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arXiv:2311.11726 · Science

Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator

Cheng Chen, Gabriel Emperauger, Guillaume Bornet, Filippo Caleca, Bastien Gély, Marcus Bintz, Shubhayu Chatterjee, Vincent S. Liu, Daniel Barredo, Norman Y. Yao, Thierry Lahaye, Fabio Mezzacapo, Tommaso Roscilde, Antoine Browaeys

Published Jun 19, 2025• 23 citations
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Abstract

The nature and spectrum of elementary excitations are defining features of a many-body system. In this study, we used a Rydberg quantum simulator to demonstrate a form of spectroscopy, called quench spectroscopy, that probes these low-energy excitations. We illustrated the method on a two-dimensional simulation of the spin-1/2 dipolar XY model. Through microscopic measurements of the spatial spin correlation dynamics following a quench, we extracted the dispersion relation of the elementary excitations for both ferro- and antiferromagnetic couplings. The ferromagnet exhibits elementary excitations behaving as linear spin waves, whereas in the antiferromagnet, spin waves appear to decay, suggesting the presence of strong nonlinearities. Our demonstration highlights the importance of power-law interactions on the excitation spectrum of a many-body system.

DOI
10.1126/science.adn0618

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The nature and spectrum of elementary excitations are defining features of a many-body system. In this study, we used a Rydberg quantum simulator to demonstrate a form of spectroscopy, called quench spectroscopy, that probes these low-energy excitations. We illustrated the method on a two-dimensional simulation of the spin-1/2 dipolar XY model. Through microscopic measurements of the spatial spin correlation dynamics following a quench, we extracted the dispersion relation of the elementary excitations for both ferro- and antiferromagnetic couplings. The ferromagnet exhibits elementary excitations behaving as linear spin waves, whereas in the antiferromagnet, spin waves appear to decay, suggesting the presence of strong nonlinearities. Our demonstration highlights the importance of power-law interactions on the excitation spectrum of a many-body system.
The elementary excitation spectrum of a many-body quantum system encodes many key properties, including phenomena as diverse as transport, thermalisation and ground state structure. Excitation spectra of strongly correlated systems are typically encoded in dynamical structure factors, which are demanding to measure experimentally and challenging to compute classically. Here we use quench spectroscopy on a superconducting quantum processor to extract excitation spectra of spin chains of L=101L=101L=101 spins. By tailoring the combination of quench protocol and observable, we selectively access distinct excitation sectors across several phases of the spin-1/21/21/2 XXZ chain, resolving free magnons, multi-magnon bound states, and two-spinon continua. Notably, we demonstrate that the protocol does not rely on ground state preparation: in the classically challenging gapless regime, we extract spectra directly from the quench dynamics of easily prepared product states, a procedure that is natural and straightforward on quantum hardware. Our work establishes quench spectroscopy as a fast and flexible probe of many-body excitation spectra on digital quantum hardware, introduces a novel quench protocol that does not require costly state preparation routines, and provides a scalable route towards regimes where classical simulation may become intractable.
The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasi-particles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional S=1/2S=1/2S=1/2 Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.
The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasiparticles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional S=1/2S=1/2S=1/2 Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the nonlocal nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed-matter physics. Here, we show theoretically that quench spectroscopy for synthetic quantum matter---which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions---can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure nonlocal spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on exact results for the quench dynamics of quantum spin chains, and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.
Quench spectroscopy is a relatively new method which enables the investigation of spectral properties of many-body quantum systems by monitoring the out-of-equilibrium dynamics of real-space observables after a quench. So far the approach has been devised for global quenches or using local engineering of momentum-resolved excitations. Here, we extend the quench spectroscopy method to local quenches. We show that it allows us to extract quantitative information about global properties of the system, and in particular the elementary excitation spectrum. Using state-of-the-art numerical methods, we simulate the out-of-equilibrium dynamics of a variety of quantum systems following various local quench protocols and demonstrate a general scheme for designing an appropriate local quench protocol for any chosen model. We provide detailed examples of how the local quench protocol can be realized in realistic current generation experiments, including ultracold atomic gases and trapped ion systems.
In this paper, we analytically compute the quench dynamics of simple product states that evolve under a spin-1/2 XY-model with power-law interactions in a staggered magnetic field. We use linear spin-wave theory as well as a low-energy theory that accounts for strong phase fluctuations. This allows us to provide an analytic expression for the dynamics of phase-type correlations with short-range interactions, where the linear spin-wave theory is known to fail. For density-type correlations the low-energy theory and the linear spin-wave theory give the same result. Our analysis is valid for arbitrary magnetic field strength and in particular provides an analytical understanding of the quench dynamics near criticality. Our results can thus provide useful tools for the experimental observation of excitation gaps and critical behavior.
Local moments with a spin S>1/2 can exhibit a rich variety of elementary quasiparticle excitations, such as quadrupolar excitations, that go beyond the dipolar magnons of conventional spin-1/2 systems. However, the experimental observation of such quadrupolar excitations is often challenging due to the dipolar selection rules of many linear response probes, rendering them invisible. Here we show that nonlinear spectroscopy, in the form of two-dimensional coherent spectroscopy (2DCS), can be used to reveal quadrupolar excitations. Considering a family of spin-1 Heisenberg ferromagnets with single-ion easy-axis anisotropy as an example, we explicitly calculate their 2DCS signature by combining exact diagonalization and generalized spin wave theory. We further demonstrate that 2DCS can provide access to the quadrupolar weight of an excitation, analogous to how linear response provides access to the dipolar weight. Our work highlights the potential of nonlinear spectroscopy as a powerful tool to diagnose multipolar excitations in quantum magnets.