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Chemical Physics

Dynamical simulation of the driven spin-boson system: The influence of interblip correlations

Manfred Winterstetter, Ulrich Weiß

Published May 1, 1997• 13 citations
Publisher
DOI
10.1016/s0301-0104(97)00021-9

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The dynamics of the density matrix of the two-state system under the influence of time-dependent deterministic and fluctuating forces is investigated. The exact formal solutions for the diagonal and off-diagonal elements are derived and transformed into coupled nonconvolutive master equations and integral relations. Thereby, the evolution of any observable relevant to the two-state system may be described. Solutions of the dynamical equations in analytic form are presented both for high and low temperatures. An iterative numerical method is put forward in which the familiar noninteracting-blip approximation is systematically improved by taking into account all bath-induced nearest-neighbor interblip correlations. The expanded treatment is found to be indispensable in studies of the dynamics of the off-diagonal elements at low temperatures. Finally, we discuss selection rules, as well as possibilities of control of tunneling, which occur in the presence of monochromatic driving.
A generalized approximation scheme is proposed to describe the dynamics of the spin-boson problem. Being nonperturbative in the coupling strength nor in the tunneling frequency, it gives reliable results over a wide regime of temperatures and coupling strength to the thermal environment for a large class of bath spectral densities. We use a path-integral approach and start from the exact solution for the two-level system population difference in the form of a generalized master equation (GME). Then, we approximate interblip and blip-sojourn interactions up to linear order, while retaining all intrablip correlations to find the kernels entering the GME in analytical form. Our approximation scheme, which we call weakly interacting blip approximation, fully agrees with conventional perturbative approximations in the tunneling matrix element (noninteracting-blip approximation) or in the system-bath coupling strength in the proper parameter regime.
We report on an experimental simulation of the spin-1 Heisenberg model with composite bosons in a one-dimensional chain based on the two-component Bose-Hubbard model. Exploiting our site- and spin-resolved quantum gas microscope, we observed faster superexchange dynamics of the spin-1 system compared to its spin-1/2 counterpart, which is attributed to the enhancement effect of multi-bosons. We further probed the nonequilibrium spin dynamics driven by the superexchange and single-ion anisotropy terms, unveiling the linear expansion of the spin-spin correlations, which is limited by the Lieb-Robinson bound. Based on the superexchange process, we prepared and verified the entangled qutrits pairs with these composite spin-1 bosons, potentially being applied in qutrit-based quantum information processing.