Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1512.05316 · Physical Review A

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap-based quantum simulator

Bryce Yoshimura, James K. Freericks

Published May 11, 2016• 5 citations
arXivHTMLPDF

Abstract

Recently a variant on Ramsey interferometry for coupled spin-$1/2$ systems was proposed to directly measure the retarded spin-spin Green's function. In conventional experimental situations, the spin system is initially in a nonequilibrium state before the Ramsey interferometry is performed, so we examine the nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excited higher-energy states via a temporally ramped transverse magnetic field. We then apply the Ramsey spectroscopy protocol to the final Hamiltonian, which has a constant transverse field. The short time allows us to extract the initial transport of many-body correlations, while the long-time behavior relates to the excitation spectra of the Hamiltonian. Compressive sensing is employed in the data analysis to efficiently extract that spectra.

DOI
10.1103/physreva.93.052314

Related papers

Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry

Michael Knap, Adrian Kantian, Thierry Giamarchi +3 more

We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.

arXiv:1307.0006•Physical Review Letters•Oct 4, 2013•164 citations

Many-body interferometry of one-dimensional integrable systems

Maksims Arzamasovs, Min Liu, Yue Zhang +4 more

We propose using many-body Ramsey interferometry to measure non-equilibrium correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into non-thermal Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, can convincingly distinguish between the GGE and thermal post-quench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring the response functions with Ramsey interferometry, which can be used to distinguish between different post-quench phases of the model. Our proposal can be realized with current ultracold atom techniques, and opens up the possibility to study dynamics in non-thermal ensembles.

arXiv:2412.15719•Dec 20, 2024•0 citations

Diabatic ramping spectroscopy of many-body excited states for trapped-ion quantum simulators

Bryce Yoshimura, Wesley C. Campbell, James K. Freericks

Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping of the transverse field and measures a low-noise observable as a function of time for a constant field to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate the experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced making such experiments feasible with current technology.

arXiv:1402.7357•Feb 28, 2014•2 citations

Many-body interferometry of one-dimensional integrable systems

Min Liu, Maksims Arzamasovs, Yue Zhang +4 more

We propose using many-body Ramsey interferometry to measure correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into nonthermal generalized Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, convincingly distinguish between the GGE and thermal postquench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring response functions with Ramsey interferometry, which can be used to distinguish between different postquench phases of the model. Our proposal can be realized with current ultracold atom techniques and opens up the possibility to study dynamics in nonthermal ensembles.

Physical Review A•May 16, 2025•1 citation

Many-Body Dephasing in a Trapped-Ion Quantum Simulator

Harvey Kaplan, Lingzhen Guo, Wen Lin Tan +4 more

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.

arXiv:2001.02477•Physical Review Letters•Sep 18, 2020•37 citations

Recent progress in quantum simulation with trapped ions

James K. Freericks

Quantum emulation of the transverse field Ising model has made significant progress recently. Ions are placed in a trap and then have an optical spin-dependent force applied to them which generates an effective spin-spin interaction between the different ions. The spin-spin interaction is long range, with a power law that can be continuously adjusted from the uniform case (power law zero) to the dipole-dipole case (power law three). I will begin with a discussion of the experimental results from the Monroe group on examining the antiferromagnetic case in a linear Paul trap with up to 16 spins [1]. Next, I will discuss the progress from the Bollinger group on examining the ferromagnetic spin-spin interactions between about 300 spins in a rotating Penning trap [2]. Both of these experiments show the challenge with scaling up these systems to large sizes, namely that it is difficult to maintain the adiabaticity condition due to experimental limitations on the coherence of the system (primarily from spontaneous emission). The diabatic evolution presents a new opportunity in determining the excitation energies of the spin systems via spectroscopic techniques. Advanced signal processing techniques that employ compressive sensing are needed to efficiently process such data. I will discuss the feasibility of such analyses for future experiments.

Bulletin of the American Physical Society•Mar 6, 2014•0 citations
Recently a variant on Ramsey interferometry for coupled spin-1/21/21/2 systems was proposed to directly measure the retarded spin-spin Green's function. In conventional experimental situations, the spin system is initially in a nonequilibrium state before the Ramsey interferometry is performed, so we examine the nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excited higher-energy states via a temporally ramped transverse magnetic field. We then apply the Ramsey spectroscopy protocol to the final Hamiltonian, which has a constant transverse field. The short time allows us to extract the initial transport of many-body correlations, while the long-time behavior relates to the excitation spectra of the Hamiltonian. Compressive sensing is employed in the data analysis to efficiently extract that spectra.
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
We propose using many-body Ramsey interferometry to measure non-equilibrium correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into non-thermal Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, can convincingly distinguish between the GGE and thermal post-quench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring the response functions with Ramsey interferometry, which can be used to distinguish between different post-quench phases of the model. Our proposal can be realized with current ultracold atom techniques, and opens up the possibility to study dynamics in non-thermal ensembles.
Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping of the transverse field and measures a low-noise observable as a function of time for a constant field to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate the experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced making such experiments feasible with current technology.
We propose using many-body Ramsey interferometry to measure correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into nonthermal generalized Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, convincingly distinguish between the GGE and thermal postquench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring response functions with Ramsey interferometry, which can be used to distinguish between different postquench phases of the model. Our proposal can be realized with current ultracold atom techniques and opens up the possibility to study dynamics in nonthermal ensembles.
How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.
Quantum emulation of the transverse field Ising model has made significant progress recently. Ions are placed in a trap and then have an optical spin-dependent force applied to them which generates an effective spin-spin interaction between the different ions. The spin-spin interaction is long range, with a power law that can be continuously adjusted from the uniform case (power law zero) to the dipole-dipole case (power law three). I will begin with a discussion of the experimental results from the Monroe group on examining the antiferromagnetic case in a linear Paul trap with up to 16 spins [1]. Next, I will discuss the progress from the Bollinger group on examining the ferromagnetic spin-spin interactions between about 300 spins in a rotating Penning trap [2]. Both of these experiments show the challenge with scaling up these systems to large sizes, namely that it is difficult to maintain the adiabaticity condition due to experimental limitations on the coherence of the system (primarily from spontaneous emission). The diabatic evolution presents a new opportunity in determining the excitation energies of the spin systems via spectroscopic techniques. Advanced signal processing techniques that employ compressive sensing are needed to efficiently process such data. I will discuss the feasibility of such analyses for future experiments.