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

Ebubechukwu O. Ilo-Okeke1,2, Manikandan Kondappan3,1, Ping Chen3,1, Yuping Mao3,1, Valentin Ivannikov1, and Tim Byrnes1,3,4,5,*

  • 1New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China; NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China; Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU Shanghai, 567 West Yangsi Road, Shanghai 200126, China
  • 2Department of Physics, School of Physical Sciences, Federal University of Technology, P. M. B. 1526, Owerri 460001, Nigeria
  • 3State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
  • 4Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi, UAE
  • 5Department of Physics, New York University, New York, New York 10003, USA

  • *tim.byrnes@nyu.edu
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Phys. Rev. A 107, 052604 – Published 8 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.052604

Abstract

We analyze a scheme that uses quantum nondemolition measurements to induce squeezing of a two-mode Bose-Einstein condensate in a double-well trap. In a previous paper [E. O. Ilo-Okeke, S. Sunami, C. J. Foot, and T. Byrnes, Phys. Rev. A 104, 053324 (2021)], we introduced a model to solve exactly the wave function 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 squeezing 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.

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Information

Phys. Rev. A 107, 052604– Published 8 May, 2023
  • Received 16 September 2022
  • Accepted 17 April 2023
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