Nondegenerate Parametric Amplifier Research Articles

Berry phase and the Mandel parameter of the non-degenerate parametric amplifier

We study the non-degenerate parametric amplifier problem from an algebraic approach of the SU(1,1) group. We write the Hamiltonian of this problem in terms of the boson generators of the SU(1,1) group and the difference operator. We apply the tilting transformation to our results to exactly solve this Hamiltonian and obtain its energy spectrum and eigenfunctions. Then, by assuming that our Hamiltonian is an explicit function of time, we calculate its Berry phase. Finally we obtain the Mandel Q-parameter of the photon numbers n a and n b .

Quadripartite quantum steering generated by single-pass cascaded nonlinear processes

Quantum steering has become an important resource for quantum information due to its unique asymmetry. In this paper, quadripartite quantum steering generated by single-pass nondegenerate optical parametric amplification cascaded with a sum-frequency process is investigated. Firstly, an idler beam is produced by a different-frequency process between pump and signal. Secondly, a sum-frequency beam is generated by a cascaded sum-frequency process between idler beam and pump in the same optical superlattice. Quadripartite quantum steering among pump, signal, idler and sum-frequency beams is demonstrated based on the criterion for multipartite quantum steering. The influences of nonlinear coupling coefficients κ, dimensionless propagation length ξ, and the initial values of pump and signal on the variation characteristic of the quadripartite steering are also investigated. The results indicate that slightly larger nonlinear coupling coefficients of cascaded nonlinear processes and weaker signals can achieve better quadripartite quantum steering. This simple quadripartite quantum steering preparation scheme does not require a resonant cavity and is easier to implement experimentally, with potential applications in quantum communication and computing.

Autonomous Distribution of Programmable Multiqubit Entanglement in a Dual-Rail Quantum Network.

We propose and analyze a scalable and fully autonomous scheme for preparing spatially distributed multiqubit entangled states in a dual-rail waveguide QED setup. In this approach, arrays of qubits located along two separated waveguides are illuminated by correlated photons from the output of a nondegenerate parametric amplifier. These photons drive the qubits into different classes of pure entangled steady states, for which the degree of multipartite entanglement can be conveniently adjusted by the chosen pattern of local qubit-photon detunings. Numerical simulations for moderate-sized networks show that the preparation time for these complex multiqubit states increases at most linearly with the system size and that one may benefit from an additional speedup in the limit of a large amplifier bandwidth. Therefore, this scheme offers an intriguing new route for distributing ready-to-use multipartite entangled states across large quantum networks, without requiring any precise pulse control and relying on a single Gaussian entanglement source only.

Effects of higher-order spatial modes on the squeezing level in optical parametric amplification with waveguides

We investigate a limiting factor of waveguide optical parametric amplifiers used for generating broadband squeezed light. We found that spatially non-degenerate optical parametric amplification (OPA) between the fundamental modes and the higher-order modes generates noise, and that this effect can be avoided by detecting the squeezed light with the optimal spatial mode. The analysis is conducted assuming the waveguides with different dimensions, offering valuable insight into the waveguide design for squeezing.

Nonlinearity and Parametric Amplification of Superconducting Nanowire Resonators in Magnetic Field

Nonlinear superconducting devices, typically based on Josephson Junction (JJ) nonlinearities, are the basis for superconducting quantum electronics, enabling, e.g., the formation of isolated two-level superconducting qubits and amplifiers. While emerging spin, hybrid spin/superconducting (including Majorana), and nano-magneto-optical quantum systems could benefit tremendously from superconducting nonlinearities, the presence of strong magnetic fields in these systems are incompatible with conventional JJ devices, which are highly sensitive to applied magnetic fields. One potential solution is the use of kinetic inductance (KI) nonlinearity. To date, only linear kinetic inductance (KI) devices have been shown to operate in high magnetic fields, while nonlinear KI device operation in high magnetic fields has received virtually no attention. Here, we study the nonlinearity of superconducting nanowire (NW) KI resonators and their performance as parametric amplifiers for in-plane magnetic fields. We study the Kerr coefficients of NW KI resonators made from 10 nm-thin NbTiN films with characteristic impedance up to 3 k$\Omega$, and demonstrate both nondegenerate and degenerate parametric amplification, at magnetic fields up to 2 T, for the first time. We find that narrow KI resonators of width 0.1 $\mu$m are robust, in terms of gain, dynamic range and noise, to magnetic fields up to $\sim$2 T, while wider KI resonators of width 1 $\mu$m suffer significant suppression in the gain around at fields well below 2 T. Around 8 dB deamplification is observed for coherent states for a 0.1 $\mu$m KI resonator, implying the capability of noise squeezing. These results open a new pathway to developing nonlinear quantum devices that operate in or generate high magnetic fields such as spin, hybrid spin/superconducting, and magneto-opto-mechanical devices.

Squeezing Limit of the Josephson Ring Modulator as a Nondegenerate Parametric Amplifier

Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any non-degenerate parametric amplifier will have an intrinsic squeezing limit in the output fields.

Generation of large-scale continuous-variable cluster states multiplexed both in time and frequency domains.

A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.

Manipulation and enhancement of asymmetric steering via down-converted nondegenerate photons

We investigate the asymmetric Gaussian steering with the nondegenerate parametric amplifier in a three-mode optomechanical system composed of two optical cavities and a mechanical oscillator. In the presence of the nondegenerate parametric amplifier, we find that the Gaussian steering between the auxiliary cavity and the mechanical resonator without direct interaction is significantly enhanced. By cooling the delocalized Bogoliubov modes over the auxiliary cavity and the mechanical oscillator, the optimal optomechanical entanglement and Gaussian steering can be realized and enhanced. Furthermore, we observe a wider range of parameters for the Gaussian steering with the case of cooling double delocalized modes. In addition, the magnitudes of the asymmetric Gaussian steering in two different directions can be adjusted by altering the decay rate of the auxiliary optical mode. Therefore, our proposal provides an effective method to manipulate and enhance the one-way Gaussian steering between the two modes.

Nonclassical properties of a non-degenerate parametric amplifier

Nonclassical properties of electromagnetic radiation propagating through a non-degenerate parametric amplifier (NDPA) are investigated. A complete quantum mechanical description is being used to describe the system. Under rotating wave approximation, the exact analytical solutions of the Heisenberg’s equations of motion for signal and idler modes are used to investigate the existence of various nonclassical properties of the radiation fields. These nonclassical properties include squeezing, intermodal entanglement and antibunching. The analytical results confirm the presence of these nonclassical properties for both the input composite number and coherent states. In addition, mixed mode squeezing is observed for input pair coherent states in both the quadratures. The analytical results are compared with their numerical counterpart obtained by QuTiP. The perfect matching of these results justifies the correctness of the analytical results.

Long-distance distribution of qubit-qubit entanglement using Gaussian-correlated photonic beams

We investigate the deterministic generation and distribution of entanglement in large quantum networks by driving distant qubits with the output fields of a nondegenerate parametric amplifier. In this setting, the amplifier produces a continuous Gaussian two-mode squeezed state, which acts as a quantum-correlated reservoir for the qubits and relaxes them into a highly entangled steady state. Here we are interested in the maximal amount of entanglement and the optimal entanglement generation rates that can be achieved with this scheme under realistic conditions taking, in particular, the finite amplifier bandwidth, waveguide losses, and propagation delays into account. By combining exact numerical simulations of the full network with approximate analytic results, we predict the optimal working point for the amplifier and the corresponding qubit-qubit entanglement under various conditions. Our findings show that this passive conversion of Gaussian into discrete-variable entanglement offers a robust and experimentally very attractive approach for operating large optical, microwave, or hybrid quantum networks, for which efficient parametric amplifiers are currently developed.

Generation of nonclassical states of light via truncation of mixed states

A possible way of generating nonclassical states of light is via the truncation of a given state in the Fock basis. In recent work, we presented an alternative scheme for such quantum scissors [Phys. Rev. A 104, 033715 (2021)PLRAAN1050-294710.1103/PhysRevA.104.033715], employing a nondegenerate parametric amplifier, a beam splitter, and photodetectors. An advantage of this setup is that it does not require the generation of Fock states beforehand, as in previous proposals. Here we extend this treatment to mixed input states. We show the possibilities of generating truncated states with either a maximum Fock number N or states having a minimum Fock number N . We discuss two specific examples of states to be truncated: (i) the thermal state and (ii) the phase-diffused coherent state. In either case, the generated field states can present sub-Poissonian statistics as well as non-Gaussian character. These nonclassical properties can be adjusted by changing the parameters of the scissors, e.g., the amplifier strength and the beam-splitter transmittance.

Beyond the standard quantum limit for parametric amplification of broadband signals

The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of 0.5, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of unity can be reached. Experimentally, we find a quantum efficiency of 0.69 ± 0.02, well beyond the SQL, by employing a flux-driven Josephson parametric amplifier and broadband thermal signals. We expect that our results allow for fundamental improvements in the detection of ultraweak microwave signals.

Atomic non-locality dynamics of two moving atoms in a hybrid nonlinear system: concurrence, uncertainty-induced non-locality and Bell inequality

The paper explores the non-locality dynamics of two moving atoms in a hybrid nonlinear system, which describes a nondegenerate parametric amplifier cavity containing two moving atoms with Stark shift interactions. Based on the Bell function, uncertainty-induced non-locality and concurrence, the two moving atomic non-locality is calculated numerically, when the cavity is filled initially by pair coherent fields. The results showed that the hybrid nonlinear qubit-cavity interactions have a high ability to generating quantum correlations. The amount of the generated quantum correlation can be improved and accelerated significantly with the increase of the time-dependent qubit location parameter. The increase of the Stark shift ratio and the difference between the mean-number photons of the two cavity fields leads to a clear deterioration of the generated quantum correlation.

Two-qubit non-locality interacting time-dependently with a parametric amplifier cavity with Stark-shift nonlinearity

We have explored the non-locality of two qubits interacting time-dependently with a nondegenerate parametric amplifier cavity fields in the presence of the Stark shift interaction term. The time-dependent two-qubit reduced density matrix is calculated numerically when the cavity fields are initially in two entangled coherent states. We investigate the non-locality via local Fisher information and negativity. It is shown that, the generated non-locality depends on the time-dependent two-qubit location, the Stark shift interaction, the difference between the mean photon numbers of the two cavity fields as well as the initial intensity coherent fields. The agreement of the generated correlations presented by the local Fisher information and the negativity depends on the physical parameters. The Stark shift non-linearity and the difference between the mean photon numbers leads to reducing the generated correlations. The local Fisher information is more robust against the Stark shift interaction than the negativity.

Dynamics of two coupled qubits in a two-mode cavity through four-photon processes: Nonclassical properties under intrinsic decoherence

The impact of the intrinsic decoherence on the dynamics of a system composed of two coupled qubits inside a two-mode cavity with a nondegenerate parametric amplifier is analytically investigated. High-order nonlinearity causes strong entanglement and mixedness, which are analyzed by using entropy, negativity, and log negativity. In the absence of intrinsic decoherence, it is found that qubit-qubit coupling improves the generation of population inversion, entanglement, and mixedness. The coupling acts as external decoherence in the presence of the intrinsic decoherence, and the quantum effects evolve monotonically to non-zero stationary values. The qubit-qubit entanglement is crucially dependent on the nonlinearity and the intrinsic decoherence. The stability of this entanglement is granted for small intrinsic decoherence.

Nonlinear interferometer based on two-port feedback nondegenerate optical parametric amplification

In this paper, we propose a nonlinear interferometer based on two-port feedback nondegenerate optical parametric amplification (NITFPA), which employs two linear beam splitters to feed the two output beams of a nondegenerate optical parametric amplifier back to its input ports. By comparing the NITFPA with the SU(1,1) interferometer (SUI), which is another typical nonlinear interferometer, we demonstrate that the NITFPA has its unique advantages in the precision enhancement of the phase estimation. In addition, we demonstrate that the NITFPA is also advantageous over the SUI in the robustness against the losses. Such a NITFPA may find its potential applications in quantum metrology.

Realization of the unconventional photon blockade based on a three-wave mixing system.

In this paper, the unconventional photon blockade is studied in a three-wave-mixing system with a non-degenerate parametric amplification. A method of only retaining the Fock-state basis in the interference path is used to calculate the optimal analytic conditions of unconventional photon blockade. The numerical results agree well with the analytic conditions, which verifies the validity of this method. Our calculations indicate that the strong photon antibunching can be obtained in the high-frequency mode of the three-wave mixing. And the influence of system parameters on photon blockade is also discussed.

Engineering optomechanical entanglement via dual-mode cooling with a single reservoir

We study reservoir-engineered entanglement for a cascaded bosonic system consisting of three modes, where the adjacent pairs couple to each other via both the beam-splitter interaction and the coherent parametric interaction with the interaction strengths being tunable. We focus on an optomechanical realization of the model by combining a nondegenerate parametric amplifier and an auxiliary cavity. A great steady-state cavity-mechanical entanglement can be achieved by optimizing the ratio of the interaction strengths, where the optomechanical cavity enacts the cold reservoir, simultaneously laser cooling the pair of hybrid modes delocalized over the auxiliary cavity and the mechanical oscillator. In comparison with the case of cooling a single delocalized mode, the dual-mode cooling approach allows one to obtain a greater amount of entanglement with higher cooling efficiencies and to explore strong entanglement in much broader parameter regions, where the rotating-wave approximation fails for the single-mode cooling case. Moreover, we show that the steady-state cavity-mechanical entanglement is robust to the mechanical thermal noise of the high temperature. The improved reservoir engineering approach can potentially be generalized to other bosonic systems with asymmetric beam-splitter and parametric interactions.

Tunable quantum and statistical features of the two-mode radiation generated by a correlated emission laser injected with squeezed radiation

The role of phase fluctuation on the quantum and statistical features of the two-mode radiation produced by a correlated emission laser which is externally injected with squeezed radiation is discussed. The considered atoms are prepared in the ground and excited states with equal probabilities before being injected into the laser cavity, and an external coherent field generates the atomic coherence that leads to the non-classical features in the quantum system. A non-degenerate parametric amplifier is also introduced into the laser cavity which is coupled to a two-mode squeezed environment. It is found that the quantum and statistical properties are very sensitive to and highly altered by the phase fluctuation when the strength of the external coherent field is weak. On the contrary, the external coherent field entirely overcomes the influence of phase fluctuation for the amplitude of the external coherent field that lies in the strong pumping regime so that the strength of squeezing and entanglement, and photon statistics of the two-mode radiation are not substantially affected by the phase fluctuation.

Continuous-Variable Entanglement Adjustable by Phase Fluctuation and Classical Pumping Field in a Correlated Emission Laser Seeded with Squeezed Light

We present the influence of phase fluctuations on the entanglement and intensity of the radiation produced by a correlated-emission laser. The three-level atoms are initially prepared in a partial coherent superposition of the ground and exited states, and the driven radiation field incoming via the input mirror induces the atomic coherence that leads to the entanglement in the quantum system. The laser cavity also contains a nondegenerate parametric amplifier and is seeded by a two-mode squeezed light. The entanglement is analyzed by applying the Duan–Giedke–Cirac–Zoller (DGCZ) and logarithmic negativity inseparability criteria for a continuous variable system. We find that the phase fluctuation remarkably reduces the amount of entanglement in the weak driving field. On the other hand, the driven field completely overcomes the influence of phase fluctuations in the strong driving field, so that the entanglement remains in its highest degree (97%) in this regime.