Quantum Transport in Driven Spin Chains

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2019

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Abstract

A one-dimensional chain of N coupled spin sites can pass an excitation along its length via dipole-dipole interaction. The Tavis-Cummings Model describes this fermionic interaction for spin chains in addition to light-matter interaction via a common cavity. We investigate spin chain transport of an excitation and the dynamical effect of adding a bosonic mode. Using Quantum Toolbox in Python (QuTiP), we approach solving systems of large N stochastically; specifically, the dynamics are represented by averaged Monte Carlo trajectories. With consideration of spin chains in experimental settings, we define three distinct, driven and dissipative systems: i) a spin chain with no cavity, ii) a spin chain coupled to a cavity at all sites, and iii) a spin chain coupled to a cavity at the Nth site. For systems ii. and iii. we show a threshold driving rate γp,thresh such that the system is saturated and cavity photon count is quenched. We then consider time-variant driving rates for several Gaussians with amplitudes A and widths σ; for a single Gaussian pulse of amplitude A>γp,thresh and width σA, the cavity occupation of systems ii and iii shows two peaks. We propose the possible application of such systems towards creating narrow pulses with well-defined spacing.

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