Many-body–localized discrete time crystal with a programmable spin-based quantum simulator

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	QuTech, Delft University of Technology
Citations	172
Analysis	Full AI Review Included

6CCVD Technical Analysis: Observation of a Many-Body-Localized Discrete Time Crystal in Diamond

Reference Paper: J. Randall et al., “Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator,” arXiv:2107.00736v1 (2021).

Executive Summary

This research establishes Single Crystal Diamond (SCD) as a critical platform for observing complex, non-equilibrium phases of matter, specifically the Many-Body-Localized Discrete Time Crystal (MBL DTC).

Core Achievement: Successful observation of the hallmark signatures of an MBL DTC using a solid-state quantum simulator based on ¹³C nuclear spins coupled to a Nitrogen-Vacancy (NV) center in diamond.
Stabilization: The DTC phase demonstrated robust spatiotemporal order, stabilized by many-body localization (MBL), ensuring stability against generic initial states.
Performance Metric: The system achieved a remarkable long-lived coherence, with a $1/e$ decay value $N_{1/e} = 472 (\pm 17)$ Floquet cycles, corresponding to an isolation lifetime of approximately $\sim 4.7$ seconds.
Material Requirement: The entire simulation hinges on the extraordinary isolation, ultra-low impurity levels, and long coherence times provided by isotopically engineered, ultra-high purity Single Crystal Diamond (SCD) substrates.
Hamiltonian Control: The platform allows for programmable simulation of many-body Hamiltonians, utilizing the NV electronic spin to control and read out a 9-spin 1D chain of ¹³C nuclear qubits.
Technical Advancement: The methodologies developed, including PulsePol initialization and nuclear-nuclear two-qubit gates, establish a scalable pathway for realizing larger 2D and 3D quantum simulators in solid-state systems.

Technical Specifications

The following quantitative parameters define the experimental setup and observed physical phenomena.

Parameter	Value	Unit	Context
Material Base	Single Crystal Diamond (SCD)	N/A	Host for NV center and ¹³C qubits
Qubit System	9	Spins	Effective 1D chain of individually controllable ¹³C nuclear spins
Operating Temperature	4	K	Cryogenic environment required for NV operation
Applied Magnetic Field ($B_z$)	$\sim 403$	G	Used to orient spins and reduce dipolar coupling to Ising form
Spin-Spin Coupling ($J_0$)	6.7 $\pm$ 0.1	Hz	Average nearest-neighbor coupling strength
Interaction Power Law ($\alpha$)	2.5 $\pm$ 0.1	N/A	Interaction falls off as $1/r^{\alpha}$, satisfying MBL criteria ($\alpha > 2d$ for $d=1$)
Strong Interaction Floquet Time ($\tau$)	5	ms	Time used to stabilize subharmonic response
Maximum Observation Cycles ($N_{max}$)	800	Cycles	Robustness demonstrated for generic initial states
Coherence Decay Value ($N_{1/e}$)	472 $\pm$ 17	Cycles	Characteristic $1/e$ decay value
System Coherence Lifetime	$\sim 4.7$	s	Measured timescale of environmental decoherence
Polishing Requirement (Implied)	Ra < 1	nm	Necessary for high-fidelity optical addressability of the NV center

Key Methodologies

The observation of the MBL DTC phase relies on the synthesis and execution of advanced quantum control sequences on the solid-state diamond platform.

Material Selection and Preparation: Utilization of ultra-high purity SCD containing a single, optically addressable Nitrogen-Vacancy (NV) center, surrounded by a controllable cluster of ¹³C nuclear spins, ensuring coherence times up to tens of seconds.
Magnetic Field and Isolation: Application of an external magnetic field ($B_z \sim 403\text{ G}$) to reduce the intrinsic dipole-dipole interactions between nuclear spins to the essential Ising form required for MBL stabilization.
Spin Chain Programming: Programming an effective 1D chain of 9 spins by carefully selecting a subset of the 27 available ¹³C spins, mapping the intrinsic 3D arrangement onto a functional 1D system with suitable short-range interactions ($\alpha \approx 2.5$).
Initialization Protocol (PulsePol): Employing the PulsePol dynamical nuclear polarization sequence to initialize the ¹³C spins into the highly polarized state $| \uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow \rangle$.
Floquet Sequence Implementation: Implementing the periodic, time-dependent Floquet sequence $U_F = [U_{int}(\tau) \cdot U_x(\theta) \cdot U_{int}(\tau)]^N$, where rotations ($U_x(\theta)$) are generated using custom multi-frequency rf pulses.
Site-Resolved Readout: Reading out individual spin states by sequentially mapping their expectation values onto the NV electronic spin via two-qubit gates (both standard electron-nuclear and customized nuclear-nuclear gates through spin-echo double resonance).
DTC Verification: Confirming the MBL DTC phase by observing a stable, long-lived, period-doubled response (subharmonic oscillation at half the drive frequency, $f=0.5$), robust against variations in initial states and external perturbation ($\theta = 0.95\pi$).

6CCVD Solutions & Capabilities

The successful execution of this MBL DTC experiment critically depends on the quality and specialized engineering of the diamond substrate. 6CCVD provides the necessary material and customization expertise to replicate and advance this research in solid-state quantum simulation.

Applicable Materials

To achieve the required qubit isolation and coherence times demonstrated in this work ($\sim 4.7$s), researchers require exceptionally pure, low-strain SCD substrates.

Material Grade	Specification	Application Alignment
Optical Grade SCD	Ultra-low [N] & [B] concentration, < 1 ppb total impurities.	Essential host material for stable, high-coherence NV center formation.
Isotopically Engineered SCD	High ¹²C enrichment (> 99.995%) OR High ¹³C enrichment (> 99%)	Required for either minimizing qubit decoherence (high ¹²C) or maximizing the available nuclear qubit register (controlled ¹³C concentration).
Precision Polishing	Substrate surface Roughness Ra < 1 nm (SCD).	Necessary for high-fidelity optical addressing and integration of microwave/RF control components.

Customization Potential

The experimental setup described necessitates precise wafer geometry, surface quality, and integration of control electronics. 6CCVD’s advanced engineering services directly support these needs:

Custom Dimensions: 6CCVD manufactures SCD plates and wafers up to 125 mm, providing ample real estate for scaling up complex quantum architectures beyond the 9-spin chain.
Thickness Control: We offer Single Crystal Diamond substrates with thicknesses ranging from 0.1 µm up to 500 µm, allowing precise management of strain and optical path length for NV excitation.
Precision Machining: The integration of microwave/RF delivery systems often requires laser cutting and precise shaping of the diamond substrate, capabilities provided by 6CCVD’s in-house engineering team.
Custom Metalization: The implementation of multi-frequency rf pulses relies on integrated on-chip wiring. 6CCVD offers internal metalization services, including thin-film deposition of Au, Pt, Pd, Ti, W, and Cu, optimized for cryogenic quantum control circuits.

Engineering Support

Replicating MBL experiments requires deep expertise in materials that balance intrinsic disorder (for MBL) with engineered purity (for coherence).

Isotope Optimization: 6CCVD’s in-house PhD team specializes in optimizing diamond material parameters, including controlling the ¹³C/¹²C ratio, essential for designing robust solid-state quantum simulators that rely on specific spin-spin coupling and minimal environmental noise.
Defect Engineering: We support researchers in controlling the placement and concentration of nitrogen impurities necessary to create high-quality NV centers, which serve as the central electronic spin coupler and readout mechanism for ¹³C nuclear qubits.
Application Expertise: 6CCVD offers consultation on substrate selection and preparation tailored specifically for solid-state quantum simulation and time crystal research, ensuring material properties satisfy stringent MBL and coherence requirements.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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

Tech Support

Original Source

DOI: https://doi.org/10.1126/science.abk0603