Using anti-squeezed Schrödinger cat states for detection of a given phase shift

Abstract

We propose to use the antisqueezing-enhanced non-Gaussian Schrödinger cat quantum states of the probing light for the task of detection of a given phase shift in optical interferometers. We show that the antisqueezing allows to increase the robustness of the setup to optical losses. We find the optimal degrees of the antisqueezing for experimentally achievable values of the Schrödinger cat amplitude and the optical losses and compare the resulting sensitivity with the one provided by the Gaussian squeezed states.

Figures (8)

• Figure 1: Two equivalent implementations of the non-Gaussian interferometer: asymmetric (top) and antisymmetric (bottom) the Mach-Zehnder interferometer. $\hat{a}_1$ and $\hat{d}_1$ -- bright input and output ports, $\hat{a}_2$ and $\hat{d}_2$ -- dark input and output ports.
• Figure 2: (Top) Diagram of the lossy interferometer; (Bottom) Diagram of the equivalent simplified optical scheme
• Figure 3: Wigner negativity volume of $V_{\rm neg}$ the an anti-squeezed SC state versus the anti-squeezing level (in dB). Red solid curve: $\eta = 0.9$; black solid line: $\eta = 1$. In bothcases, $\alpha = 10$. The blue vertical dashed line marks the validity threshold of the approximation $s_{\rm max}$, see Eq. \ref{['eq:v-neg-approx-eq-applicability-condition']}.
• Figure 4: Total error probability $p_{\rm tot}$ as a function of the displacement $\delta_0$ and antisqueeze factor $r$ for $\alpha = 2.0$ and $\eta = 0.975$.
• Figure 5: Photon-number distributions of the optimized anti-squeezed SC state for the case of $\alpha = 2.0$ and $\eta = 0.975$, $r=0.56$ ($5\,{\rm dB}$). Top: no signal, $\delta_0=0$, bottom: with signal, $\delta_0=0.68$. The red bars constitute the detection error.