Force Sensing Beyond the Standard Quantum Limit in a Hybrid Optomechanical Platform

TL;DR

The paper addresses the fundamental SQL barrier in force sensing by proposing a hybrid optomechanical platform that couples a cavity with a movable mirror to a quantum-dot ensemble and an intracavity OPA. It develops a linearized quantum Langevin description and identifies a CQNC condition under which back-action noise cancels, enabling force measurements beyond SQL. The authors show that the added-noise spectral density can be dramatically reduced and that higher OPA gain lowers the required drive power, with robustness against moderate parameter mismatches. This work provides a practical route to SQL beating in precision metrology and has potential implications for gravitational-wave sensing and quantum information processing.

Abstract

We theoretically investigate quantum measurement noise in a hybrid optomechanical system, focusing on radiation pressure back action and its impact on force sensing. The setup consists of an optomechanical cavity with a movable mirror, a fixed semi transparent mirror, an ensemble of quantum dots (QD) coupled to the cavity mode, and an intracavity optical parametric amplifier (OPA). We show how the QD induced response, together with the system nonlinearity, modifies the noise spectral density and thereby improves the force measurement sensitivity. In this setup, coherent quantum noise cancellation (CQNC) can completely remove the back action noise. In addition, increasing the OPA pump gain enables sensitivity beyond the standard quantum limit (SQL) at reduced laser power. These combined effects allow weak force sensing beyond the SQL.

Figures (5)

• Figure 1: Schematic diagram of a Hybrid optomechanical system equipped with an ensemble of quantum dots and Optical Parametric Amplifier (OPA).
• Figure 2: Noise Power Spectral Density for standard optomechanical system, optomechanical system with OPA for parametric gain $G/\kappa = 0, 0.1$ and $0.3$ and optomechanical hybrid system with CQNC scheme. The spectral densities are normalized by $\hbar m \omega _m \gamma _m$ in order to be represented in units of $\rm{N^2 Hz^{-1}}$. The different lines in the plot represent the standard optomechanical system (blue curve), the hybrid electro-optomechanical system with OPA (orange and green curves), and the hybrid system with the CQNC scheme (the red line at the bottom). The parameters used wimmer2014coherentsingh2023enhanced: $g_0 = 300 \times 2\pi$ Hz, $\Omega= 300 \times 2\pi$ KHz, $\gamma_m = 30 \times 2\pi$ Hz, $\kappa= 2\pi$ MHz, $P=100$ mW, $\omega_L = 384 \times 2\pi$ THz
• Figure 3: Noise Power Spectral Density at resonance (i.e., $\omega=\Omega$) as a function of laser driving power for the standard optomechanical system and the electro-optomechanical hybrid system with the CQNC scheme. The blue line represents the standard optomechanical system, whereas, the orange and green curve indicate hybrid system with OPA gain $G/\kappa = 0.1$ and $0.3$ respectively. (Parameters are the same as in Fig.\ref{['PSD1']})
• Figure 4: Variation of noise spectral density with frequency. The blue solid line represents SQL, the orange and green dashed lines indicates the noise spectral densities with the hybrid model with OPA gain 0.1 and 0.2 respectively. The red line is for perfect CQNC and the black dashed line represents the mismatched CQNC with $\delta = 0.3$.
• Figure 5: Variation of noise spectral density with frequency. The blue solid line represents SQL, the orange and green dashed lines indicates the noise spectral densities with the hybrid model with OPA gain 0.1 and 0.2 respectively. The red line is for perfect CQNC and the black line represents the mismatched CQNC with $\epsilon = 0.01$.