Photon blockade effect from synergistic optical parametric amplification and driving force in Kerr-medium single-mode cavity

TL;DR

This work analyzes photon blockade in a Kerr-nonlinear single-mode cavity coupled to an optical parametric amplifier (OPA). By deriving a master equation and performing a two-photon truncation, it obtains an analytic optimal blockade condition: $G = \dfrac{2F^2(\cos 2\phi + \sin 2\phi)}{\kappa + 2\Delta}$, and confirms this against numerical simulations of $g^{(2)}(0)$ and the mean photon number $N$. The results show robust blockade across a wide range of Kerr strengths, with the driving phase $\phi$ controllably shifting and shaping the blockade region, and resonance enhancing brightness. The blockade is explained by destructive interference between two excitation paths to the two-photon state, a mechanism that persists despite Kerr-induced energy shifts, implying a universal photon blockade feature and potential for tunable, high-purity single-photon sources.

Abstract

This work investigates photon blockade control in a hybrid quantum system containing a Kerr-nonlinear cavity coupled to an optical parametric amplifier (OPA). The dynamics are governed by a master equation derived from an effective Hamiltonian that includes cavity decay. To obtain analytical solutions, the system's quantum state is expanded in the Fock basis up to the two-photon level. Solving the steady-state Schrodinger equation yields probability amplitudes and the analytical conditions for optimal photon blockade. Results confirm that photon blockade is achievable with suitable parameters. Excellent agreement is found between the analytical solutions and numerical simulations for the steady-state, equal-time second-order correlation function, validating both the analytical method and the blockade effect. Numerically, the average intracavity photon number increases significantly under resonance, providing a theoretical pathway for enhancing single-photon source brightness. Furthermore, the driving phase is shown to regulate the optimal blockade region: it shifts the parabolic region within the two-dimensional parameter space of driving strength and OPA nonlinearity and can even reverse its opening direction. The influence of Kerr nonlinearity is also examined. Photon blockade remains robust across a wide range of Kerr strengths. Physical analysis attributes the effect to destructive quantum interference between two distinct excitation pathways that suppress two-photon states. While Kerr nonlinearity shifts the system's energy levels, it does not disrupt this interference mechanism, explaining the effect's stability over a broad parameter range.

Figures (5)

• Figure 1: Logarithmic value of the equal-time second-order correlation function ${g^{\left( 2 \right)}}\left( 0 \right)$ versus different physical parameters are presented: (a) Logarithmic value of ${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of the driving strength $F/\kappa$ and the optical parametric amplifier nonlinear coefficient $G/\kappa$ of the optical parametric amplifier, where$\phi = {\pi} /12$ and $U/\kappa=0.5$; (b) logarithmic value of ${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of the optical parametric amplifier nonlinear coefficient $G/\kappa$ and the driving phase $\phi$, where $F/\kappa = 0.1$ and $U/\kappa=0.5$. In both figures, the white dashed lines, derived from Eq. (13), indicate the analytical solutions corresponding to the optimal conditions for photon blockade.
• Figure 2: Logarithmic value of the average photon number $N$ versus different parameters: (a) $\lg(N)$ as a function of detuning $\varDelta/\kappa$ at different driving strengths $F/\kappa$; (b) phase dependence of $\lg(N)$ under varying of the optical parametric amplifier nonlinear coefficients $G/\kappa$; (c) detuning dependence of $\lg(N)$ for different optical parametric amplifier nonlinear coefficients $G/\kappa$; (d) $\lg(N)$ versus detuning $\varDelta/\kappa$ at distinct Kerr nonlinearity strengths $U/\kappa$.
• Figure 3: Logarithmic value of ${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of the driving strength $F/\kappa$ and the nonlinear coefficient $G/\kappa$ of the optical parametric amplifier under different driving phases $\phi$: (a) $\phi =\pi/12$; (b) $\phi =\pi/6$; (c) $\phi =\pi/4$; (d) $\phi =\pi/3$; (e) $\phi =5\pi/12$; (f) $\phi =\pi/2$. In all panels, the white dashed lines, derived from Eq. (13), represent the analytical solutions for the optimal photon blockade conditions. The Kerr nonlinearity strength was consistently set to $U/\kappa=0.5$ in the numerical simulations.
• Figure 4: Logarithmic value of ${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of the driving strength $F/\kappa$ and the nonlinear coefficient $G/\kappa$ of the optical parametric amplifier under different Kerr nonlinearity strength $U/\kappa$: (a) $U/\kappa$=0.1; (b) $U/\kappa$=1.0; (c) $U/\kappa$=2.0; (d) $U/\kappa$=5.0. In all panels, the white dashed lines, derived from Eq. (13), represent the analytical solutions for the optimal photon blockade conditions.
• Figure 5: Schematic diagram of the system energy-level and the transition paths between different photon states: (a) Energy level diagram; (b) photon state transition pathways.