Degenerate Optical Parametric Oscillator Research Articles

5-bit all-optical quantum random number generator based on a time-multiplexed optical parametric oscillator.

Random numbers are of critical importance in many applications, including secure communication, photonics computing and cryptography. Due to the non-deterministic nature of the quantum processes, a degenerate optical parametric oscillator (DOPO) constitutes a solution to produce true randomness. Nevertheless, one of the existing challenges for DOPO in this field is bit sequence scalability. Here, we experimentally report on the generation of 5-bit random number streams in a time-multiplexed femtosecond DOPO system. A multi-pass cell is added to elongate the OPO cavity to scale up the bit sequences. To this end, for a ∼15 m long all free space OPO cavity, resonating 5 signal pulses with a repetition rate of 50 MHz is demonstrated. The above-threshold binary phase nature originates from vacuum fluctuations of a DOPO ensuring the randomness of the system. The phase state of the output is characterized by the interference pattern between the output pulses and the fundamental pump pulses. Different bit sequences are presented here by turning on and off the OPO. Conditional probability is performed to verify the randomness of the output for 1200 bits. Our scheme provides a new direction for an all-optical random number generator.

Combinatorial optimization solving by coherent Ising machines based on spiking neural networks

Spiking neural network is a kind of neuromorphic computing that is believed to improve the level of intelligence and provide advantages for quantum computing. In this work, we address this issue by designing an optical spiking neural network and find that it can be used to accelerate the speed of computation, especially on combinatorial optimization problems. Here the spiking neural network is constructed by the antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. A nonlinear transfer function is chosen to mitigate amplitude inhomogeneities and destabilize the resulting local minima according to the dynamical behavior of spiking neurons. It is numerically shown that the spiking neural network-coherent Ising machines have excellent performance on combinatorial optimization problems, which is expected to offer new applications for neural computing and optical computing.

A quantum algorithm for finding collision-inducing disturbance vectors in SHA-1

Modern cryptographic protocols rely on sophisticated hash functions to generate quasi-unique numbers that serve as signatures for user authentication and other security verifications. The security could be compromised by finding texts hash-mappable to identical numbers, forming so-called collision attack. Seeding a disturbance vector in the hash mapping to obtain a successful collision is that a major focus of cryptography study in the past two decades to improve hash protocols. We propose an algorithm that takes advantage of entangled quantum states for concurrent seeding of candidate disturbance vectors, out of which the one entailing collision is selected through a combination of quantum search, phase gating, diffusion gating, and information feedbacks from classical computing machinery. The complexity reduction is shown to be on the order of where n is the number of qubits encoding addresses. We demonstrate the practicality of the proposed by an implementation scheme based on degenerate optical parametric oscillators.

Dissipative solitons characterization in singly resonant optical parametric oscillators: A variational formalism

In this work, the emergence of single-peak temporal dissipative solitons in singly-resonant degenerate optical parametric oscillators is investigated analytically. Applying the Kantarovitch optimization method, through a Lagrangian variational formalism, an approximate analytical soliton solution is computed using a parameter-dependent ansatz. This permits to obtain analytical estimations for the DS energy, peak power, and boundaries of the DS existence region, which are of great value for experimentalist. To confirm the validity of this procedure, these analytical results are compared with a numerical study performed in the context of pure quadratic systems, showing a good agreement.

Monolithically integrated femtosecond optical parametric oscillators

Synchronously pumped optical parametric oscillators (OPOs) are highly efficient sources of long-wavelength pulses and nonclassical light, making them invaluable for applications in spectroscopy, metrology, multi-photon microscopy, and quantum computation. Typical systems based on free-space cavities either operate non-degenerately, which limits their efficiency, or use active feedback control to achieve degenerate operation, which limits these systems to dedicated low-noise environments. In this work, we demonstrate a femtosecond monolithically integrated OPO. In contrast with bulk OPOs, our monolithic 10 GHz cavity, based on reverse-proton-exchanged lithium niobate, operates stably without active locking. By detuning the repetition rate of the free-running pump laser from the cavity free spectral range, we control the intracavity pulse dynamics and observe many of the operating regimes previously encountered in free-space degenerate OPOs, such as box-pulsing and quadratic bright-dark solitons (simultons), in addition to non-degenerate operation. When operated in the simulton regime and pumped with 125 fs pulses at 1 µm, this monolithic OPO chip outputs broadband sech2 pulses (63 nm, 3 dB) with tens of milliwatts of average power.

Experimental observation of chimera states in spiking neural networks based on degenerate optical parametric oscillators

The phenomenon of partial synchronization has attracted significant interest in the field of nonlinear dynamics, largely due to observations of related phenomena in real-world situations. In particular, the coexistence of synchronized and desynchronized phases, known as a chimera state, has been the subject of intense study. In this work, we experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate optical parametric oscillators can exhibit various chimera states in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode shift induces a significant change in the spiking frequency despite all neurons having the same natural spiking frequency, which encourages the generation of chimera states.

Depletion-limited Kerr solitons in singly resonant optical parametric oscillators.

We analyze the impact of pump depletion in the generation of parametrically driven Kerr cavity solitons in a degenerate optical parametric oscillator. Using variational methods, we derive an analytical expression that describes the soliton existence region. We use this expression to study the energy conversion efficiency and compare it to a linearly driven Kerr resonator modeled by the Lugiato-Lefever equation. Parametric driving is more efficient at high walk-off between the continuous wave driving and the soliton.

Observing a Phase Transition in a Coherent Ising Machine

A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of the spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the obtained temperature, we confirmed that the thermodynamic quantities obtained with the CIM exhibited a phase-transition-like behavior that better matches the analytical and numerical results than the mean field one.

Robust Pulse-Pumped Quadratic Soliton Assisted by Third-Order Nonlinearity

The generation of a quadratic soliton in a pulse-pumped microresonator has attracted significant interest in recent years. The strong second-order nonlinearity and high peak power of pumps offer a straightforward way to increase efficiency. In this case, the influence of the third-order nonlinearity effect becomes significant and cannot be ignored. In this paper, we study the quadratic soliton in a degenerate optical parametric oscillator driven synchronously by the pulse pump with third-order nonlinearity. Our simulations verify that the robustness of quadratic soliton generation is enhanced when the system experiences a perturbation from pump power, cavity detuning, and pump pulse width. These results represent a new way of manipulating frequency comb in resonant microphotonic structures.

Phase-locked degenerate backward wave optical parametric oscillator

We report a self-phase-locked and degenerate backward wave optical parametric oscillator (BWOPO) generating a counterpropagating signal and an idler in the spectral band of optical communication. The device is based on a periodically poled Rb-doped KTiOPO4 crystal with a poling period of 433 nm. To the best of our knowledge, this is the shortest quasi-phase matching period reported in the bulk of a ferroelectric crystal. The spectral and coherence properties of the BWOPO at degeneracy are investigated. We observe a single pass conversion efficiency of 40%. At degeneracy, the counterpropagating signal and idler generate phase-matched sum-frequency generation in both directions. We confirm the phase-locked state at degeneracy by interfering the pump with the frequency-doubled backward wave. The phase-locked state is stable during the entire duration of the experiment without active stabilization.

Speed-up coherent Ising machine with a spiking neural network.

Coherent Ising machine (CIM) is a hardware solver that simulates the Ising model and finds optimal solutions to combinatorial optimization problems. However, for practical tasks, the computational process may be trapped in local minima, which is a key challenge for CIM. In this work, we design a CIM structure with a spiking neural network by adding dissipative pulses, which are anti-symmetrically coupled to the degenerate optical parametric oscillator pulses in CIM with a measurement feedback system. We find that the unstable oscillatory region of the spiking neural network could assist the CIM to escape from the trapped local minima. Moreover, we show that the machine has a different search mechanism than CIM, which can achieve a higher solution success probability and speed-up effect.

Control of amplitude homogeneity in coherent Ising machines with artificial Zeeman terms

A coherent Ising machine (CIM) is an open-dissipative Ising solver using optical pulses generated from a degenerate optical parametric oscillator as analog magnetizations. When solving real-world optimization problems with CIM, this solver has two difficulties: mutual coupling induced amplitude inhomogeneity and absence of natural way to implement Zeeman terms. For the approximate Gaussian formulation of CIMs with amplitude control feedback, we add artificial Zeemam terms using the target amplitude information. Here we show, for 16-spin CIM with Zeeman terms, the amplitude control increases the performance, particularly when Zeeman terms are competing against mutual coupling coefficients.

Potts model solver based on hybrid physical and digital architecture

The Potts model describes Ising-model-like interacting spin systems with multivalued spin components, and ground-state search problems of the Potts model can be efficiently mapped onto various integer optimization problems thanks to the rich expression of the multivalued spins. Here, we demonstrate a solver of this model based on hybrid computation using physical and digital architectures, wherein a digital computer updates the interaction matrices in the iterative calculations of the physical Ising-model solvers. This update of interactions corresponds to learning from the Ising solutions, which allows us to save resources when embedding a problem in a physical system. We experimentally solved integer optimization problems (graph coloring and graph clustering) with this hybrid architecture in which the physical solver consisted of coupled degenerate optical parametric oscillators.

L0 regularization-based compressed sensing with quantum–classical hybrid approach

L0-regularization-based compressed sensing (L0-RBCS) has the potential to outperform L1-regularization-based compressed sensing (L1-RBCS), but the optimization in L0-RBCS is difficult because it is a combinatorial optimization problem. To perform optimization in L0-RBCS, we propose a quantum–classical hybrid system consisting of a quantum machine and a classical digital processor. The coherent Ising machine (CIM) is a suitable quantum machine for this system because this optimization problem can only be solved with a densely connected network. To evaluate the performance of the CIM-classical hybrid system theoretically, a truncated Wigner stochastic differential equation (W-SDE) is introduced as a model for the network of degenerate optical parametric oscillators, and macroscopic equations are derived by applying statistical mechanics to the W-SDE. We show that the system performance in principle approaches the theoretical limit of compressed sensing and this hybrid system may exceed the estimation accuracy of L1-RBCS in actual situations, such as in magnetic resonance imaging data analysis.

Mid-IR optical parametric oscillation and second harmonic generation of repetitively pulsed output of a fibre-laser pumped Tm3+ :YAP laser in a fan-out periodically poled MgO:LiNbO3 crystal

The nonlinear optical frequency conversions of repetitively pulsed output of a 1941-nm Tm3+ : YAP laser pumped by a cw 1670-nm fibre laser are studied experimentally. Both mid-IR optical parametric oscillation (OPO) and second harmonic generation (SHG) are obtained in the same periodically poled MgO : LiNbO3 crystal with a fan-out domain design by tuning the grating period and temperature. The energy conversion efficiency of the degenerate OPO at 3820 – 3970 nm exceeds 43 % at a 0.5 kHz repetition rate, while the energy conversion efficiency of SHG at 970.5 nm reaches 34 %.

Ultrashort pulse generation from continuous-wave driven degenerate optical parametric oscillators

Degenerate <inline-formula><tex-math notation="LaTeX">$\chi ^{(2)}$</tex-math></inline-formula> optical parametric oscillators (OPOs) pumped by continuous-wave (cw) lasers in bulk or integrated format represent a promising platform for the study of classical as well as quantum phenomena, enabling interesting applications such as squeezing and random number generation. When subjected to phase modulation, such devices can generate ultrashort output pulses. In this report, we study pulse generation and spectral broadening in degenerate OPOs with intracavity electro-optic modulator (EOM). We numerically investigate ultrashort pulse generation from a cw-driven degenerate OPO based on MgO:PPLN as the nonlinear gain medium. The phase sensitive gain provided by the quadratic nonlinear medium in a detuned cavity and the inherent self-phase-locking of the degenerate field with that of the pump govern the signal amplification. Using high-performance computing tools, we study the full intracavity complex field evolution over 10000 round trips, as the OPO reaches the steady state. Taking advantage of the high nonlinear gain and low threshold of degenerate OPO, and using an intracavity EOM synchronized to the free-spectral-range of the cavity in combination with spectral filtering, we show that a stable, uniform, and periodic train of picosecond pulses of <inline-formula><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula>5 ps duration with FWHM spectral bandwidth of 0.4 THz can be generated. The results of our theoretical model are valid for <inline-formula><tex-math notation="LaTeX">$\chi ^{(2)}$</tex-math></inline-formula> OPOs in bulk and integrated format.

Experimental scheme of non-critical squeezed light field detection

The squeezed state, as an important quantum resource, has great potential applications in quantum computing, quantum communication and precision measurement. In the noncritically squeezed light theory, the predicted noncritically squeezed light can be generated by breaking the spontaneous rotational symmetry occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. The reliability of this kind of squeezing is crucially important, as its quantum performance is robust to the pump power in experiment. However, the detected squeezing degrades rapidly in detection, because the squeezed mode orientation diffuses slowly, resulting in a small mode mismatch during the homodyne detection. In this paper, we propose an experimentally feasible scheme to detect noncritically squeezing reliable by employing the spatial mode swapping technic. Theoretically, the dynamic fluctuation aroused by random mode rotation in the squeezing detection can be compensated for perfectly, and 3 dB squeezing can be achieved robustly even with additional vacuum noise. Our scheme makes an important step forward for the experimental generation of noncritically squeezed light.

Dynamic control of photon lifetime for quantum random number generation

In a passive cavity geometry, there exists a trade-off between resonant enhancement and response time, which is inherently limited by the cavity photon lifetime. We demonstrate frequency-selective, dynamic control of the photon lifetime using a silicon-nitride coupled-ring resonator. The photon lifetime is tuned by controlling an avoided mode crossing using thermo-optic tuning of the cavity resonance with integrated heaters. Using this effect, we achieve fast turn-on/off of a χ ( 3 ) degenerate optical parametric oscillator (DOPO) and on-chip true random number generation. Our approach allows us to overcome the Q -limited generation rate of a single-ring-based DOPO and offers a path toward the development of a scalable integrated high-quality entropy source for modern cryptographic systems.

Generating and detecting entangled cat states in dissipatively coupled degenerate optical parametric oscillators

Non-Gaussian continuous variable states play a central role both in the foundations of quantum theory and for emergent quantum technologies. In particular, "cat states", i.e., two-component macroscopic quantum superpositions, embody quantum coherence in an accessible way and can be harnessed for fundamental tests and quantum information tasks alike. Degenerate optical parametric oscillators can naturally produce single-mode cat states and thus represent a promising platform for their realization and harnessing. We show that a dissipative coupling between degenerate optical parametric oscillators extends this to two-mode entangled cat states, i.e., two-mode entangled cat states are naturally produced under such dissipative coupling. While overcoming single-photon loss still represents a major challenge towards the realization of sufficiently pure single-mode cat states in degenerate optical parametric oscillators, we show that the generation of two-mode entangled cat states under such dissipative coupling can then be achieved without additional hurdles. We numerically explore the parameter regime for the successful generation of transient two-mode entangled cat states in two dissipatively coupled degenerate optical parametric oscillators. To certify the cat-state entanglement, we employ a tailored, variance-based entanglement criterion, which can robustly detect cat-state entanglement under realistic conditions.

Accuracy-enhanced coherent Ising machine using the quantum adiabatic theorem.

The coherent Ising machine (CIM) implemented by degenerate optical parametric oscillator (DOPO) networks is a novel optical platform to accelerate computation of hard combinatorial optimization problems. Nevertheless, with the increase of the problem size, the probability of the machine being trapped by local minima increases exponentially. According to the quantum adiabatic theorem, a physical system will remain in its instantaneous ground state if the time-dependent Hamiltonian varies slowly enough. Here, we propose a method to help the machine partially avoid getting stuck in local minima by introducing quantum adiabatic evolution to the ground-state-search process of the CIM, which we call A-CIM. Numerical simulation results demonstrate that A-CIM can obtain improved solution accuracy in solving MAXCUT problems of vertices ranging from 10 to 2000 than CIM. The proposed machine that is based on quantum adiabatic theorem is expected to solve optimization problems more correctly.