Nondegenerate Optical Parametric Oscillator Research Articles

Squeezing and EPR correlations in divide-by-3 self-phase-locked optical parametric oscillators

We analyze the dynamics, two-mode squeezing as well as Einstein–Podolsky–Rozen (EPR) correlations of the signal–idler beams in a cavity with two resonant cascaded nonlinear crystals. The subharmonic system is trifurcated and self-phase-locked, and enables the existence of stable steady bright-beam/dark-beam solutions, leading to different properties of squeezing and EPR correlations. Compared with conventional nondegenerate optical parametric oscillators, our results can be helpful to quantum information processing as well metrology.

Antibunched photon-pair source based on photon blockade in a nondegenerate optical parametric oscillator

Nonclassical light sources, such as correlated photon-pairs, play an important role in quantum optics and quantum information processing systems. This study proposes a process to generate antibunched photon-pairs in a nondegenerate optical parametric oscillator. It is found that when the parameters of the system satisfy certain conditions, the generated photons in subharmonic modes exhibit a strong antibunching behavior and are strongly correlated with one another. In particular, the average photon-pair number is resonantly enhanced. It is also observed that the conventional photon blockade contributes to this phenomenon. In addition, it is interesting to note that fundamental mode photons can blockade the subharmonic mode photons. We refer to this phenomenon as a heterogeneous photon blockade.

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators.

We analytically and numerically show that the Hillery-Zubairy’s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

Symbiotic quadratic soliton mode-locked non-degenerate optical parametric oscillators.

We analytically and numerically unveil the existence condition of symbiotic solitons in doubly resonant non-degenerate optical parametric oscillators. Resonant signal and idler with terahertz comb bandwidth and femtosecond pulse duration in the mid-infrared are attainable through this symbiotic soliton mode-locking technique. The group velocity mismatches between the three interacting waves are the dominant cause of the symbiotic soliton perturbation, and their effects are numerically investigated in detail. The principle can be applied to commonly used mid-infrared material platforms, making it a competitive ultrashort pulse and broadband comb source architecture.

Frequency-dependent squeezing generation with EPR entanglement

The sensitivity of gravitational wave interferometric detectors is ultimately limited by the quantum noise, which arises from the quantum nature of light and it is driven by vacuum fluctuations of the optical field entering from the dark port of the interferometer. One way to improve the sensitivity of gravitational wave interferometers is to inject squeezed vacuum into the dark port. This has been already demonstrated for the main gravitational wave detectors (GEO, Advanced LIGO and Advanced VIRGO). We are studying tricks to produce a “frequency- dependent squeezing”: a standard method is to filter the squeezed optical field with one or more optical cavities (300 m long cavities). An alternative method using a pair of squeezed EPR (Einstein-Podolsky-Rosen) entangled beams to produce frequency-dependent squeezing by a non-degenerate OPO (Optical Parametric Oscillator) will be discussed in this paper. This method promises to achieve a frequency-dependent optimization of the injected squeezed light fields without the need for an external filter cavity.

Generating robust entanglement via quantum feedback

Generating entangled states is one of the most important tasks in quantum information technology. However, in reality any entanglement generator must contain some characteristic uncertainty, and as a result the produced entangled state becomes an undesirable mixed state. This paper develops a coherent feedback control scheme that suppresses the characteristic uncertainty of a typical entanglement generator (the non-degenerate optical parametric oscillator) for producing robust Gaussian entangled states. In particular, we examine a two-mode squeezed state and Gaussian four-mode cluster states to demonstrate the effectiveness of the proposed control method.

Exact solution of degenerate and nondegenerate optical parametric oscillator coupled with a squeezed thermal bath

We solve exactly the master equation of the degenerate and nondegenerate parametric oscillator in the presence of a squeezed reservoir. We show that the formal solutions of both systems can be obtained in terms of the density operator by applying squeeze transformations and using the superoperators formalism.

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.

Controlled Asymmetry of Einstein-Podolsky-Rosen Steering with an Injected Nondegenerate Optical Parametric Oscillator.

We propose and analyze a nonlinear optical apparatus in which the direction of asymmetric steering is controllable within the apparatus, rather than by adding noise to measurements. Using a nondegenerate parametric oscillator with an injected signal field, we show how the directionality and extent of the steering can be readily controlled for output modes that can be up to one octave apart. The two down-converted modes, which exhibit the greater violations of the steering inequalities, can also be controlled to exhibit asymmetric steering in some regimes.

Entanglement analyses of a nondegenerate optical parametric oscillator with a higher-transmissivity cavity mirror

Nondegenerate optical parametric oscillator (NOPO) above threshold is a simple set-up to generate entangled beams. To more accurately calculate the entanglement between the generated twin beams from the NOPO, we use the Langevin equations for the NOPO with a higher-transmissivity cavity mirror. The obtained new expressions for the amplitude-difference and phase-sum noise spectra suggest that increasing the transmissivity of the output mirror can enhance the entanglement beyond the previous expectation.

Quantum random number generator based on twin beams.

We produce two strings of quantum random numbers simultaneously from the intensity fluctuations of the twin beams generated by a nondegenerate optical parametric oscillator. Two strings of quantum random numbers with bit rates up to 60 Mb/s are extracted simultaneously with a suitable post-processing algorithm. By post-selecting the identical data from two raw sequences and using a suitable hash function, we also extract two strings of identical quantum random numbers. The obtained random numbers pass all NIST randomness tests. The presented scheme shows the feasibility of generating quantum random numbers from the intensity of a macroscopic optical field.

Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism

We study the nondegenerate optical parametric oscillator in a planar interferometer near threshold, where critical phenomena are expected. These phenomena are associated with nonequilibrium quantum dynamics that are known to lead to quadrature entanglement and squeezing in the oscillator field modes. We obtain a universal form for the equation describing this system, which allows a comparison with other phase transitions. We find that the unsqueezed quadratures of this system correspond to a two-dimensional XY-type model with a tricritical Lifshitz point. This leaves open the possibility of a controlled experimental investigation into this unusual class of statistical models. We evaluate the correlations of the unsqueezed quadrature using both an exact numerical simulation and a Gaussian approximation, and obtain an accurate numerical calculation of the non-Gaussian correlations.

Experimental quantum state engineering with time-separated heraldings from a continuous-wave light source: A temporal-mode analysis

Conditional preparation is a well-established technique for quantum state engineering of light. A general trend is to increase the number of heralding detection events in such realization to reach larger photon-number states or their arbitrary superpositions. In contrast to pulsed implementations, where detections only occur within the pulse window, for continuous-wave light the temporal separation of the conditioning detections is an additional degree of freedom and a critical parameter. Based on the theoretical study by A.E.B. Nielsen and K. Molmer and on a continuous-wave two-mode squeezed vacuum from a nondegenerate optical parametric oscillator, we experimentally investigate the generation of two-photon state with tunable delay between the heralding events. The present work illustrates the temporal multimode features in play for conditional state generation based on continuous-wave light sources.

Quantum analysis and experimental investigation of the nondegenerate optical parametric oscillator with unequally injected signal and idler

We developed a quantum analysis of the nondegenerate optical parametric oscillator (NOPO) with unequally injected signal and idler. Both the steady-state output field and the two-mode quantum correlation spectrum are investigated under the condition of different injected idler-to-signal ratios (ISRs) and the relative phase between the pump and the injected seed. It is found that when the seed is injected through the output coupler, the NOPO allows for the robust generation of two-mode quantum entanglement even if the relative phase is free running and the ISR is as high as 0.7. At the specific relative phase of zero, a high degree of entanglement can exist across a whole range of ISRs. An experimental study of the NOPO with unequal seeds is presented, and the observed results verify the theoretical predictions.

Direct production of three-color polarization entanglement for continuous variable

The direct generation of discrete-variable three-photon polarization entanglement has been recently demonstrated [Nat. Photonics8, 801 (2014)10.1038/nphoton.2014.218NPAHBY1749-4885]. Here, we propose a feasible scheme to generate continuous-variable (CV) three-color polarization entangled states of light in a deterministic way. The method initially prepares a tripartite quadrature entanglement based on two cascaded nondegenerate optical parametric oscillators. The entangled modes are then coupled, respectively, with three strong coherent optical beams on polarized beam splitters, leading to the generation of the three-color CV polarization entanglement. The polarization entanglement is then verified by inseparability criterion and positive partial transposition criterion. Additionally, optimal parameters in practical conditions are obtained through numerical simulations, which could provide useful guidance for experimental implementations. The demonstrated CV three-color polarization entanglement is suitable in quantum information processing tasks relying on the direct interaction between spin of atoms and polarization of light.

Quantum limits for cascaded nondegenerate optical parametric oscillators

The continuous variable multicolor entangled state of optical modes is one of the essential quantum resources for constructing quantum information networks composed of many nodes and channels. It has been well proved that the cascaded nondegenerate optical parametric oscillators (CNOPOs) are the most successful devices to produce bright entangled optical beams with different wavelengths. Here, we discuss the dependence of the possibly obtained largest-size multicolor entangled state and the entanglement degree on optical parameters of CNOPOs. Each NOPO in the cascaded system is operated above its oscillation threshold. One of two output optical beams produced by a NOPO is used for the pump light of the subsequent one, and the remained another beam serves as a submode of the multicolor entangled state. The obtainable maximal number of entangled submodes and the multicolor entanglement degree are numerically calculated under experimentally accessible conditions. The calculated results provide direct references for the design of generation systems of multicolor entangled optical beams.

Compact picosecond nondegenerate four-wave mixing mirrorless optical parametric oscillator in silicon waveguide

The compact picosecond nondegenerate four-wave mixing mirrorless optical parametric oscillator based on multimode silicon waveguide is proposed and investigated numerically. Two counterpropagating picosecond pulses of fundamental mode can generate new pulses of second-order mode at different wavelengths due to the large modal dispersion between the fundamental mode and the second-order mode. The frequency of the newly generated waves can be tuned to 0.6 THz by adjusting the pump frequency difference of 5 THz. The output signal wave exhibits pulse width of 50 ps when the pump pulse is 100 ps. The proposed mirrorless optical parametric oscillator exhibits compact configuration and low threshold, which can find important applications in integrated optical source and ultrafast all-optical signal processing.

Bright three-color entangled state produced by cascaded optical parametric oscillators

We propose a generation system of continuous-variable (CV) three-color entangled state of bright optical beams based on two cascaded standard nondegenerate optical parametric oscillators (NOPOs) above the threshold. One of signal and idler beams produced by the first NOPO is used for the pump light of the second NOPO. The three-color entanglement among signal and idler beams produced by the second NOPO and the retained another beam of the first NOPO is theoretically demonstrated. The symplectic eigenvalues of the partial transposition covariance matrix of the generated optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions of the cascaded NOPOs system for obtaining high entanglement are found. The calculated results explicitly demonstrate that the OPO action can transfer entanglement. Due to that the cavity parameters and the nonlinear crystals of the two NOPOs can be freely chosen, the flexibility of the proposed protocol is relatively good and the system can be also extended to prepare entangled states with more parts easily.

Analysis of directly produce pump, signal, and idler three-color continuous-variable entanglement

Analysis is presented in this paper to directly produce three-color continuous-variable (CV) entanglement by nondegenerate optical parametric oscillator (NOPO) with an injected signal. The quantum entanglement among the pump, signal, and idler beams are calculated by applying sufficient inseparability criteria for CV entanglement which proposed by van Loock and Furusawa [Phys. Rev. A 67, 052315 (2003)]. The results indicates that strong three-color CV entangled beams, i.e. pump, signal, and idler beams, can be generated when the NOPO operating above the threshold. The degree of entanglement dependence on damping rates is also investigated.

Continuous-variable three-color tripartite entangled state generated by a non-degenerate optical parameter oscillator

The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.