Dynamics of nonuniform excitations in one-dimensional spin systems

U. Brandt, K. Jacoby

S. -A. Guo, J. Ye, J. -Y. Tan +11 more

Previous experimental realizations of Dicke model in atomic or ionic systems are based on global observables assuming uniform spin-boson coupling, while inevitable experimental nonuniformity on the one hand requires site-resolved measurement of spin states, and on the other hand provides potential quantum advantage on the simulation of multi-spin distributions. Here we report the quantum simulation of a nonuniform Dicke-like model in a two-dimensional (2D) crystal of up to 200 ions. We explicitly demonstrate the sensitivity of few-spin observables and multi-spin distributions to the spatial inhomogeneity of the model, and examine the thermalization dynamics of the nonuniform model by measuring the subsystem entropies of selected ion groups. Our work enables the study of Dicke-like models beyond the symmetric subspace, paving the way toward understanding the role of disorder in its thermalization and quantum chaos behavior.

Ashley Milsted, Jutho Haegeman, Tobias J. Osborne +1 more

We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically expandable) finite region with fixed boundary conditions. The suppression of nonphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 antiferromagnetic Heisenberg model and the ${\ensuremath{\phi}}^{4}$ model.

M. S. Makivić, Mark Jarrell

Yuya Imaeda, Kazuya Fujimoto, Yuki Kawaguchi

We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein condensate periodically driven by a quadratic Zeeman coupling. This phenomenon is closely related to the Shapiro steps in superconducting Josephson junctions, and the previous experimental work [B. Evrard et al., Phys. Rev. A 100, 023604 (2019)] for a spin-1 bosonic system observed the resonant dynamics and then called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii equation, we study the Shapiro resonance beyond the single-mode approximation used in the previous work, which assumes that all components of the spinor wave function have the same spatial configuration. Considering resonant dynamics starting from a polar state, we analytically calculate the Floquet-Lyapunov exponents featuring an onset of the resonance under a linear analysis and find that spin waves with finite wave numbers can be excited. This kind of nonuniform excitation cannot be described by the single-mode approximation. Furthermore, to study the long-time resonant dynamics beyond the linear analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii equation, finding that the nonresonant hydrodynamic variables also grow at wavelengths of even multiples of the resonant one due to the nonlinear effect.

Alf Sjölander