arXiv:2110.08990v1 [physics.atom-ph] 18 Oct 2021 Robustness of non-Gaussian quantum nondemolition measurement induced entanglement between Bose-Einstein condensates Shuai Gao, 1, ∗ Ebubechukwu O. Ilo-Okeke, 2, 3 Yuping Mao, 1, ∗ Manikandan Kondappan, 1 Juan E. Aristizabal-Zuluaga, 2, 4 Valentin Ivannikov, 2 and Tim Byrnes 2, 1, 5, 6, 7 , † 1 State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China 2 New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China 3 Department of Physics, School of Science, Federal University of Technology, P. M. B. 1526, Owerri, Imo state 460001, Nigeria 4 Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia 5 NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China 6 National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan 7 Department of Physics, New York University, New York, NY 10003, USA (Dated: October 19, 2021) We study the robustness of quantum nondemolition (QND) measurement induced entanglement between Bose-Einstein Condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach-Zehnder interferometer, and a QND interaction creates entangle- ment between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement and correlation criteria. Our analysis does not use the Holstein-Primakoff approximation, and is capable of modelling long light-atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than 1/ √ N , where N is the number of atoms in the BEC. For photon loss, the entangled states generated by long inter- action times show a remarkable robustness that makes the scheme promising for various quantum information applications. I. INTRODUCTION Quantum mechanics has been traditionally associated with the microscopic world. Since Schrödinger’s famous gendanken cat experiment, a point that has puzzled physicists is how quantum mechanics at the microscopic level manifests to produce the macroscopic reality de- scribed by classical physics [1, 2]. It is now better recog- nized through an understanding of decoherence that the difficulty in observing quantum phenomena is not only due to the macroscopic nature of the physical system, but the nature of the particular state involved. Cer- tain types of states, such as Schrödinger cat states are highly sensitive to decoherence, while other states such as coherent states are relatively insensitive [3]. For an appropriate type of quantum state, it is therefore possi- ble to produce macroscopic quantum states involving a large number of particles. Examples of these are atomic ensembles [4], Bose-Einstein condensates (BECs) [5, 6], and micromechanical resonators [7]. Of particular interest are macroscopic states that pos- sess entanglement. The most common type of macro- * These authors contributed equally † Electronic address: tim.byrnes@nyu.edu scopic entangled state that is studied are squeezed states, where the uncertainty in one measurement is reduced while increasing the uncertainty of a conjugate variable [8–13]. Experimentally this is most widely achieved in optical systems [12, 14, 15] however analogous procedures can be applied to atomic systems such as atomic ensem- bles which have primarily been considered for applica- tions in quantum metrology [16, 17]. Here, spin squeezed states have been used to improve the sensitivity beyond the standard quantum limit [18]. There are a variety of different interactions that exhibit noise reduction in measurement of the internal spin levels such as the in- teractions of an atomic ensemble inside an optical cavity with either a coherent or optically squeezed light field [16, 19–24]. Examples of useful squeezing interactions using BECs are the one and two-axis counter-twisting Hamiltonians [5, 6, 18, 25–32]. In particular quantum nondemolition (QND) measurements have been used as a method of generating squeezing in atomic ensembles [33–42]. Such entangled states have useful applications in quantum metrology [43–48]. A great majority of the studies regarding entanglement in atomic ensembles and BEC have been for single atomic ensembles. Recently there has been a growing interest in entanglement between two or more atomic ensembles or BECs [49–55]. The first experiments to demonstrate this in atomic ensembles were performed by the Polzik group,