Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states

TL;DR

This paper introduces photon-added and photon-subtracted superpositions of squeezed-vacuum states with sub-Planck phase-space structures, demonstrating their enhanced sensitivity to displacements for quantum sensing applications.

Contribution

It presents a new class of compass-like states derived from squeezed-vacuum states with photon addition or subtraction, showing their sub-Planck structures and high displacement sensitivity.

Findings

States exhibit phase-space structures smaller than the Planck scale.

Sensitivity to displacements exceeds the standard quantum limit.

Photon addition yields higher photon numbers and greater sensitivity.

Abstract

The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work, we introduce compass-like states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that, when a significant quantity of photons is added (or subtracted), the Wigner function of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.