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In a traveling wave microresonator, the cascaded four-wave mixing (FWM) between optical modes allows the generation of frequency combs, including intriguing dissipative Kerr solitons (DKS). In this study, we explore the quantum fluctuations of frequency combs and unveil the quantum features of solitons. The entanglement of DKS exhibits two distinct characteristics. For modes located at the spectral edge with a small number of excitations, different comb modes with multiple colors become entangled due to photon-pair generation and coherent photon conversion stimulated by the FWM. Notably, we observe a sudden disappearance of quantum entanglement in the center of the DKS spectrum, which is attributed to the self-locking phenomena in the FWM network. Our findings demonstrate the prominent quantum nature of DKS, which is of fundamental significance in quantum optics and has the potential to be utilized in quantum networking and distributed quantum sensing applications., Comment: 7 pages,3 figures

Materials with strong $\chi^{(2)}$ optical nonlinearity, especially lithium niobate, play a critical role in building optical parametric oscillators (OPOs). However, chip-scale integration of low-loss $\chi^{(2)}$ materials remains challenging and limits the threshold power of on-chip $\chi^{(2)}$ OPO. Here we report the first on-chip lithium niobate optical parametric oscillator at the telecom wavelengths using a quasi-phase matched, high-quality microring resonator, whose threshold power ($\sim$30 $\mu$W) is 400 times lower than that in previous $\chi^{(2)}$ integrated photonics platforms. An on-chip power conversion efficiency of 11% is obtained at a pump power of 93 $\mu$W. The OPO wavelength tuning is achieved by varying the pump frequency and chip temperature. With the lowest power threshold among all on-chip OPOs demonstrated so far, as well as advantages including high conversion efficiency, flexibility in quasi-phase matching and device scalability, the thin-film lithium niobate OPO opens new opportunities for chip-based tunable classical and quantum light sources and provides an potential platform for realizing photonic neural networks.

Superconducting cavity electro-optics (EO) presents a promising route to coherently convert microwave and optical photons and distribute quantum entanglement between superconducting circuits over long-distance through an optical network. High EO conversion efficiency demands transduction materials with strong Pockels effect and excellent optical transparency. Thin-film Lithium Niobate (TFLN) offers these desired characteristics however so far has only delivered unidirectional conversion with efficiencies on the order of $10^{-5}$, largely impacted by its prominent photorefractive (PR) effect at cryogenic temperatures. Here we show that, by mitigating the PR effect and associated charge-screening effect, the device's conversion efficiency can be enhanced by orders of magnitude while maintaining stable cryogenic operation, thus allowing a demonstration of conversion bidirectionality and accurate quantification of on-chip efficiency. With the optimized monolithic integrated superconducting EO device based on TFLN-on-sapphire substrate, an on-chip conversion efficiency of 1.02% (internal efficiency, 15.2%) is realized. Our demonstration indicates that with further device improvement, it is feasible for TFLN to approach unitary internal conversion efficiency.

Quantum key distribution (QKD) can generate secure key bits between remote users with quantum mechanics. However, the gap between the theoretical model and practical realizations gives eavesdroppers opportunities to intercept secret key. The most insidious attacks, known as quantum hacking, are the ones with no significant discrepancy of the measurement results using side-channel loopholes of QKD systems. Depicting full-time-scale characteristics of the quantum signals, the quantum channel, and the QKD system can provide legitimate users extra capabilities to defeat malicious attacks. For the first time, we propose the method exploring temporal ghost imaging (TGI) scheme to perceive quantum hacking with temporal fingerprints and experimentally verify its validity. The scheme presents a common approach to promote QKD's practical security from a new perspective of signals and systems., Comment: 11 pages, 6 figures

Single-mode high-index-contrast waveguides have been ubiquitously exploited in optical, microwave, and phononic structures for achieving enhanced wave-matter interactions. Although micro-scale optomechanical and electro-optical devices have been widely studied, optomagnonic devices remain a grand challenge at the microscale. Here, we introduce a planar optomagnonic waveguide platform based on a ferrimagnetic insulator that simultaneously supports single transverse mode of spin waves (magnons) and highly confined optical modes. The co-localization of spin and light waves gives rise to enhanced inverse Faraday effect, and as a result, magnons are excited by an effective magnetic field generated by interacting optical photons. Moreover, the strongly enhanced optomagnonic interaction allows us to observe such effect using low-power (milliwatt level) light signals in the continuous-wave form, as opposed to high-intensity (megawatt peak power) light pulses that are typically required in magnetic bulk materials or thin films. The optically-driven magnons are detected electrically with preserved phase coherence, showing the feasibility for launching spin waves with low-power continuous optical fields.

We report intracavity Bragg scattering induced by photorefractive (PR) effect in high-Q lithium niobate (LN) ring resonators at cryogenic temperatures. We show that, when a cavity mode is strongly excited, the PR effect imprints a long-lived periodic space-charge field. This residual field in turn creates a refractive index modulation pattern that dramatically enhances the back scattering of an incoming probe light, and results in selective and reconfigurable mode splittings. This PR-induced Bragg scattering effect, despite being undesired for many applications, could be utilized to enable optically programmable photonic components.

Microresonators on a photonic chip could enhance nonlinear optics effects, thus are promising for realizing scalable high-efficiency frequency conversion devices. However, fulfilling phase matching conditions among multiple wavelengths remains a significant challenge. Here, we present a feasible scheme for degenerate sum-frequency conversion that only requires the two-mode phase matching condition. When the drive and the signal are both near resonance to the same telecom mode, an efficient on-chip photon-number conversion efficiency upto 42% was achieved, showing a broad tuning bandwidth over 250GHz. Furthermore, cascaded Pockels and Kerr nonlinear optical effects are observed, enabling the parametric amplification of the optical signal to a distinct wavelength in a single device. The scheme demonstrated in this work provides an alternative approach to realizing high-efficiency frequency conversion and is promising for future studies on communications, atom clocks, sensing, and imaging., Comment: 6 pages, 4 figures

In the development of quantum microwave-to-optical (MO) converters, excessive noise induced by the parametric optical drive remains a major challenge at milli-Kelvin temperatures. Here we study the extraneous noise added to an electro-optic transducer in its quantum ground state under an intense pulsed optical excitation. The integrated electro-optical transducer leverages the inherent Pockels effect of aluminum nitride microrings, flip-chip bonded to a superconducting resonator. Applying a pulsed optical drive with peak power exceeding the cooling power of the dilution refrigerator at its base temperature, we observe efficient bi-directional MO conversion, with near-ground state microwave thermal excitation ($\bar{n}_\mathrm{e}=0.09\pm0.06$). Time evolution study reveals that the residual thermal excitation is dominated by the superconductor absorption of stray light scattered off the chip-fiber interface. Our results shed light on suppressing microwave noise in a cavity electro-optic system under intense optical drive, which is an essential step towards quantum state transduction between microwave and optical frequencies.

A multimode microcavity sensor based on a self-interference microring resonator is demonstrated experimentally. The proposed multimode sensing method is implemented by recording wideband transmission spectra that consist of multiple resonant modes. It is different from the previous dissipative sensing scheme, which aims at measuring the transmission depth changes of a single resonant mode in a microcavity. Here, by combining the dissipative sensing mechanism and the machine learning algorithm, the multimode sensing information extracted from a broadband spectrum can be efficiently fused to estimate the target parameter. The multimode sensing method is immune to laser frequency noises and robust against system imperfection, thus our work presents a great step towards practical applications of microcavity sensors outside the research laboratory. The voltage applied across the microheater on the chip was adjusted to bring its influence on transmittance through the thermo-optic effects. As a proof-of-principle experiment, the voltage was detected by the multimode sensing approach. The experimental results demonstrate that the limit of detection of the multimode sensing by the general regression neural network is reduced to 6.7% of that of single-mode sensing within a large measuring range., Comment: 9 pages, 7 figures

Single-photon transport in non-ideal chiral photon-atom interaction structures generally contains information backflow and thus limits the capabilities to transfer information between distant emitters in cascaded quantum networks. Here, in the non-ideal chiral case, a V -type atom coupled to a waveguide is proposed to realize completely unidirectional transmission of the single photons in a superposition state of different frequencies. A microwave field is introduced to drive the two excited states of the atom and results in photon conversion between two transitions. By adjusting the Rabi frequency and the phase of the external driving field, the transport behaviors of incident photons with specific frequencies can be optimized to complete transmission or reflection. Based on the constructive interferences between photons from different traveling paths, the transmission probabilities of the specific-frequency photons could be enhanced. Due to photon conversions with compensating the dissipations and ensuring the complete destructive interference, the ideal unidirectional transmission contrast can be maintained to 1, even when the atom has dissipations into the non-waveguide modes., Comment: 8 pages, 6 figures

The realization of optical non-reciprocity is crucial for many device applications, and also of fundamental importance for manipulating and protecting the photons with desired time-reversal symmetry. Recently, various new mechanisms of magnetic-free non-reciprocity have been proposed and implemented, avoiding the limitation of the strong magnetic field imposed by the Faraday effect. However, due to the difficulties in suppressing the drive and its induced noises, these devices exhibit limited isolation performances and leave the quantum noise properties rarely studied. Here, we demonstrate a new approach of magnetic-free non-reciprocity by optically induced magnetization in an atom ensemble. Excellent isolation of signal (highest isolation ratio is 51.4 dB) is observed over a power dynamic range of 7 orders of magnitude, with the noiseless property verified by quantum statistics measurement. The approach is applicable to other atoms and atom-like emitters in solids, paving the way for future studies of integrated photonic non-reciprocal devices, unidirectional quantum storage and state transfer, as well as topological photonics technologies., Comment: 6 pages, 5 figures

The absence of the single-photon nonlinearity has been a major roadblock in developing quantum photonic circuits at optical frequencies. In this paper, we demonstrate a periodically-poled thin film lithium niobate microring resonator (PPLNMR) that reaches 5,000,000%/W second harmonic conversion efficiency---almost 20-fold enhancement over the state-of-the-art---by accessing its largest $\chi^{(2)}$ tensor component $d_{33}$ via quasi-phase matching. The corresponding single photon coupling rate $g/2\pi$ is estimated to be 1.2 MHz, which is an important milestone as it approaches the dissipation rate $\kappa/2\pi$ of best available lithium niobate microresonators developed in the community. Using a figure of merit defined as $g/\kappa$, our devices reach a single photon nonlinearity approaching 1%. We show that, by further scaling of the device, it is possible to improve the single photon nonlinearity to a regime where photon-blockade effect can be manifested.

The generalized Poor-Verdu error lower bound established in [1] for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric channel (BSC), the minimum probability of error (under maximum likelihood decoding) has a relative deviation from the generalized bound that grows at most linearly in blocklength. This result directly implies that for arbitrary codes used over the BSC, decoder ties can only affect the subexponential behavior of the minimum probability of error., Comment: arXiv admin note: text overlap with arXiv:2001.01159

We numerically model key building blocks of a phononic integrated circuit that enable phonon routing in high-acoustic-index waveguides. Our particular focus is on Gallium Nitride-on-sapphire phononic platform which has recently demonstrated high acoustic confinement in its top layer without the use of suspended structures. We start with systematic simulation of various transverse phonon modes supported in strip waveguides and ring resonators with sub-wavelength cross-section. Mode confinement and quality factors of phonon modes are numerically investigated with respect to geometric parameters. Quality factor up to $10^{8}$ is predicted in optimized ring resonators. We next study the design of the phononic directional couplers, and present key design parameters for achieving strong evanescent couplings between modes propagating in parallel waveguides. Last, interdigitated transducer electrodes are included in the simulation for direct excitation of a ring resonator and critical coupling between microwave input and phononic dissipation. Our work provides comprehensive numerical characterization of phonon modes and functional phononic components in high-acoustic-index phononic circuits, which supplements previous theories and contributes to the emerging field of phononic integrated circuits., Comment: 11 pages, 11 figures

Cavity optomagnonics has emerged as a promising platform for studying coherent photon-spin interactions as well as tunable microwave-to-optical conversion. However, current implementation of cavity optomagnonics in ferrimagnetic crystals remains orders of magnitude larger in volume than state-of-the-art cavity optomechanical devices, resulting in very limited magneto-optical interaction strength. Here, we demonstrate a cavity optomagnonic device based on integrated waveguides and its application for microwave-to-optical conversion. By designing a ferrimagnetic rib waveguide to support multiple magnon modes with maximal mode overlap to the optical field, we realize a high magneto-optical cooperativity which is three orders of magnitude higher compared to previous records obtained on polished YIG spheres. Furthermore, we achieve tunable conversion of microwave photons at around 8.45 GHz to 1550 nm light with a broad conversion bandwidth as large as 16.1 MHz. The unique features of the system point to novel applications at the crossroad between quantum optics and magnonics.

The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein-Laub formulation, which can reconcile those conflicts, was suggested as an alternative to the Lorentz formulation. However, intense debates on the exact force are still going on due to lack of experimental evidence. Here, we report the first experimental investigation of angular symmetry of optical force inside a solid dielectric, aiming to distinguish the two formulations. The experiments surprisingly show that the optical force exerted by a Gaussian beam has components with the angular mode number of both 2 and 0, which cannot be explained solely by the Lorentz or the Einstein-Laub formulation. Instead, we found a modified Helmholtz theory by combining the Lorentz force with additional electrostrictive force could explain our experimental results. Our results represent a fundamental leap forward in determining the correct force formulation, and will update the working principles of many applications involving electromagnetic forces.

Kerr soliton microcombs have recently emerged as a prominent topic in integrated photonics and enabled new horizons for optical frequency metrology. Kerr soliton microcombs, as its name suggests, are based on the high-order cubic optical nonlinearity. It is desirable to exploit quadratic photonic materials, namely Pockels materials, for soliton generation and on-chip implementation of 1f-2f comb self-referencing. Such quadratically-driven solitons have been theoretically proposed, but have not yet been observed in a nanophotonic platform despite of recent progresses in quadratic comb generation in free-space and crystalline resonators. Here we report photonic chip-based Pockels microcomb solitons driven by three-wave mixing in an aluminum nitride microring resonator. In contrast to typical Kerr solitons, our Pockels soliton features unity soliton generation fidelity, two-by-two annihilation of multi-soliton states, favorable tuning dynamics, and high pump-to-soliton conversion efficiency.

Dissipative Kerr soliton offers broadband coherent and low-noise frequency comb and stable temporal pulse train, having shown great potential applications in spectroscopy, communications, and metrology. Breathing soliton is a particular dissipative Kerr soliton that the pulse duration and peak intensity show periodic oscillation. However, the noise and stability of the breathing soliton is still remaining unexplored, which would be the main obstacle for future applications. Here, we have investigated the breathing dissipative Kerr solitons in the silicon nitride (SiN) microrings, while the breather period shows uncertainties around MHz in both simulation and experiments. By applying a modulated pump, the breathing frequency can be injectively locked to the modulation and tuned over tens of MHz with frequency noise significantly suppressed. Our demonstration offers an alternative knob for the controlling of soliton dynamics in microresonator and paves a new avenue towards practical applications of breathing soliton.

We present an experimental study on the cavity-atom ensemble system, and realize the doubly-resonant cavity enhanced electromagnetically induced transparency, where both the probe and control lasers are resonant with a Fabry-Perot cavity. We demonstrate the precise frequency manipulating of the hybrid optical-atomic resonances, through either temperature or cavity length tuning. In such a system, the control power can be greatly enhanced due to the cavity, and all-optical switching is achieved with a much lower control laser power compared to previous studies. A new theoretical model is developed to describe the effective three-wave mixing process between spin-wave and optical modes. Interesting non-Hermitian physics are predicted theoretically and demonstrated experimentally. Such a doubly-resonant cavity-atom ensemble system without a specially designed cavity can be used for future applications, such as optical signal storage and microwave-to-optical frequency conversion., Comment: 8 pages, 5 figures

Despite very efficient superconducting nanowire single-photon detectors (SNSPDs) reported recently, combining their other performance advantages such as high speed and ultra-low timing jitter in a single device still remains challenging. In this work, we present a perfect absorber model and corresponding detector design based on a micron-long NbN nanowire integrated with a 2D-photonic crystal cavity of ultra-small mode volume, which promises simultaneous achievement of near-unity absorption, gigahertz counting rates and broadband optical response with a 3 dB bandwidth of 71 nm. Compared to previous stand-alone meandered and waveguide-integrated SNSPDs, this perfect absorber design addresses the trade space in size, efficiency, speed and bandwidth for realizing large on-chip single-photon detector arrays.

This paper demonstrates cooling of the center-of-mass motion of 10 $\mu$m-diameter optically levitated silica spheres to an effective temperature of $50\pm22 \mu$K, achieved by minimizing the technical pointing noise of the trapping laser. This low noise leads to an acceleration and force sensitivity of $95\pm41$ n$g/\sqrt{\mathrm{Hz}}$ ($g = 9.8$ m/s$^2$) and $0.95\pm0.11$ aN$/\sqrt{\mathrm{Hz}}$, respectively, at frequencies near 50 Hz. This force sensitivity is comparable to that demonstrated for optically levitated nanospheres that are $10^4$ times less massive, corresponding to an acceleration sensitivity that is several orders of magnitude better. It is further shown that under these conditions the spheres remain stably trapped at pressures of $\sim 10^{-7}$ mbar with no active cooling for periods longer than a day. Feedback cooling is still necessary in the moderate-pressure regime, motivating a comprehensive study of the loss mechanisms of the microspheres and providing better understanding of the requirements for feedback-free optical trapping in vacuum. This work can enable high-sensitivity searches for accelerations and forces acting on micron-sized masses, including those that could be produced by new physics beyond the Standard Model.

Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10-GHz phonons are resonantly coupled with photons in a superconducting and a nanophotonic cavities at the same time. Benefited from the achieved large piezo-mechanical cooperativity ($C_\mathrm{em}\sim7$) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons.

The generalized Poor-Verdu error lower bound for multihypothesis testing is revisited. Its asymptotic expression is established in closed-form as its tilting parameter grows to infinity. It is also shown that the asymptotic generalized bound achieves the error exponent (or reliability function) of the memoryless binary symmetric channel at zero coding rates.

We present a generic theoretical framework to describe non-reciprocal microwave circulation in a multimode cavity magnonic system and assess the optimal performance of practical circulator devices. We show that high isolation (> 56 dB), extremely low insertion loss (< 0.05 dB), and flexible bandwidth control can be potentially realized in high-quality-factor superconducting cavity based magnonic platforms. These circulation characteristics are analyzed with materials of different spin densities. For high-spin-density materials such as yttrium iron garnet, strong coupling operation regime can be harnessed to obtain a broader circulation bandwidth. We also provide practical design principles for a highly integratible low-spin-density material (vanadium tetracyanoethylene) for narrow-band circulator operation, which could benefit noise-sensitive quantum microwave measurements. This theory can be extended to other coupled systems and provide design guidelines for achieving tunable microwave non-reciprocity for both classical and quantum applications.

Breaking the time-reversal symmetry of light is of great importance for fundamental physics and has attracted increasing interest in the study of non-reciprocal photonic devices. Here, we experimentally demonstrate a chiral cavity QED system with multiple atoms strongly coupled to a Fabry-Perot cavity. By polarizing the internal quantum state of the atoms, the time-reversal symmetry of the atom-cavity interaction is broken. The strongly coupled atom-cavity system can be described by non-reciprocal quasiparticles, i.e., the cavity polariton. When it works in the linear regime, the inherent nonreciprocity makes the system work as a single-photon-level optical isolator. Benefiting from the collective enhancement of multiple atoms, an isolation ratio exceeding 30~dB on the single-quanta level (~0.1 photon on average) is achieved. The validity of the non-reciprocal device under zero magnetic field and the reconfigurability of the isolation direction are also experimentally demonstrated. Moreover, when the cavity polariton works in the nonlinear regime, the quantum interference between polaritons with weak anharmonicity induces non-reciprocal nonclassical statistics of cavity transmission from coherent probe light., Comment: 10 pages, 6 figures

Phononic wire waveguides of subwavelength cross-section support two orthogonal polarization modes: the out-of-plane motion dominated Rayleigh-like and the in-plane motion dominated Love-like modes, analogous to transverse-electric and transverse-magnetic modes in photonic waveguides. Due to the anisotropic elasticity of the substrate material, the polarization states of phonons propagating along certain crystallographic orientations can strongly hybridize. Here we experimentally investigate the orientation-dependent mode hybridization in phononic wire waveguides patterned from GaN-on-sapphire thin films. Such mode hybridization allows efficient actuation of piezoelectrically inactive Love-like modes using common interdigital electrodes designed for Rayleigh-like modes, and further enables on-chip polarization conversion between guided transverse modes. Both are important for on-chip implementation of complex phononic circuits.

We propose an optomechanical dissipation engineering scheme by introducing an ancillary mechanical mode with a large decay rate to control the density of states of the optical mode. The effective linewidth of the optical mode can be reduced or broadened, manifesting the dissipation engineering. To prove the ability of our scheme in improving the performances of the optomechanical system, we studied optomechanical entanglement and phonon cooling. It is demonstrated that the optomechanical entanglement overwhelmed by thermal phonon excitations could be restored via dissipation engineering. For the phonon cooling, an order of magnitude improvement could be achieved. Our scheme can be generalized to other systems with multiple bosonic modes, which is experimentally feasible with advances in materials and nanofabrication, including optical Fabry-Perot cavities, superconducting circuits, and nanobeam photonic crystals., Comment: 8 pages, 6 figures

Cooling microwave resonators to near the quantum ground state, crucial for their operation in the quantum regime, is typically achieved by direct device refrigeration to a few tens of millikelvin. However, in quantum experiments that require high operation power such as microwave-to-optics quantum transduction, it is desirable to operate at higher temperatures with non-negligible environmental thermal excitations, where larger cooling power is available. In this Letter, we present a radiative cooling protocol to prepare a superconducting microwave mode near its quantum ground state in spite of warm environment temperatures for the resonator. In this proof-of-concept experiment, the mode occupancy of a 10-GHz superconducting resonator thermally anchored at 1.02~K is reduced to $0.44\pm0.05$ by radiatively coupling to a 70-mK cold load. This radiative cooling scheme allows high-operation-power microwave experiments to work in the quantum regime, and opens possibilities for routing microwave quantum states to elevated temperatures.

The construction of photon-photon quantum phase gate based on photonic nonlinearity has long been a fundamental issue, which is vital for deterministic and scalable photonic quantum information processing. It requires not only strong nonlinear interaction at the single-photon level, but also suppressed phase noise and spectral entanglement for high gate fidelity. In this paper, we propose that high-quality factor microcavity with strong $\chi^{(2)}$ nonlinearity can be quantized to anharmonic energy levels and be effectively treated as an artificial atom. Such artificial atom has a size much larger than the photon wavelength, which enables passive and active ultra-strong coupling to traveling photons. High-fidelity quantum control-phase gate is realized by mediating the phase between photons with an intermediate artificial atom in a photonic molecule structure. The scheme avoids the two-photon emission and thus eliminates the spectral entanglement and quantum phase noises. Experimental realization of the artificial atom can be envisioned on the integrated photonic chip and holds great potential for single-emitter-free, room-temperature quantum information processing., Comment: 16 Pages,3 figures

Synthetic gauge fields have recently emerged, arising in the context of quantum simulations, topological matter, and the protected transportation of excitations against defects. For example, an ultracold atom experiences a light-induced effective magnetic field when tunnelling in an optical lattice, and offering a platform to simulate the quantum Hall effect and topological insulators. Similarly, the magnetic field associated with photon transport between sites has been demonstrated in a coupled resonator array. Here, we report the first experimental demonstration of a synthetic gauge field in the virtual dimension of bosonic modes in a single optomechanical resonator. By employing degenerate clockwise (CW) and counter-clockwise (CCW) optical modes and a mechanical mode, a controllable synthetic gauge field is realized by tuning the phase of the driving lasers. The non-reciprocal conversion between the three modes is realized for different synthetic magnetic fluxes. As a proof-of-principle demonstration, we also show the dynamics of the system under a fast-varying synthetic gauge field. Our demonstration not only provides a versatile and controllable platform for studying synthetic gauge fields in high dimensions but also enables an exploration of ultra-fast gauge field tuning with a large dynamic range, which is restricted for a magnetic field., Comment: 6 pages, 3 figures