Multi-particle quantum walks and Fisher information in one-dimensional lattices

Abstract

Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D) lattices. However the roles of interaction and quantum statistics in such a kind of walks are little known at a many-body level. In this letter, using time-evolving block decimation algorithm and many-body perturbation theory we rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs) for three indistinguishable bosons and fermions in 1D lattices. We show that such strongly correlated many-body QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states, two- and three-body bound states, but also present a quantum enhanced precision measurement of the gravitational force. It turns out that in contrast to the walks of the fermions, the QWs of three bosons exhibit richer dynamics of co-walkings and competitive Bloch oscillations, which remarkably present a surprising time scaling $t^3$ of FI below a characteristic time $t_0$ and saturate to the fundamental limit of $t^2$ for $t>t_0$.

6+16 pages, 5+11 figures

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Cited by in corpus (14)

• Simulating lossy Gaussian boson sampling with matrix product operators
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• Flux enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder
• Flux induced re-entrant dynamics in the quantum walk of interacting bosons
• Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\text{SU}(N)$ Hubbard Models
• Nonstabilizerness generation in a multiparticle quantum walk
• Few-magnon excitations in a frustrated spin-$S$ ferromagnetic chain with single-ion anisotropy
• First-detection-time statistics in many-body quantum transport
• Non-Rayleigh signal of interacting quantum particles
• Quantum walk on a square lattice with identical particles
• Optimization for the propagation of a multiparticle quantum walk in a one-dimensional lattice
• Correlated dynamics of three-particle bound states induced by emergent impurities in Bose-Hubbard model
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Lissajous dynamics of a quantum particle in a tilted two-dimensional discrete lattice