magnetic field for photons, we numerically demonstrate a photonic de Haas-van Alphen effect. We show that in a dynamically modulated photonic resonator lattice exhibiting an effect magnetic field, the trajectories of the light beam at a given frequency have the same shape as the constant energy contour for the photonic band structure of the lattice in the absence of the effective magnetic field.
The parametric phase-locked oscillator (PPLO), also known as a parametron, is a resonant circuit in which one of the reactances is periodically modulated. It can detect, amplify, and store binary digital signals in the form of two distinct phases of self-oscillation. Indeed, digital computers using PPLOs based on a magnetic ferrite ring or a varactor diode as its fundamental logic element were successfully operated in 1950s and 1960s. More recently, basic bit operations have been demonstrated in an electromechanical resonator, and an Ising machine based on optical PPLOs has been proposed. Here…
We study the possibility of realizing quantum anomalous Hall effect (QAHE) with tunable Chern number through doping magnetic elements in the multi-layer topological insulator film. We find that high Chern number QAHE phases exist in the ideal neutral samples and it can make transition to another QAHE phase directly by means of tuning the exchange field strength or sample thickness. With the help of an extended Haldane model, we demonstrate the physical mechanism of the tunable Chern number QAHE phase. Further, we study the phenomena in the realistic samples with the Fermi energy being gating-m…
Oscillators, which produce continuous periodic signals from direct current power, are central to modern communications systems, with versatile applications such as timing references and frequency modulators. However, conventional oscillators typically consist of macroscopic mechanical resonators such as quartz crystals, which require excessive off-chip space. Here we report oscillators built on micron-size, atomically-thin graphene nanomechanical resonators, whose frequencies can be electrostatically tuned by as much as 14\%. The self-sustaining mechanical motion of the oscillators is generate…
