Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering

I will present recent work at Caltech on the integration of optomechanical crystals for light and sound with electronic superconducting quantum circuits. Utilizing the silicon-on-insulator (SOI) wafer platform, we have made key advances in the fabrication and integration of extremely low loss microwave phonon structures and low loss microwave superconducting resonators of high impedance. These technical advancements offer several intriguing opportunities for quantum information processing and networking with phonons, photons, and electrons in an integrated, wafer-scale platform. The focus of my talk will be on two examples of our efforts in this direction: (i) nonreciprocal photon transport and amplification arising from synthetic magnetic flux and reservoir engineering in an optomechanical crystal circuit, and (ii) waveguide-QED systems consisting of microwave-bandgap circuits with embedded transmon-like qubits.

Scattering coefficients can diverge at spectral singularities. In such situation, the stationary solution becomes a laser solution with outgoing waves only. We explore a parity-time (PT)-symmetric non-Hermitian two-arm Aharonov-Bohm interferometer consisting of three coupled resonators enclosing synthetic magnetic flux. The synthetic magnetic flux does not break the PT symmetry, which protects the symmetric transmission. The features and conditions of symmetric, asymmetric, and unidirectional lasing at spectral singularities are discussed. We elucidate that lasing affected by the interference is asymmetric; asymmetric lasing is induced by the interplay between the synthetic magnetic flux and the system's non-Hermiticity. The product of the left and right transmissions is equal to that of the reflections. Our findings reveal that the synthetic magnetic flux affects light propagation, and the results can be applied in the design of lasing devices.

Matter transport is a fundamental process in nature. Understanding and manipulating flow in a synthetic media often have rich implications for modern device design. Here we experimentally demonstrate directional transport of photons in a two-dimensional quantum walk, where the light propagation is highly tunable through dissipation and synthetic magnetic flux. The directional flow hereof underlies the emergence of the non-Hermitian skin effect, with its orientation continuously adjustable through the photon-loss parameters. By contrast, the synthetic magnetic flux originates from an engineered geometric phase, which, by inducing localized cyclotron orbits, suppresses the bulk flow through magnetic confinement. We further demonstrate how the directional flow and synthetic flux impact the dynamics of the Floquet topological edge modes along an engineered boundary. Our results exemplify an intriguing strategy for engineering directed light transport, highlighting the interplay of non-Hermiticity and gauge fields in synthetic systems of higher dimensions.

We report the experimental observation of tunable, nonreciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parameters. We demonstrate that the nonreciprocity originates from the interplay of the synthetic magnetic flux and the laser-induced loss, which simultaneously breaks the inversion and the time-reversal symmetries. Our results open up the avenue for investigating nonreciprocal dynamics in cold atoms, and highlight the dissipative AB ring as a flexible building element for applications in quantum simulation and quantum information.

Gauge magnetic fields have a close relation to breaking time-reversal symmetry in condensed matter. In the presence of the gauge fields, we might observe nonreciprocal and topological transport. Inspired by these, there is a growing effort to realize exotic transport phenomena in optical and acoustic systems. However, due to charge neutrality, realizing analog magnetic flux for phonons in nanoscale systems is still challenging in both theoretical and experimental studies. Here we propose a novel mechanism to generate synthetic magnetic field for phonon lattice by Floquet engineering auxiliary qubits. We find that, a longitudinal Floquet drive on the qubit will produce a resonant coupling between two detuned acoustic cavities. Specially, the phase encoded into the longitudinal drive can exactly be transformed into the phonon–phonon hopping. Our proposal is general and can be realized in various types of artificial hybrid quantum systems. Moreover, by taking surface-acoustic-wave (SAW) cavities for example, we propose how to generate synthetic magnetic flux for phonon transport. In the presence of synthetic magnetic flux, the time-reversal symmetry will be broken, which allows one to realize the circulator transport and analog Aharonov–Bohm effects for acoustic waves. Last, we demonstrate that our proposal can be scaled to simulate topological states of matter in quantum acoustodynamics system.

Photons do not directly interact with magnetic fields. Recent progress in synthetic gauge fields have stimulated investigations in various fields. In this study, we explore the enclosed synthetic magnetic flux in a parity-time ($\mathcal{PT}$)-symmetric system of three coupled optical resonators; this flux suppresses the $\mathcal{PT}$ transition and affects the topological structure of $\mathcal{PT}$ transition points. Although the phase rigidities of the coalesced states no longer vanish at exceptional points (EPs), the orders of the EPs (which are affected by the magnetic flux) can be identified. At a three-state coalescence, the intensity of an initial excitation increases according to a power law, and at a two-state coalescence, the intensity can behave as invariant, oscillatory, quadratic increase, and oscillatory quadratic increase. Our findings provide an insight into the interplay between non-Hermiticity and the effective magnetic flux.

A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric non-Hermitian lattice. The proposed flat band has entirely real energy and is formed at an appropriate match between synthetic magnetic flux and non-Hermiticity. The flat band energy is tunable. At a weak intercell coupling, the flat band is isolated, whereas at a strong intercell coupling, it intersects with the dispersive band at the non-Hermitian phase transition point. The eigenstates of the flat band are compact localized states and are confined in one, two, or three unit cells at the edges or inside the non-Hermitian lattice.

We study the properties of nonlinear Bloch waves in a diamond chain waveguide lattice in the presence of a synthetic magnetic flux. In the linear limit, the lattice exhibits a completely flat (wavevector k-independent) band structure, resulting in perfect wave localization, known as Aharonov–Bohm caging. We find that in the presence of nonlinearity, the Bloch waves become sensitive to k, exhibiting bifurcations and instabilities. Performing numerical beam propagation simulations using the tight-binding model, we show how the instabilities can result in either the spontaneous or controlled formation of localized modes, which are immobile and remain pinned in place due to the synthetic magnetic flux.

The interplay between matter particles and gauge fields in physical spaces with nontrivial geometries can lead to novel topological quantum matter. However, detailed microscopic mechanisms are often obscure, and unconventional spaces are generally challenging to construct in solids. Highly controllable atomic systems can quantum simulate such physics, even those inaccessible in other platforms. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux. We observe a symmetry-protected topological band structure emerging on this Hall cylinder but disappearing in the planar counterpart. BEC’s transport observed as Bloch oscillations in the band structure is analogous to traveling on a Möbius strip in the momentum space, revealing topological band crossings protected by a nonsymmorphic symmetry. We demonstrate that breaking this symmetry induces a topological transition manifested as gap opening at band crossings, and further manipulate the band structure and BEC’s transport by controlling the axial synthetic magnetic flux. Our work opens the door for using atomic quantum simulators to explore intriguing topological phenomena intrinsic in unconventional spaces.5 MoreReceived 10 August 2021Accepted 7 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010316Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose-Einstein condensatesQuantum simulationSynthetic gauge fieldsPhysical SystemsUltracold gasesTechniquesAtom & ion coolingAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized photonic-phononic resonances occur. A resonant cavity structure formed by perturbing a ;;linear defect' waveguide of optical and acoustic waves in a silicon optomechanical crystal slab is shown to support an optical resonance at wavelength lambda(0) approximately 1.5 mum and a mechanical resonance of frequency omega(m)/2pi approximately 9.5 GHz. These resonances, due to the simultaneous pseudo-bandgap of the waveguide structure, are simulated to have optical and mechanical radiation-limited Q-factors greater than 10(7). The optomechanical coupling of the optical and acousticresonances in this cavity due to radiation pressure is also studied, with a quantum conversion rate, corresponding to the scattering rate of a single cavity photon via a single cavity phonon, calculated to be g/2pi = 292 kHz.

A survey of various methods of optical excitation of ionic states, including excimer states, of molecules demonstrates the extensive potential optical pumping and makes it possible to determine the trends that are promising for further searches. Noticeable among them, firstly, is direct optical excitation and its accompanying secondary chemical processes with phototransport of electrons, which offer the researchers the largest choice of specific molecules and excitation mechanisms. We have shown, with molecular chlorine as the example, that the search for working media for optical pumping need not be limited to heavy molecules. The use of a complicated isotopic composition of molecules, Zeeman splitting of levels in a magnetic field, and impact broadening of spectral lines makes it possible to extend, within reasonable limits, the method of wide-band pumping to include also light molecules. As to secondary exchange reactions with charge transfer, in which optically excited molecules participate, it can be seen from the results of estimates of the cross sections that they constitute the largest class of excimerformation reactions and are characterized by additional possibilities of spectrally controlling the course of the reactions for the purpose of obtaining various products. Other promising methods considered here are production of ionic photodissociation states, including polar photodissociation, and also chemical radiative collisions. Note particularly the need for continuing the search for polyatomic excimers. It is obvious that production of such excimers is possible in media having a more complicated molecular composition, where such an advantage of optical pumping as the absence of induced absorption at the lasing wavelength is most strongly manifested.

Non-Hermiticity and synthetic gauge fields play two fundamental roles in engineering exotic phases and dynamics in artificial quantum systems. Here, we explore the mean-field dynamics of interacting bosons in a two-leg ladder with synthetic magnetic flux and nonreciprocal hopping under the open boundary condition. In the Hermitian limit, we showcase the breakdown of the flux-driven chiral dynamics due to the nonlinear self-trapping effect. We further find that the nonreciprocity can drive the transition between chiral dynamics and antichiral dynamics. The antichiral motion is manifested as the non-Hermitian skin dynamics along the same direction on two legs that are not suppressed by the magnetic flux, while the chiral-antichiral transition is flux tunable. We also reveal the trap-skin dynamics with the coexistence of the self-tapping and skin dynamics in the ladder. Dynamical phase diagrams with respect to the chiral-antichiral dynamics, skin dynamics, self-trapping dynamics, and trap-skin dynamics are presented. Our results shed light on intriguing dynamical phenomena under the interplay among non-Hermiticity, nonlinearity, and artificial gauge fields.

Degeneracy (exceptional) points embedded in energy band are distinct by their topological features. We report different hybrid two-state coalescences (EP2s) formed through merging two EP2s with opposite chiralities that created from the type III Dirac points emerging from a flat band. The band touching hybrid EP2, which is isolated, is induced by the destructive interference at the proper match between non-Hermiticity and synthetic magnetic flux. The degeneracy points and different types of exceptional points are distinguishable by their topological features of global geometric phase associated with the scaling exponent of phase rigidity. Our findings not only pave the way of merging EPs but also shed light on the future investigations of non-Hermitian topological phases.

We study a multi-functional device for cold atoms consisting of a three-terminal ring circuit pierced by a synthetic magnetic flux, where the ring can be continuous or discretized. The flux controls the atomic current through the ring via the Aharonov-Bohm effect. Our device shows a flux-induced transition of reflections from an Andreev-like negative density to positive density. Further, the flux can direct the atomic current into specific output ports, realizing a flexible non-reciprocal switch to connect multiple atomic systems or sense rotations. By changing the flux linearly in time, we convert constant matter wave currents into an AC modulated current. This effect can be used to realize an atomic frequency generator and study fundamental problems related to the Aharonov-Bohm effect. We experimentally demonstrate Bose-Einstein condensation into the light-shaped optical potential of the three-terminal ring. Our work opens up the possibility of novel atomtronic devices for practical applications in quantum technologies.

We propose a theoretical scheme to realize nonreciprocal transition between\ntwo energy levels that can not coupled directly. Suppose they are coupled\nindirectly by two auxiliary levels with a cyclic four-level configuration, and\nthe four transitions in the cyclic configuration are controlled by external\nfields. The indirectly transition become nonreciprocal when the time reversal\nsymmetry of the system is broken by the synthetic magnetic flux, i.e., the\ntotal phase of the external driving fields through the cyclic four-level\nconfiguration. The nonreciprocal transition can be identified by the\nelimination of a spectral line in the spontaneous emission spectrum. Our work\nintroduces a feasible way to observe nonreciprocal transition in a wide range\nof multi-level systems, including natural atoms or ions with parity symmetry.\n