Entropy production and statistical relaxation of dipolar bosons and fermions in interaction quench dynamics

Abstract

We study the out-of-equilibrium dynamics of dipolar bosons and fermions after a sudden change in the interaction strength from zero to a finite repulsive value. We simulate the interaction quench on the initial state which is the ground state of harmonic potential with noninteracting bosons and fermions. We solve the time-dependent many-boson Schr\"odinger equation exactly using numerical methods. To understand the many-body dynamics we analyze several measures of many-body information entropy, monitoring their time evolution and assessing their dependence on interaction strength. We establish that for weak interaction quench the dynamics is statistics independent, both dipolar bosons and fermions do not relax. Whereas it is significantly different for dipolar bosons from that of dipolar fermions in the stronger interaction quench. When dipolar bosons exhibit concurrent signature of relaxation in all entropy measures, dipolar fermions fail to relax. For dipolar bosons and for larger interaction quench, the many-body information entropy measures dynamically approach the value predicted for the Gaussian orthogonal ensemble of random matrices, implying statistical relaxation. The relaxation time is uniquely determined when the orbital fragmentation exhibits a $1/M$ population in each orbital ($M$ is the number of orbitals) and all entropy measures saturate to the maximum entropy values. The relaxation time also becomes independent of the strength of dipolar interaction. Whereas, for the same quench protocol, dipolar fermions exhibit modulated oscillations in all entropy dynamics. Our study is also complemented by the measures of delocalization in Hilbert space, clearly establishing the onset of chaos for strongly interacting dipolar bosons. It highlights the importance of many-body effects with a possible exploration in quantum simulation with ultracold atoms.