Hybrid approximation approach to generation of atomic squeezing with quantum nondemolition measurements

TL;DR

This paper presents a hybrid approximation method for generating atomic squeezing via quantum nondemolition measurements in a Bose-Einstein condensate, providing analytical insights into the dynamics and correlations induced by measurements.

Contribution

The authors develop an approximate analytical approach combining Holstein-Primakoff and exact light treatment to analyze atomic squeezing in short and long interaction regimes.

Findings

Measurement induces correlations and superposition states in the condensate.

Derived simple variance expressions match exact solutions in short interaction times.

Qualitative agreement with exact solutions in long interaction time regime.

Abstract

We analyze a scheme that uses quantum nondemolition measurements to induce squeezing of a spinor Bose-Einstein condensate in a double well trap. In a previous paper [Ilo-Okeke et al. Phys. Rev. A \textbf{104}, 053324 (2021)], we introduced a model to solve exactly the wavefunction for all atom-light interaction times. Here, we perform approximations for the short interaction time regime, which is relevant for producing squeezing. Our approach uses a Holstein-Primakoff approximation for the atoms while we treat the light variables exactly. It allows us to show that the measurement induces correlations within the condensate, which manifest in the state of the condensate as a superposition of even parity states. In the long interaction time regime, our methods allow us to identify the mechanism for loss of correlation. We derive simple expressions for the variances of atomic spin variables conditioned on the measurement outcome. We find that the results agree with the exact solution in the short interaction time regime. Additionally, we show that the expressions are the sum of the variances of the atoms and the measurement. Beyond the short interaction time regime, our scheme agrees qualitatively with the exact solution for the spin variable that couples to light.