Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential

Abstract

In a previous paper, Das et al (2013 J. Phys. B: At. Mol. Opt. Phys. 46 035501), it was shown that the unitary quantum phase operators play a particularly important role in quantum dynamics of bosons and fermions in a one-dimensional (1D) double-well (DW) when the number of particles is small. In this paper, we define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. The usual two-mode number squeezing parameter, also used to describe two-mode entanglement of a quantum field, is defined considering phase as a classical variable. However, when phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy an uncertainty relation. As a result, the usual definition of number squeezing parameter becomes modified. Two-mode number squeezing occurs when the number fluctuation goes below the SQL at the cost of enhanced phase fluctuation. As an application of number-phase uncertainty, we consider bosons or fermions trapped in a quasi-1D DW potential interacting via a 3D finite-range two-body interaction potential with large scattering length as. Under tight-binding or two-mode approximation, we describe in detail the effects of the range of interaction on the quantum dynamics and number-phase uncertainty in the strongly interacting or unitarity regime . Our results show intriguing coherent dynamics of number-phase uncertainty with number squeezing for bosons and ph squeezing for fermions. Our results may be important for exploring new quantum interferometry, Josephson oscillations, Bose–Hubbard and Fermi–Hubbard physics with ultracold atoms in DW potentials or DW optical lattices. Particularly interesting will be the question of the importance of quantum phase operators in two-atom interferometry and entanglement.