Quantum-enhanced estimation of signal field amplitudes with critical squeezed states of photonic modes

Abstract

Critical phenomena of quantum systems offer a promising strategy to improve measurement precision. So far, many criticality-enhanced quantum metrological schemes have been proposed by using the adiabatically evolved photonic states of composite systems involving a qubit and a field interacting with each other. These schemes focus on the measurement of the system's inherent frequencies. We here propose a criticality-enhanced quantum sensing protocol, aiming to estimate the amplitude of an external signal field with the interacting qubit-photon system. The signal field is coupled to the photonic mode, so that the composite system has a unique dark state, where the photonic mode follows a squeezed vacuum state. The information about the signal field amplitude is encoded in one quadrature of the quantized photonic mode, which exhibits a divergent behavior near the critical point. The measurement precision can approach the Heisenberg limit with respect to the time to encode the signal and the photon number of the field mode.

Figures (2)

• Figure 1: The QFI $\mathcal{I}_\eta$ versus the control parameter $\eta$. The horizontal axis is truncated at the point where $\eta = 0.995$. As $\eta$ approaches $1$, $\mathcal{I}_\eta$ exhibits a pronounced divergence.
• Figure 2: (a) Dependence of $\eta$ on the dimensionless time variable $kt$. (b) Fidelity $F$ of the qubit-photon state with respect to the ideal dark state as a function of $\eta_t$. In both panels, the parameter $\eta$ evolves according to Eq. (\ref{['eq:varepsilon_t']}) with a rate constant $k=\Omega/200$. In (b), the horizontal axis is truncated at the point where $\eta = 0.995$. Crucially, as $\eta_t$ approaches $0.995$, the fidelity remains consistently above $99.96\%$, demonstrating that high-fidelity adiabatic evolution is preserved even in the vicinity of the quantum critical point.