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Optomechanical systems are known to exhibit self-sustained limit cycles once driven above the parametric instability point. By increasing the driving in the unresolved sideband limit, they reach chaotic regime through the cascaded period doubling process. Here, we study classical nonlinear dynamics of optomechanical systems operating in the resolved sideband regime ( ω m / κ ≫ 1 ) having a high mechanical Q - factor. We combine numerical simulations and analytical calculations to predict new nonlinear phenomena, so far unexplored in optomechanics. In the regime of single optical mode in the cavity, we connect the dynamical multistability to the hidden attractors, i.e., stable periodic state whose basin of attraction does not overlap with the neighbourhood of an unstable equilibrium point. In the regime where more than one optical modes are involved, we show that complex dynamics like metamorphoses of basin boundaries take place. These metamorphoses, which are revealed through the creation (or disappearance) of some new (or old) basin sets, are induced via the increase of the input driving field. Interestingly, we point out also the frequency locking effect which prevents all routes to chaos in the system. However, the locking range shrinks rapidly as the optical linewidth increases. The concept of hidden attractors introduced here provides new opportunities to generate nonclassical states. Moreover, the frequency locking effect can be useful for stable clock oscillations, for metrological applications and to control oscillations in optomechanics.

This paper presents a voltage-controlled phase shifter (VCPS) capable of 360° continuous adjustment, applied in laser frequency-locking systems to obtain maximum amplitude error signals with minimal dispersion. The phase-shifting unit is realized through CMOS integrated circuit design, utilizing comparators, logic gate control modules, and filters. Simulations verify the VCPS, composed of three cascaded units, achieves 360° continuous phase adjustment. A printed circuit board (PCB) was fabricated with the integration of electronic components. The test results demonstrate that the VCPS exhibits a continuous 360° phase shift in one direction with increasing control voltage. It operates from kHz to 50 MHz and maintains a peak-to-peak output amplitude of 5 V or 10 V. The proposed VCPS has been successfully applied in cold-atom interferometry, quantum memory experiments, and optical frequency standards.

The basic principle of quantum mechanics1 guarantees the unconditional security of quantum key distribution (QKD)2–6 at the cost of forbidding the amplification of a quantum state. As a result, and despite remarkable progress in worldwide metropolitan QKD networks7,8 over the past decades, a long-haul fibre QKD network without a trusted relay has not yet been achieved. Here, through the sending-or-not-sending protocol9, we achieve twin-field QKD10 and distribute secure keys without any trusted repeater over a 511 km long-haul fibre trunk that links two distant metropolitan areas. The fibre trunk contains 12 fibres in the cable, three of which are used for the quantum channel, optical synchronization and frequency locking, respectively. The remaining nine are used for classical fibre communication. Our secure key rate is around three orders of magnitude greater than that expected if the previous QKD field-test system was applied over the same length. Efficient quantum-state transmission and stable single-photon interference over such a long-haul deployed fibre pave the way to large-scale fibre quantum networks.A field test of twin-field quantum key distribution was implemented through a 511 km optical fibre. To this end, precise wavelength control of remote independent laser sources and fast time- and phase-compensation systems are developed.

The effect of time-delayed feedback and fast harmonic excitation (FHE) on stationary periodic vibration and quasi-periodic responses in a parametric and self-excited weakly nonlinear oscillator is analyzed in this paper. The method of direct partition of motion and two stages of multiple scales analysis are conducted to obtain analytical approximation for quasi-periodic oscillation envelopes and frequency-locking area near primary resonance. A parameter study shows that, in the absence or the presence of high-frequency excitation, time-delayed feedback may reduce significantly the amplitude and the envelopes of quasi-periodic oscillations leading to a quasi synchronization of the response over the whole frequency range around the resonance. The results presented for the parameters tested agree well with results obtained by numerical simulation.

We report a coherent tri-frequency microwave signal generation approach using an optoelectronic oscillator (OEO). In the previous literature, the OEO-based schemes can only generate coherent microwave signals with dual frequencies. In this work, we demonstrate that the generation of coherent tri-frequency microwave signals is also possible using an OEO loop. The key component in our scheme is a tri-passband electrical filter, which has a narrow passband in the middle and two wide passbands on both sides. The OEO loop initially oscillates at the central frequency of the narrow passband with a single-tone f1. By injecting a microwave signal, finj, into the OEO loop, down- and up-converted microwave signals at frequencies of f2 = f1 − finj and f3 = f1 + finj, respectively, are generated by frequency mixing in a microwave mixer. The two wide passbands of the electrical filter allow the oscillation of the converted signals at a wide frequency bandwidth by simply tuning the frequency of the injected signal. Moreover, the tri-frequency microwave signals are phase-locked through frequency mixing and mutual injection locking. The proposed scheme is theoretically analyzed and experimentally validated. In the experiments, coherent tri-frequency microwave signals with low phase noise are successfully generated at a fixed frequency of 14 GHz and two tunable frequency ranges from 9 to 12 GHz and from 16 to 19 GHz, respectively.

Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The demonstration of soliton formation via self-injection locking of the pump laser to the microresonator has significantly relaxed the requirement on the external driving lasers. Yet to date, the nonlinear dynamics of this process has not been fully understood. Here, we develop an original theoretical model of the laser self-injection locking to a nonlinear microresonator, i.e., nonlinear self-injection locking, and construct state-of-the-art hybrid integrated soliton microcombs with electronically detectable repetition rate of 30 GHz and 35 GHz, consisting of a DFB laser butt-coupled to a silicon nitride microresonator chip. We reveal that the microresonator’s Kerr nonlinearity significantly modifies the laser diode behavior and the locking dynamics, forcing laser emission frequency to be red-detuned. A novel technique to study the soliton formation dynamics as well as the repetition rate evolution in real-time uncover non-trivial features of the soliton self-injection locking, including soliton generation at both directions of the diode current sweep. Our findings provide the guidelines to build electrically driven integrated microcomb devices that employ full control of the rich dynamics of laser self-injection locking, key for future deployment of microcombs for system applications. Self-injection locking of the pump laser for a soliton microcomb has significantly relaxed the requirements for laser drives. Here the authors study self-injection locking in experiment and theory and reveal that the soliton formation is feasible with detunings unreachable according to previous theories.

Soliton microcombs are a promising new approach for photonic-based microwave signal synthesis. To date, however, the tuning rate has been limited in microcombs. Here, we demonstrate the first microwave-rate soliton microcomb whose repetition rate can be tuned at a high speed. By integrating an electro-optic modulation element into a lithium niobate comb microresonator, a modulation bandwidth up to 75 MHz and a continuous frequency modulation rate up to 5.0 × 10 14 Hz/s are achieved, several orders-of-magnitude faster than existing microcomb technology. The device offers a significant bandwidth of up to tens of gigahertz for locking the repetition rate to an external microwave reference, enabling both direct injection locking and feedback locking to the comb resonator itself without involving external modulation. These features are especially useful for disciplining an optical voltage-controlled oscillator to a long-term reference and the demonstrated fast repetition rate control is expected to have a profound impact on all applications of frequency combs. A microwave-rate soliton microcomb whose repetition rate can be modulated at 75 MHz. Moreover, the repetition rate can be locked to an external microwave reference by direct injection locking or feedback locking without external modulation.

The past decade has witnessed major advances in the development and system-level applications of photonic integrated microcombs, that are coherent, broadband optical frequency combs with repetition rates in the millimeter-wave to terahertz domain. Most of these advances are based on harnessing of dissipative Kerr solitons (DKS) in microresonators with anomalous group velocity dispersion (GVD). However, microcombs can also be generated with normal GVD using localized structures that are referred to as dark pulses, switching waves or platicons. Compared with DKS microcombs that require specific designs and fabrication techniques for dispersion engineering, platicon microcombs can be readily built using CMOS-compatible platforms such as thin-film (i.e., thickness below 300 nm) silicon nitride with normal GVD. Here, we use laser self-injection locking to demonstrate a fully integrated platicon microcomb operating at a microwave K-band repetition rate. A distributed feedback (DFB) laser edge-coupled to a Si 3 N 4 chip is self-injection-locked to a high- Q ( > 10 7 ) microresonator with high confinement waveguides, and directly excites platicons without sophisticated active control. We demonstrate multi-platicon states and switching, perform optical feedback phase study and characterize the phase noise of the K-band platicon repetition rate and the pump laser. Laser self-injection-locked platicons could facilitate the wide adoption of microcombs as a building block in photonic integrated circuits via commercial foundry service. ’Here the authors provide the demonstration of platicon comb generation in an integrated photonic chip using laser self-injection locking, They take advantage of platicons generation in normal GVD resonators, which significantly relaxes the material and geometry design restrictions

Photonic generation of Terahertz (THz) carriers displays high potential for THz communications with a large tunable range and high modulation bandwidth. While many photonics-based THz generations have recently been demonstrated with discrete bulky components, their practical applications are significantly hindered by the large footprint and high energy consumption. Herein, we present an injection-locked heterodyne source based on generic foundry-fabricated photonic integrated circuits (PIC) attached to a uni-traveling carrier photodiode generating high-purity THz carriers. The generated THz carrier is tunable within the range of 0–1.4 THz, determined by the wavelength spacing between the two monolithically integrated distributed feedback (DFB) lasers. This scheme generates and transmits a 131 Gbits −1 net rate signal over a 10.7-m distance with −24 dBm emitted power at 0.4 THz. This monolithic dual-DFB PIC-based THz generation approach is a significant step towards fully integrated, cost-effective, and energy-efficient THz transmitters. A photonic Terahertz source based on injection-locking an integrated dual-laser chip generates and transmits a 131 Gbps THz signal over 10.7-m distance, showing great potential towards fully integrated and energy-efficient THz transmitters for 6G.

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete time-translation symmetry in periodically-forced physical systems can create a discrete time crystal (DTC) constituting a state of matter possessing properties like temporal rigid long-range order and coherence, which are inherently desirable for quantum computing and information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and significant aspects of their behavior remain unexplored. Here, we report the experimental observation and theoretical investigation of DTCs in a Kerr-nonlinear optical microcavity. Empowered by the self-injection locking of two independent lasers with arbitrarily large frequency separation simultaneously to two same-family cavity modes and a dissipative Kerr soliton, this versatile platform enables realizing long-awaited phenomena such as defect-carrying DTCs and phase transitions. Combined with monolithic microfabrication, this room-temperature system paves the way for chip-scale time crystals supporting real-world applications outside sophisticated laboratories. Discrete time crystals are described by a subharmonic response with respect to an external drive and have been mostly observed in closed periodically-driven systems. Here, the authors demonstrate a dissipative discrete time crystal in a Kerr-nonlinear optical microcavity pumped by two lasers.