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arXiv:2402.07461 · Physical Review A

Simulating the spin-boson model with a controllable reservoir in an ion trap

G. -X. Wang, Yukai Wu, R. Yao, Wentao Lian, Zhi-Wen Cheng, Y.-L. Xu, C. Zhang, Yue Jiang, Yong Xu, Ben Qi, Pan‐Yu Hou, Z.-C. Zhou, Longfei He, L.-M. Duan

Published Jun 3, 2024• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.109.062402

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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.
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.
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 arranged in Coulomb crystals provide us with the elements to study the physics of a single spin coupled to a boson bath. In this work, we show that optical forces allow us to realize a variety of spin-boson models, depending on the crystal geometry and the laser configuration. We study in detail the ohmic case, which can be implemented by illuminating a single ion with a traveling wave. The mesoscopic character of the phonon bath in trapped ions induces effects such as the appearance of quantum revivals in the spin evolution.
We demonstrate a trapped-ion system with engineered competing dissipation channels, implemented independently on two ion species co-trapped in a Paul trap. We use control of the spin-oscillator couplings via motional sideband drives and engineered decay rates via optical pumping to explore the phase diagram of this system, which is analogous to that of a (phonon) laser. Reconstruction of the phonon distribution via the readout of the motional sideband oscillation allows us to show the phase transition from a dark to the bright and coherent lasing phase. In contrast to earlier work [1] our laser works close to the quantum ground state with average phonon numbers below ten. In the lasing phase, we demonstrate phase locking of the oscillator to an additional resonant drive. We use readout of the characteristic function [2] to show symmetry breaking of the Wigner function when locked. We also observe the intrinsic phase diffusion of the lasing process starting from a displaced coherent state. The readout of the characteristic function once again shows washing out of the initial asymmetry. The toolbox of techniques is extensible to squeezed laser systems through the use of additional laser drives, is predicted to offer advantages in sensing [3], and provides methods for the general use of the mixed-ion-species platform in the simulation of dissipative spin-boson systems.
Trapped atomic ion crystals are a leading platform for quantum simulations of spin systems, with programmable and long-range spin-spin interactions mediated by excitations of phonons in the crystal. We describe a complementary approach for quantum simulations of bosonic systems using phonons in trapped-ion crystals, here mediated by excitations of the trapped-ion spins. The scheme enables a high degree of programability across a dense graph of bosonic couplings, utilizing long-lived collective phonon modes in a trapped-ion chain. As such, it is well suited for tackling hard problems such as boson sampling and simulations of long-range bosonic and spin-boson Hamiltonians.