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arXiv:2405.14624 · Nature Communications

Quantum simulation of spin-boson models with structured bath

Ke Sun, Mingyu Kang, Hanggai Nuomin, George Schwartz, David N. Beratan, Kenneth R. Brown, Jungsang Kim

Published Apr 29, 2025• 41 citations
arXivHTMLPDF

Abstract

Abstract The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems that describe many dissipative processes in physical, chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models, by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons, respectively. We demonstrate a fully programmable method to simulate dissipative dynamics of spin-boson models using a chain of trapped ions, where the initial temperature and the spectral densities of the boson bath are engineered by controlling the state of the motional modes and their coupling with qubit states. Our method provides a versatile and precise experimental tool for studying open quantum systems.

DOI
10.1038/s41467-025-59296-y

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Abstract The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems that describe many dissipative processes in physical, chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models, by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons, respectively. We demonstrate a fully programmable method to simulate dissipative dynamics of spin-boson models using a chain of trapped ions, where the initial temperature and the spectral densities of the boson bath are engineered by controlling the state of the motional modes and their coupling with qubit states. Our method provides a versatile and precise experimental tool for studying open quantum systems.
The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions in which a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates that the ion trap is a powerful platform for simulating open quantum dynamics with complicated reservoir structures.
We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. The protocol is especially well-suited to simulate spin-boson models with structured environments. We propose to work with mixed-species crystals such that one species serves to encode the spin while the other species is used to cool the vibrational degrees of freedom to engineer the environment. The strength of the dissipation on the spin can be controlled by tuning the coupling between spin and vibrational degrees of freedom. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. We illustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian.
We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. We propose to work with mixed-species crystals such that one species serves to encode the spin while the other species is used to cool the vibrational degrees of freedom to engineer the environment. The strength of the dissipation on the spin can be controlled by tuning the coupling between spin and vibrational degrees of freedom. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. We illustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian.
Trapped ions offer a controlled and versatile platform for the simulation of spin and spin-boson quantum systems. The Coulomb interaction between ions trapped in a harmonic potential can be used to mediate interactions between effective spins in the ion chain. Generally, coherent operations on ions are performed on ground-state qubits encoded in magnetically insensitive hyperfine sublevels. In this thesis, we extend this toolbox with the aim of simultaneously manipulating both ground-state and optical qubits, with the latter encoded in metastable optically excited states. The optical qubit provides another set of coherent and dissipative operations that can be performed on the ions, opening new avenues for quantum computing and simulation. In our experiment, we use 171Yb+ and 172Yb+ ions to encode ground-state and optical qubits. We discuss the laser setup needed to address the narrow quadrupole transition from 2S1/2 →2 D3/2 of 3.02 Hz linewidth, and we describe spectroscopy techniques to study this transition in both the isotopes. We describe how the low linewidth allows resolved sideband cooling on the shared motional modes in an ion chain, enabling sympathetic cooling with one ion, 172Yb+ , while simultaneously performing coherent operations on the 171Yb+ ion. Finally, we discuss the prospects of using this tool for light-shift entangling gates, showing the flexibility of this trapped-ion system for simulating coherent as well as dissipative quantum systems.
We propose and demonstrate an experimental scheme to engineer thermal baths with independently tunable temperatures and dissipation rates for the motional modes of a trapped-ion system. This approach enables robust thermal-state preparation and quantum simulations of open-system dynamics in bosonic and spin-boson models at well-controlled finite temperatures. We benchmark our protocol by experimentally realizing out-of-equilibrium dynamics of a charge-transfer model at different temperatures. We observe that, when the process occurs at a higher temperature, the transfer rate spectrum broadens, with reduced rates at small donor-acceptor energy gaps and enhanced rates at large gaps. We then employ our scheme to study local-temperature effects in a two-mode vibrationally assisted exciton transfer system, where we observe thermally activated interference pathways for excitation transfer.
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.