Finite-size effects in a bosonic Josephson junction

Year: 2021

Authors: Wimberger S., Manganelli G., Brollo A., Salasnich L.

Autors Affiliation: Univ Parma, Dipartimento Sci Matemat Fis & Informat, Parco Area Sci 7-A, I-43124 Parma, Italy; Ist Nazl Fis Nucl, Grp Collegato Parma, Sez Milano Bicocca, Parco Area Sci 7-A, I-43124 Parma, Italy; niv Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, Scuola Galileiana Studi Super, Via San Massimo 33, I-35129 Padua, Italy; Univ Padua, Padua Quantum Technol Res Ctr, Via Gradenigo 6-B, I-35131 Padua, Italy; Ist Nazl Fis Nucl, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; CNR INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy

Abstract: We investigate finite-size quantum effects in the dynamics of N bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACSs) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find 1/N corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self-trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we also find that, for a few atoms, the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also, the numerical results of SSB are better reproduced by the ACS approach than with the MF approach. Instead, the onset of MQST is correctly reproduced by ACS theory only in the large N regime and, for this phenomenon, the 1/N correction to the MF formula is not reliable.


Volume: 103 (2)      Pages from: 023326-1  to: 023326-7

More Information: The authors thank A. Cappellaro, L. Dell´Anna, A. Notari, V. Penna, and F. Toigo for useful discussions. L.S. acknowledges the BIRD project “Superfluid properties of Fermi gases in optical potentials” of the University of Padova for financial support.
KeyWords: Josephson effect
DOI: 10.1103/PhysRevA.103.023326