Room-Temperature Quantum Simulation with Atomically Thin Nuclear Spin Layers in Diamond

TL;DR

The paper demonstrates a scalable, room-temperature quantum simulator built from an atomically thin ${}^{13}$C spin layer in diamond, initialized and read via nearby NV centers. By leveraging NOVEL polarization under Hartmann–Hahn matching and dipolar-coupled nuclear spins, the authors realize strong, tunable interactions and characterize spin coherence with dynamic decoupling. They validate the platform by observing discrete time-crystalline order in a 2D-like spin layer and by matching the data to a small interacting spin model, indicating genuine many-body dynamics beyond single-spin physics. This ambient-condition approach offers a practical route to study strongly correlated quantum phenomena and non-equilibrium phases at scale, with potential extensions to scanning-probe control and engineered disorder.

Abstract

Quantum simulation aims to recreate complex many-body phenomena in controlled environments, offering insights into dynamics that are otherwise difficult to model. Existing platforms, however, are often complex and costly to scale, typically requiring ultra-pure vacuum or low temperatures. Here, we realize a room-temperature quantum simulator using a thin ${}^{13}\text{C}$ nuclear spin layer in diamond. Nearby nitrogen-vacancy centers enable polarization, readout, and, combined with radio-frequency fields, coherent control of the nuclear spins. We demonstrate strong, tunable interactions among the nuclear spins and use the system to investigate discrete time-crystalline order. By combining ease of use with operation at ambient temperatures, our work opens new opportunities for investigating strongly correlated many-body effects.

Figures (5)

• Figure 1: Sample fabrication and characterization. a Structure of our diamond samples with numbered overgrowth steps, with layer colors indicating the used carbon isotope. The zoom shows an accurate representation of the atomic structure of the ${}^{13}$C layer and the red arrows highlight the implantation steps for sample A and B. b AXY spectra of N-$V$ centers with different distances to the nuclear spin layer. The spectra show two dips around the Larmor frequency (red dashed line) and a higher harmonic (dark blue dashed line), with distance-dependent linewidths. c Distance distribution for both diamond samples up to the estimation limit, marked by the red line. The black line represents the product of the implantation-induced vacancy density [V] and nitrogen density [N]. The inset visualizes the relative angle of the ${}^{13}$C layer to the N-$V$ center's symmetry axis.
• Figure 2: Initialization and control of the nuclear spin layer. a NOVEL pulse sequence used to polarize the nuclear spins with typical measurement results. The y-axis corresponds to the N-$V$ center's spin flip-flop probability and the inset shows the comparison to a diamond with a natural abundance of ${}^{13}$C. b ODMR measurement of the Overhauser shift (in non-angular frequency units). The color indicates the initialized state of the nuclear spins. c Matching the experimental settings, the image visualizes the addressed nuclear spins during the Overhauser shift measurement, assuming a layer thickness of 1 nm. The color of the nuclear spins corresponds to their perpendicular hyperfine coupling, which is proportional to the flip-flop frequency london2013detecting. d Rabi measurements of the ${}^{13}$C layer for different N-$V$ centers. The Rabi frequencies are given in non-angular frequency units. The y-axis is proportional to the collective nuclear $\langle I_z\rangle$ expectation value.
• Figure 3: Spin properties of the ${}^{13}$C layer. a Depolarization lifetime measurement in sample B, showing a significantly reduced $T_1$. The pulse sequence contains laser pulses to periodically reset the N-$V$ center into $m_s=0$. b Ramsey measurements with corresponding pulse sequence. During the experiment, the nuclear spins are subject to on-site disorder (first pictogram from left) and nuclear dipole-dipole interactions (second pictogram). c Designed to suppress on-site disorder, the Hahn echo measurements show minimal improvements and exhibit oscillations attributed to nuclear dipole-dipole interactions. d Homonuclear decoupling through the WAHUHA sequence efficiently decouples the nuclear spins from each other. The different colors correspond to different pulse spacings $\tau$.
• Figure 4: Exploring discrete time-crystalline order with the nuclear spin layer. a Representative discrete time-crystal (DTC) measurements for different interaction times $\tau$. For $\tau=0\,\text{\textmu s}$, the signal shows a beating caused by the applied over-rotation with rotation angle $\theta=1.03\,\pi$, which vanishes for increasing $\tau$. The x-axis corresponds to the Floquet cycles $N$ and the solid lines show the fit result. b Power spectral density of the measurement data for different interaction times $\tau$. Each row corresponds to the data presented in sub-figure a. c Pulse sequence of the DTC experiment. The blue blocks correspond to a free evolution time for duration $\tau$ and the gray block denotes a rf rotation pulse of angle $\theta$. The N-$V$ center is re-initialized into $m_s=0$ through a laser pulse in each repetition $N$. d Calculating the crystalline fraction $\mathcal{C}$ for different interaction times $\tau$ allows to visualize the transition to the DTC phase. The measurement data agrees well with the simulated phase transition of a 2D layer (solid line) consisting of nine nuclear spins, showing a stable DTC ($\mathcal{C}>0.99$) after $40\,\text{\textmu s}$. e Decay rate $\Gamma$ (in Floquet units) of the time-crystalline order for different rotation angles $\theta$ at $\tau=125\,\text{\textmu s}$. The decay rates are extracted through an stretched exponential fit supplement. Markovian dephasing predicts a quadratic dependence of $\Gamma$ on $\theta$, which we test by fitting the data with a quadratic function (red line) yielding $R^2=82.81\,\%$. f Decay rates as a function of the interaction time $\tau$ for $\theta=1.03\,\pi$. The blue points represent the measurement data, while the red lines shows a simulation of a single nuclear spin subject to Markovian dephasing. The green line corresponds to the simulation of a 2D layer with nine coupled nuclear spins, matching the data well at the initial measurement points. g Lifetime of the time-crystalline order for increasing $\tau$.
• Figure 5: Distance Estimation. a Corresponding distances of the extracted variances of the fitted, simulated AXY spectra. The red line (fit) shows the transfer function that is used to estimate the distance of the N-$V$ center to the ${}^{13}$C layer. b Depth distribution of a 5 keV implantation. The black solid line shows the product of the simulated vacancy density [V] and nitrogen density [N].