Full-counting statistics and quantum information of dispersive readout with a squeezed environment

Abstract

Motivated by the importance of dispersive readout in quantum technology, we study a prototypical dispersive readout setup that is probed by a squeezed vacuum in a time-reversal-symmetric fashion. To this end, we develop a full-counting-statistics framework for dispersive readout and analyze its measurement information, accompanied by a generalized mean-field approach suitable to deal with non-unitary dynamics. Distinct from conventional input-output theory, our full-counting-statistics approach enables the direct calculation of arbitrary-order cumulants for the measured cumulative (i.e., time-integrated) photonic distribution while maintaining applicability to nonlinear systems. The corresponding Fisher information exhibits an exponential dependence on the squeezing parameter and a robustness against residual nonlinearity, which can even approach the quantum Fisher information, setting an upper limit. This work introduces a conceptually streamlined and computationally efficient framework for continuous quantum measurements, making it well suited for widespread adoption in quantum technologies.

Figures (3)

• Figure 1: (a) Sketch of the dispersive-readout setup to estimate the frequency shift of the resonator, which is probed from the left port with Rabi frequency $\Omega$. Here, a phase-sensitive amplifier (A) is placed between the circulator (C) and the resonator, such that the incoming vacuum field is both squeezed and antisqueezed before finally reaching the measurement setup, consisting of a beam splitter, a local oscillator (LO), and two photon detectors determining the photon number difference. (b) Probability distribution of the accumulated photon-number difference. (c) Cumulative Fisher information as a function of detuning for increasing nonlinearities $U_2=0, U_2=10^{-4}\Omega, U_2=10^{-3}\Omega$ depicted in the top, middle, and bottom panels, respectively. The numerical (analytical) results for various squeezing strengths $r$, annotated in the legend, are depicted by dashed (pentagrams), dashed-dotted (rhombi), dotted (squares), and solid (circles) lines. (d) Cumulative and quantum Fisher information as a function of squeezing depth for $\omega_\Delta=0$. The cumulative Fisher information [blue dashed line (numerics), circle markers (analytics)] increases exponentially and approaches the quantum Fisher Information [red dashed line (numerics), triangle markers (analytics)] as the squeezing depth increases. The cumulative Fisher information in the presence of non-linearity [green (dashed-dotted) and yellow (solid)] exhibits a turnover. Overall parameters are $\beta^2=10\Omega$, $\gamma=0.4\Omega$.
• Figure 2: First four cumulants as a function of detuning for different squeezing strenghts. Overall parameters are the same as in Fig. \ref{['figSystem']}.
• Figure 3: Fisher information versus Kerr nonlinearity $U_2$. Overall parameters are the same as in Fig. \ref{['figSystem']}.