Quantum dynamics and macroscopic quantum tunneling of two weakly coupled condensates

TL;DR

This paper investigates the quantum dynamics of a Bose Josephson junction, revealing new dynamical states, energy spectrum changes, and macroscopic quantum tunneling phenomena through an effective potential approach.

Contribution

It introduces a quantum mechanical analysis of dynamical states and tunneling in a BJJ, highlighting the role of an effective potential and energy spectrum degeneracies.

Findings

Identification of $$-oscillation and MST states and their stability regions.

Observation of energy spectrum changes and degenerate excited states above critical coupling.

Demonstration of macroscopic quantum tunneling causing decay of metastable states.

Abstract

We study the quantum dynamics of a Bose Josephson junction(BJJ) made up of two coupled Bose-Einstein condensates. Apart from the usual ac Josephson oscillations, two different dynamical states of BJJ can be observed by tuning the inter-particle interaction strength, which are known as '$\pi$-oscillation' with relative phase $\pi$ between the condensates and 'macroscopic self-trapped' (MST) state with finite number imbalance. By choosing appropiate intial state we study above dynamical branches quantum mechanically and compare with classical dynamics. The stability region of the '$\pi$-oscillation' is separated from that of 'MST' state at a critical coupling strength. Also a significant change in the energy spectrum takes place above the critical coupling strength, and pairs of (quasi)-degenerate excited states appear. The original model of BJJ can be mapped on to a simple Hamiltonian describing quantum particle in an 'effective potential' with an effective Planck constant. Different dynamical states and degenerate excited states in the energy spectrum can be understood in this 'effective potential' approach. Also possible novel quantum phenomena like 'macroscopic quantum tunneling'(MQT) become evident from the simple picture of 'effective potential'. We study decay of metastable '$\pi$-oscillation' by MQT through potential barrier. The doubly degenerate excited states in the energy spectrum are associated with the classically degenerate MST states with equal and opposite number imbalance. We calculate the energy splitting between these quasi-degenerate excited states due to MQT of the condensate between classically degenerate MST states.