Steady State and Dynamical Properties of an Impurity in a BEC in a Double Well Potential

Abstract

<p>The subject of this work is the theoretical analysis of the mean-field and many-body properties of an impurity in a Bose-Einstein condensate in a double well potential. By investigating the stationary mean-field properties we show that a critical value of the boson-impurity interaction energy, W_c, corresponds to a pitchfork bifurcation in the number difference variable in the mean-field theory. Comparing W_c to the value of W where the many-body ground state wave function begins to split shows a direct correlation signaling a connection between the many-body and mean-field theories. Investigation of the mean-field dynamics shows that chaos emerges for W > W_c in the vicinity of an unstable equilibrium point generated by the pitchfork bifurcation. An entropy is defined to quantify the chaos and compared to the entanglement entropy between the BEC and the impurity. The mean-field entropy shows a large gradient at W_c whereas the entanglement entropy shows no apparent features around the same value of W. An increase in correlations between nearest neighbour many-body eigenvalues is seen as W is increased providing evidence for ``quantum chaos''.</p>