Surpassing Quantum Noise Limits with Nonlinear Amplification

Abstract

Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or non-classical resources. To surpass this limitation, we propose a nonlinear quantum amplification strategy that exploits the interplay between a gain-stabilized bright eigenmode of a coupled two-mode bosonic system and Kerr nonlinearity. We demonstrate that this interplay enables the signal gain to surpass the noise gain in a selected quadrature, leading to a net increase in the SNR beyond the quantum limits of conventional linear amplifiers. Our work thus establishes a novel nonlinear amplification paradigm capable of enhancing the SNR, with promising applications across quantum information processing, quantum communications, and quantum metrology.

Figures (4)

• Figure 1: Schematic of the proposed nonlinear quantum amplifier based on a coupled two-mode bosonic system, where gain and Kerr nonlinearity are incorporated into the mode $a$ (output), and mode $b$ (input) is driven at a frequency $\omega_d$.
• Figure 2: Signal gain $10\mathrm{log_{10}}G_{s}$ versus normalized gain rate $\kappa_g/\kappa_b$ for: $N_\mathrm{in}=0.5$, $K=1\times10^{-4}\kappa_b$ (circle); $N_\mathrm{in}=0.5$, $K=5\times10^{-5}\kappa_b$ (square); $N_\mathrm{in}=0.7$, $K=5\times10^{-5}\kappa_b$ (triangle). Parameters: $\omega_d=\omega_a-0.3\kappa_b$, $\omega_b=\omega_a+0.2\kappa_b$, $\kappa_a=0.25\kappa_b$, $J=\sqrt{3}\kappa_b/2$, $\theta_s=\mathrm{Arg}(1-0.5i)$.
• Figure 3: (a) Noise figure $10\mathrm{log_{10}}F$ versus normalized gain rate $\kappa_g/\kappa_b$ for: $N_\mathrm{in}=0.5$, $K=1\times10^{-4}\kappa_b$ (circle); $N_\mathrm{in}=0.5$, $K=5\times10^{-5}\kappa_b$ (square); $N_\mathrm{in}=0.7$, $K=5\times10^{-5}\kappa_b$ (triangle). (b) Noise figure $10\mathrm{log_{10}}F^{bm}$, and (c) signal gain $10\mathrm{log_{10}}G_{s}^{bm}$ (solid), noise gain $10\mathrm{log_{10}}G_{n}^{bm}$ (dotted) versus normalized decay rate $\kappa_a/\kappa_b$ for $N_\mathrm{in}=0.5$, $K=1\times10^{-4}\kappa_b$, $\kappa_n=0.6\kappa_b$. Other parameters are the same as in Fig. 2.
• Figure 4: (a) Signal gain $10\mathrm{log_{10}}G_{s}$ and (b) noise figure $10\mathrm{log_{10}}F$ versus normalized detuning $\delta/\kappa_b$ for: $N_\mathrm{in}=0.5$, $K=1\times10^{-4}\kappa_b$ (circle); $N_\mathrm{in}=0.5$, $K=5\times10^{-5}\kappa_b$ (square); $N_\mathrm{in}=0.7$, $K=5\times10^{-5}\kappa_b$ (triangle). (c) Normalized operational bandwidth $\delta\omega/\kappa_b$ (star) and peak signal gain $10\mathrm{log_{10}}G_{s}^{p}$ (rhombus) versus $N_\mathrm{in}$. (d) Normalized $\mathrm{GBP}/\kappa_b$ versus $N_\mathrm{in}$. In (c,d), $K=1\times10^{-4}\kappa_b$ (solid) and $K=5\times10^{-5}\kappa_b$ (dotted). Parameters: $\omega_d=\omega_a-0.3\kappa_b+\delta$, $\kappa_n=0.6\kappa_b$; other parameters are the same as in Fig. 2.