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Modern Physics Letters A

Enhancement of photonic entanglement and antibunching of the emitted waves from a non-degenerate parametric amplifier

R. Usefi, Mohammad Kazem Tavassoly

Published Aug 7, 2025• 2 citations
Publisher

Abstract

Our purpose in this paper is to investigate the response of a well-known nonlinear quantum optical medium, i.e. non-degenerate parametric amplifier (NDPA), to the pair coherent and two-mode squeezed states, distinctly, both analytically and numerically. To achieve the aim, we start from the NDPA quantum Hamiltonian in the rotating wave approximation (RWA) and via solving the Heisenberg equations of motion of signal and idler modes of the dynamical system is derived, by which we can achieve the time evolution of the NDPA response to the above-mentioned input field states. Accordingly, we are able to evaluate two important nonclassical properties, i.e. photonic entanglement and photon statistics (second-order correlation function and antibunching effect) after the interaction with NDPA for the output emitted fields, and compare the results with the associated quantities for the input field states. Summing up, our numerical simulations show that the amplification (and in some cases the appearance) of the considered nonclassical properties of the radiation field in the output states is clearly confirmed. The results can be beneficial for various quantum science and technology protocols, i.e. quantum communication, quantum metrology, quantum teleportation and quantum computing.

DOI
10.1142/s0217732325501238

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Our purpose in this paper is to investigate the response of a well-known nonlinear quantum optical medium, i.e. non-degenerate parametric amplifier (NDPA), to the pair coherent and two-mode squeezed states, distinctly, both analytically and numerically. To achieve the aim, we start from the NDPA quantum Hamiltonian in the rotating wave approximation (RWA) and via solving the Heisenberg equations of motion of signal and idler modes of the dynamical system is derived, by which we can achieve the time evolution of the NDPA response to the above-mentioned input field states. Accordingly, we are able to evaluate two important nonclassical properties, i.e. photonic entanglement and photon statistics (second-order correlation function and antibunching effect) after the interaction with NDPA for the output emitted fields, and compare the results with the associated quantities for the input field states. Summing up, our numerical simulations show that the amplification (and in some cases the appearance) of the considered nonclassical properties of the radiation field in the output states is clearly confirmed. The results can be beneficial for various quantum science and technology protocols, i.e. quantum communication, quantum metrology, quantum teleportation and quantum computing.
This study investigates the entanglement and squeezing characteristics of light generated by a non-degenerate, three-level laser with a non-degenerate parametric amplifier, which is pumped by electron bombardment to the top level and coupled to a two-mode vacuum reservoir through a single-port mirror. By normal ordering the noise operators, we simplified the calculations and derived the evolution equations for the atomic operators using the master equation. From the steady-state solutions, we determined the average of the photon number, the quadrature variance of radiation, entanglement, the normalized second-order correlation of the cavity radiation, and fluctuations in intensity difference. Our findings indicate that higher spontaneous emission rates significantly decrease the average photon number, while the amplitude of the pumping mode interacting with the parametric amplifier ( ɛ ) increases it. Enhanced squeezing is observed with increasing ( ɛ ), reaching a peak at ɛ = 0 . 02 ( 78 . 5 % ) . Moreover, spontaneous emission enhances squeezing for some interval of r a . A direct correlation between quadrature squeezing and entanglement is found, with greater quadrature squeezing associated with increased entanglement. This research offers potential advancements in quantum technologies, such as quantum communication, computing, and sensing, where controlled squeezing and entanglement are crucial for improving performance.
Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a non-degenerate parametric oscillator is exhibited. Without using the usual rotating wave approximation (RWA), the analytical solutions of the field operators are used to investigate the antibunching of photons of the input radiation field coupled to the non-degenerate parametric oscillator. By using the symbolic calculation, the antibunching of photons for both the signal and idler modes are investigated. In particular, the effects of the inclusion of rotating wave approximated terms on the antibunching of photons are clearly indicated. To substantiate the analytical results, the temporal evolution of signal photon and idler photons, and the antibunching effects of the signal and idler modes are investigated numerically by using the QuTip 3.1.0. The exact numerical results obtained by QuTip 3.1.0 matches extremely well with those of the analytical results. The present article and hence the analytical method might be of use for investigating the situations of having ultra-strongly and deep-strongly coupled systems where the possibilities of using RWA is completely ruled out.
The process of quantum-injection into an amplifier operating in a novel entangled configuration is adopted to “amplify” into a large dimensionality spin-12 Hilbert space the superposition properties of the entangled photon-couples generated by parametric down-conversion. The process is applied to the cases of mode-degenerate and mode non-degenerate Parametric Amplification. The quantum structure of the Wigner function and of the field correlation functions shows in both cases that the Schroedinger-cat behavior of the emitted field is largely detectable against the squeezed-vacuum noise. The absence of decoherence is explained in terms of a basic property of nonlinear complex systems.
The proposal for single-photon generation utilizing quantum interference of two coupled cavity modes with weak Kerr nonlinearity under resonant coherent driving has been successfully put forward in previous work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. 104, 183601 (2010)]. Here we suggest an alternative scheme to explore the statistical properties of the photons and their control in a parametrically amplified photonic molecule that is composed of a pair of coupled cavities, both containing the degenerate optical parametric amplifier (DOPA), by means of extending the model of Liew and Savona. Due to the destructive quantum interference effect between different paths for two-photon excitation, the photons in both cavity modes can exhibit a strong antibunching effect when one of the two cavities is coherently driven by an external laser field. In order to intuitively understand the strong photon antibunching phenomenon occurring in our DOPA photonic molecule, the approximate analytical solutions of the system are provided via the Schr\"odinger equation and further are compared with the full numerical solutions via the master equation. The in-depth results reveal that the two solutions are in good agreement. For the two cavity modes, we achieve the optimal antibunching conditions in terms of the nonlinear gain and the strength ratio between the two pump laser fields based on analytical calculations, gaining deep insight into the rich physics of photon statistics. We also show that the statistical properties of the photons can be well controlled by regulating the relative phase between the two pump laser fields and the tunneling rate between the two cavity modes. Furthermore, we address the second-order cross-correlation function between the two cavity modes and find that a strong intermodal antibunching can be efficiently generated. Our approach via the DOPA photonic molecule architecture can be useful to generate tunable single-photon sources or controlled photonic quantum gates.
The time evolution of squeezed vacuum states, taken to be SU(1,1) coherent states, interacting with a two-photon medium is examined using numerical methods. The non-photon-conserving medium is modeled by a Hamiltonian which consists of the free-field term, a non-photon-conserving term in the form of a degenerate parametric amplifier, and an anharmonic term which gives rise to optical bistability. This system has previously been shown to produce enhanced squeezing when interacting with ordinary coherent light. In the present work we find that the squeezing property is generally revoked by the anharmonic term and increased by the nonconserving term. The combined effects are not additive, however, and a quantum interference effect is observed in the calculations.