Exact Many-body Quantum Dynamics in One-Dimensional Baths via "Superspins"

TL;DR

This paper introduces a symmetry-based method using 'superspins' to efficiently compute exact many-body quantum dynamics in one-dimensional baths, reducing computational complexity and revealing new physical insights.

Contribution

The authors develop a novel symmetry exploitation technique that groups qubits into superspins, enabling exact calculations of large-scale many-body quantum dynamics beyond traditional methods.

Findings

Efficient computation of superradiant dynamics in large qubit arrays.

Identification of non-conservation of total spin length in superradiance.

Discovery of long-time dark states with entanglement for quantum metrology.

Abstract

Computing the exact dynamics of many-body quantum systems becomes intractable as system size grows. Here, we present a symmetry-based method that provides an exponential reduction in the complexity of a broad class of such problems $\unicode{x2014}$ qubits coupled to one-dimensional electromagnetic baths. We identify conditions under which partial permutational symmetry emerges and exploit it to group qubits into collective multi-level degrees of freedom, which we term ''superspins.'' These superspins obey a generalized angular momentum algebra, reducing the relevant Hilbert space dimension from exponential to polynomial. Using this framework, we efficiently compute many-body superradiant dynamics in large arrays of qubits coupled to waveguides and ring resonators, showing that $\unicode{x2014}$ unlike in conventional Dicke superradiance $\unicode{x2014}$ the total spin length is not conserved. At long times, dark states become populated. We identify configurations where these states exhibit metrologically useful entanglement. Our approach enables exact treatment of complex dissipative dynamics beyond the fully symmetric limit and provides a rigorous benchmark for approximate numerical methods.