Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator

All-optical Stern-Gerlach effect in the time domain

The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.

Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension

Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non-Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.

Probing ultra-fast dephasing via entangled photon pairs

We demonstrate how the Hong-Ou-Mandel (HOM) interference with polarization-entangled photons can be used to probe ultrafast dephasing. We can infer the optical properties like the real and imaginary parts of the complex susceptibility of the medium from changes in the position and the shape of the HOM dip. From the shift of the HOM dip, we are able to measure 22 fs dephasing time using a continuous-wave (CW) laser even with optical loss > 97 %, while the HOM dip visibility is maintained at 92.3 % (which can be as high as 96.7 %). The experimental observations, which are explained in terms of a rigorous theoretical model, demonstrate the utility of HOM interference in probing ultrafast dephasing.

On-chip electro-optic frequency shifters and beam splitters

Efficient frequency shifting and beam splitting are important for a wide range of applications, including atomic physics^1,2, microwave photonics^3-6, optical communication^7,8 and photonic quantum computing^9-14. However, realizing gigahertz-scale frequency shifts with high efficiency, low loss and tunability-in particular using a miniature and scalable device-is challenging because it requires efficient and controllable nonlinear processes. Existing approaches based on acousto-optics^6,15-17, all-optical wave mixing^10,13,18-22 and electro-optics^23-27 are either limited to low efficiencies or frequencies, or are bulky. Furthermore, most approaches are not bi-directional, which renders them unsuitable for frequency beam splitters. Here we demonstrate electro-optic frequency shifters that are controlled using only continuous and single-tone microwaves. This is accomplished by engineering the density of states of, and coupling between, optical modes in ultralow-loss waveguides and resonators in lithium niobate nanophotonics²⁸. Our devices, consisting of two coupled ring-resonators, provide frequency shifts as high as 28 gigahertz with an on-chip conversion efficiency of approximately 90 per cent. Importantly, the devices can be reconfigured as tunable frequency-domain beam splitters. We also demonstrate a non-blocking and efficient swap of information between two frequency channels with one of the devices. Finally, we propose and demonstrate a scheme for cascaded frequency shifting that allows shifts of 119.2 gigahertz using a 29.8 gigahertz continuous and single-tone microwave signal. Our devices could become building blocks for future high-speed and large-scale classical information processors^7,29 as well as emerging frequency-domain photonic quantum computers^9,11,14.

Two-photon scattering and correlation in a four-terminal waveguide system

Scattering and correlation properties of a two-photon (TP) pulse are studied in a four-terminal waveguide system, i.e., two one-dimensional waveguides connected by a Jaynes-Cummings emitter (JCE). The wave function approach is utilized to exactly calculate the real-time dynamic evolution of the TP transport. When the width of the incident TP Gaussian pulse is much larger than the photon wavelength, the TP transmission spectra approach that of the corresponding single photon cases and are almost independent of the pulse width. On the contrary, as the pulse width is comparable to the photon wavelength, the TP transmission and correlation both show strong dependence on the pulse width. The resonant scattering due to the JCE and the photon interference together determine the TP correlation. When the distance between the TPs is small, the TP correlations between any two terminals for the scattered TP pulse are much different from those for the incident TP pulse and therefore, such a four-terminal waveguide system provides a way to control the TP correlation.

Tunable frequency matching for efficient four-wave-mixing Bragg scattering in microrings

We propose and theoretically study a tunable frequency matching method for four-wave-mixing Bragg-scattering frequency conversion in microring resonators. A tunable coupling between the clockwise and counterclockwise propagating modes in the resonators was designed to introduce adjustable mode splitting, thus compensating for the frequency mismatching under different wavelengths. Using a silicon nitride ring resonator as an example, we showed that the tuning bandwidth approaches 35 number of FSRs. Numerical simulations further revealed that the phase-matching strategy is valid under different wavelength combinations and is robust to variations in waveguide geometry and fabrication. These results suggest promising applications in high-efficiency frequency conversion, integrated nonlinear photonics, and quantum optics.

Arbitrary linear transformations for photons in the frequency synthetic dimension

Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.

Generating arbitrary topological windings of a non-Hermitian band

The nontrivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature of non-Hermitian systems is the nontrivial winding of the energy band in the complex energy plane. We provide experimental demonstrations of such nontrivial winding by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations, and by directly characterizing the complex band structures. Moreover, we show that the topological winding can be controlled by changing the modulation waveform. Our results allow for the synthesis and characterization of topologically nontrivial phases in nonconservative systems.

Fully Arbitrary Control of Frequency-Bin Qubits

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.