Quantum dynamics and macroscopic quantum tunnelling of two weakly coupled condensates

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 'π-oscillation' with relative phase π 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 'π-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 'π-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.

Dissipative Bose-Josephson junction coupled to bosonic baths

“…z with anti-ferromagnetic interaction for U > 0 describes the BJJ within tight binding approximation [29]. Various interesting properties of this Hamiltonian related to many-body states, semiclassical spectrum and quantum dynamics have been explored theoretically [19,[30][31][32][33][34][35][36]. To simplify the model further, we consider a linear shift of the bath modes bik = b ik − √ 2Sλ ik 2 ω k followed by an unitary transformation of the bosonic operators,…”

Localization–delocalization transition of dipolar bosons in a four-well potential

“…In the subsequent interval U 0 /2 < U 1 < U 0 , where σ = +1 but u 1 > 1, the new solutions (23), (24) have been found in addition to the uniform solution. Since…”

“…This represents the ground-state energy for U 1 < U 0 /2, namely, when u 1 < 1 and σ = +1 (ultraweak dipolar interaction). In the subsequent interval U 0 /2 < U 1 < U 0 , where σ = +1 but u 1 > 1, the new solutions ( 23), (24) have been found in addition to the uniform solution. Since…”

“…where the range of τ is determined by 0 ≤ τ ≤ (u 1 + 1)/8. Note that g ≡ f given by equation (24). The inequality defining the upper bound can be rewritten in the more explicit form J ≤ N(2U 1 − U 0 )/8 showing that J ≤ NU 0 /8 for U 1 → U + 0 , and T ≤ NU 1 /8 for a generic, arbitrarily large U 1 > U 0 .…”

“…To explore the new scenario we resort to the semiquantum approach applied in several papers (see, e.g., [20][21][22][23]) which reduces the Schrödinger problem of many-boson models to a diagonalizable form. A 'dual' version of this method is also known which has been developed for spin models and applied to two-mode bosonic systems [24]. In the sequel, we refer to this method as the continuous variable picture (CVP).…”