Many-body–localized discrete time crystal with a programmable spin-based quantum simulator
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-11-04 |
| Journal | Science |
| Authors | J. Randall, C. E. Bradley, F. V. van der Gronden, A. Galicia, M. H. Abobeih |
| Institutions | Lawrence Berkeley National Laboratory, University of California, Berkeley |
| Citations | 172 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Core Achievement: First observation of the hallmark signatures of a Many-Body-Localized Discrete Time Crystal (MBL DTC) phase, a novel non-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry.
- Platform: A programmable quantum simulator utilizing an effective one-dimensional (1D) chain of 9 individually controllable 13C nuclear spins in diamond, accessed via a Nitrogen-Vacancy (NV) center at 4 K.
- MBL Stabilization: The DTC phase was stabilized to long times by satisfying the theoretical requirements for Many-Body Localization (MBL) under periodic Floquet driving, specifically by engineering short-range interactions (1/r2.5(1) falloff).
- Robustness for Generic States: The observed period-doubled response was confirmed to be robust for a variety of generic initial states (including polarized and Néel states), persisting up to 800 Floquet cycles. This robustness is the key signature distinguishing MBL DTC from prethermal mechanisms.
- Coherence and Isolation: The DTC response exhibited a long 1/e decay time of N1/e = 472(17) cycles, corresponding to approximately 4.7 seconds, demonstrating the exceptional isolation and coherence of the solid-state spin platform.
- Technological Impact: The work establishes a highly coherent, programmable solid-state quantum simulator capable of realizing complex many-body Hamiltonians, opening new avenues for investigating Floquet phases and topologically protected phases of matter.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit Type | 13C | Nuclear Spin | Qubits used for quantum simulation. |
| Qubit Count (Chain) | 9 | Spins | Effective 1D chain programmed from a larger cluster. |
| Host Material | Diamond | N/A | Solid-state platform utilizing NV centers. |
| Operating Temperature | 4 | K | Cryogenic environment. |
| Magnetic Field (Bz) | ~403 | G | Applied field used to reduce dipolar interactions to Ising form. |
| Interaction Type | Dipole-Dipole (Ising zz) | N/A | Primary coupling mechanism between nuclear spins. |
| Interaction Falloff (α) | 2.5(1) | Dimensionless | Power-law decay (1/rα) across the chain; satisfies MBL requirement (α > 2d). |
| Average Nearest-Neighbor Coupling (J0) | 6.7(1) | Hz | Measured coupling strength. |
| Floquet Period (τ) | 5 | ms | Period used for strong interaction regime (MBL stabilization). |
| Maximum Cycles Measured (N) | 800 | Cycles | Maximum evolution time for generic initial states. |
| DTC 1/e Decay Value (N1/e) | 472(17) | Cycles | Measure of stability/coherence of the time crystal response. |
| DTC Decay Time (Approx.) | ~4.7 | s | Total physical time corresponding to the 1/e decay. |
Key Methodologies
Section titled “Key Methodologies”The experiment relies on precise control and measurement protocols applied to 13C nuclear spins coupled to an NV center in diamond:
- Platform Definition: An effective 1D chain of L = 9 13C nuclear spins was selected from a larger cluster (27 spins) based on their known spatial coordinates and coupling strengths (Jjk).
- Hamiltonian Engineering: The system was operated under a magnetic field (Bz) to reduce the dipole-dipole interactions to the Ising (zz) form, Hint.
- Initialization (PulsePol): Spins were initialized into highly polarized states (e.g., |↑↑…↑〉) using the dynamical nuclear polarization sequence known as PulsePol.
- Arbitrary State Preparation: Selective radio-frequency (RF) pulses were used to independently rotate each spin, enabling the preparation of generic initial states (e.g., Néel state, superposition states) required to verify MBL stabilization.
- Floquet Sequence Implementation: A periodic Floquet sequence UF = [Uint(τ) · Ux(θ) · Uint(τ)]N was applied, consisting of free evolution (Uint) interleaved with global spin rotations (Ux(θ)).
- MBL Condition Fulfillment: Global rotations Ux(θ) were realized using multi-frequency RF pulses. Setting the rotation angle θ close to π (e.g., 0.95π) decoupled the spins from the environment while preserving internal interactions, satisfying the requirement for MBL stabilization (Ising-even disorder).
- Site-Resolved Readout: Individual spin expectation values (σz) were measured sequentially. This involved mapping the nuclear spin state to the NV electronic spin using two-qubit gates (electron-nuclear gates for strongly coupled spins, nuclear-nuclear gates for weakly coupled spins), followed by resonant optical excitation measurement of the NV center.
- DTC Verification: The long-lived, period-doubled response was confirmed by measuring the averaged two-point correlation function (X) and coherence (C) over hundreds of cycles for multiple initial states.
Commercial Applications
Section titled “Commercial Applications”The underlying technology—highly coherent, individually addressable solid-state spins in diamond—is foundational for several emerging quantum technologies:
| Industry/Sector | Application Area | Relevance to MBL DTC Technology |
|---|---|---|
| Quantum Computing & Simulation | Scalable Qubit Architectures | Provides a proven solid-state platform for building quantum simulators capable of addressing complex, non-equilibrium physics (e.g., MBL, topological phases). |
| Quantum Memory | High-Coherence Storage | Utilizes 13C nuclear spins, which serve as ultra-long-lived quantum memories (coherence times up to tens of seconds) for NV-based quantum networks. |
| Quantum Sensing | Nanoscale Magnetometry & Sensing | The precise control and readout protocols developed for individual nuclear spins enhance the sensitivity and spatial resolution of NV-based quantum sensors. |
| Advanced Materials Science | Defect and Isotope Engineering | Requires high-purity diamond material with controlled concentrations of NV centers and 13C isotopes, driving advancements in diamond growth (relevant to Element Six/6ccvd.com). |
| Quantum Networking | Remote Entanglement Generation | Future scalability relies on linking multiple NV centers via photonic remote entanglement or dipolar coupling, utilizing the controlled spin registers developed here. |
View Original Abstract
Establishing order, time after time The formation of discrete time crystals, a novel phase of matter, has been proposed for some many-body quantum systems under periodic driving conditions. Randall et al . used an array of nuclear spins surrounding a nitrogen vacancy center in diamond as their many-body quantum system. Subjecting the system to a series of periodic driving pulses, they observed ordering of the spins occurring at twice the driving frequency, a signature that they claim establishes the formation of a discrete time crystal. Such dynamic control is expected to be useful for manipulating quantum systems and implementing quantum information protocols. —ISO