[Paper Review] Reply to Comment on "Space-Time Crystals of Trapped Ions"

Tongcang Li, Zhexuan Gong+6 more|arXiv (Cornell University)|Dec 31, 2012

Spectroscopy and Quantum Chemical Studies3 citations

TL;DR

This paper responds to a critical comment on the original proposal for space-time crystals in trapped ion systems, reaffirming the theoretical framework that enables time-translation symmetry breaking via periodic driving and many-body interactions. The authors demonstrate that the system exhibits stable, long-lived periodic order in both space and time, establishing a new phase of quantum matter with potential for topological quantum computation.

ABSTRACT

This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).

Motivation & Objective

• To address concerns raised by Patrick Bruno regarding the feasibility and consistency of space-time crystals in trapped ions.
• To reaffirm the theoretical basis for time-translation symmetry breaking in many-body quantum systems.
• To clarify the role of periodic driving and many-body interactions in stabilizing space-time crystalline order.
• To demonstrate the robustness of the proposed phase against decoherence and perturbations.

Proposed method

• The authors employ a theoretical analysis of a periodically driven trapped ion chain with long-range interactions.
• They use the rotating frame transformation to derive an effective Hamiltonian that captures the time-periodic dynamics.
• The stability of the time-crystalline phase is assessed via linear response theory and dynamical mean-field approximations.
• Numerical simulations are used to verify the persistence of periodic order in both spatial and temporal dimensions.
• The system's response to external perturbations is analyzed to confirm long-lived coherence.
• The role of many-body localization and quantum Zeno effects is examined to ensure phase stability.

Experimental results

Research questions

• RQ1 Can time-translation symmetry be spontaneously broken in a trapped ion system under periodic driving?
• RQ2 What is the role of long-range interactions in stabilizing space-time crystalline order?
• RQ3 How robust is the time-crystalline phase against decoherence and external perturbations?
• RQ4 Can the system exhibit stable, long-lived periodic order in both space and time simultaneously?
• RQ5 What are the conditions under which the effective Hamiltonian supports a stable time-crystalline phase?

Key findings

• The system exhibits stable, long-lived periodic order in both space and time, confirming the existence of a space-time crystal phase.
• The time-crystalline order persists even under significant decoherence, indicating robustness.
• The effective Hamiltonian derived via the rotating frame transformation supports a stable phase with broken time-translation symmetry.
• Numerical simulations confirm the persistence of periodic oscillations in the system's correlation functions.
• The phase is stabilized by the interplay of periodic driving and long-range interactions, preventing thermalization.
• The system remains in a non-thermal, coherent state over extended time scales, supporting the existence of a new quantum phase.