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arxiv: 2410.05625 · v2 · pith:ZQBGSBVNnew · submitted 2024-10-08 · 🪐 quant-ph · cond-mat.stat-mech

Sensing with discrete time crystals

Leo Joon Il Moon , Paul M. Schindler , Ryan J. Smith , Emanuel Druga , Zhuo-Rui Zhang , Marin Bukov , Ashok Ajoy This is my paper

Pith reviewed 2026-05-23 19:46 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords discrete time crystalsprethermal DTCquantum sensingAC magnetic fieldsnuclear spinsdipolar interactionsdiamond
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The pith

Prethermal discrete time crystals serve as sensors for AC magnetic fields by turning drive deviations into a resonant signal.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that prethermal discrete time crystals in driven nuclear spins can detect time-varying magnetic fields by incorporating the field into the periodic drive. This produces an exponential extension of the crystal lifetime up to 44,204 cycles and a sharp resonant peak in the order parameter. The resulting sensor has a linewidth set only by the crystal lifetime itself because interspin interactions stabilize the order against other noise. The method works in the 0.5-50 kHz band and remains effective even when the drive protocol contains errors or the sample is inhomogeneous.

Core claim

We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, with improvements of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50kHz range and attains a competitive 0.

What carries the argument

The prethermal discrete time crystal order parameter, whose response to small deviations in the drive is converted into a detectable signal while the AC field itself extends the lifetime.

If this is right

  • The sensor linewidth is set solely by the PDTC lifetime because interspin interactions suppress other decoherence.
  • The device functions across the 0.5-50 kHz band where atomic-vapor and electronic-spin sensors are difficult to operate.
  • PDTC sensors remain functional despite drive-protocol errors and sample inhomogeneities.
  • The same sensing principle applies without change to superconducting qubits, neutral atoms, and trapped ions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The lifetime-extension mechanism could be combined with other many-body stabilized phases to create hybrid sensors.
  • Because the approach is platform-agnostic, it offers a route to sensing in systems where conventional sensors cannot tolerate drive imperfections.

Load-bearing premise

The resonant response of the order parameter arises only from the AC field and the linewidth equals the inverse of the PDTC lifetime with no other decoherence channels dominating.

What would settle it

Observation of a resonant linewidth substantially wider than the inverse of the measured PDTC lifetime of 44,204 cycles in the same system.

Figures

Figures reproduced from arXiv: 2410.05625 by Ashok Ajoy, Emanuel Druga, Leo Joon Il Moon, Marin Bukov, Paul M. Schindler, Ryan J. Smith, Zhuo-Rui Zhang.

Figure 1
Figure 1. Figure 1: System and Principle. (A) System consists of dipolar interacting 13C nuclear spins, hyperpolarized by NV centers using optical and chirped microwave excitation. (B) Protocol (i) uses a concatenated two-tone drive with 𝑁 spin-locking (pink) 𝜃(xˆ)-pulses separated by 𝜏, interspersed with spin-flip 𝛾(yˆ)-pulses (yellow). This time block, of total period 𝑇, is repeated 𝑀 times. The protocol causes switching be… view at source ↗
Figure 2
Figure 2. Figure 2: PDTC lifetime extension under resonant AC fields. (A) Effect of AC field phase ΦAC. (i) Schematic: AC field phase ΦAC is measured relative to the application of the 𝛾𝑦 pulses, with ΦAC=0, 𝜋 indicating AC field troughs and peaks align with center of 𝛾𝑦 kicks. (ii) Lifetime extension fidelity 𝐹 (Eq. (1)) as a function of AC field phase ΦAC at fixed amplitude 𝐵AC=8.24 𝜇T on resonance. Signal increase is stron… view at source ↗
Figure 3
Figure 3. Figure 3: PDTC based AC magnetic field sensing. (A) Narrow linewidth AC sensing: The fidelity 𝐹 (blue points) is measured by sweeping the frequency 𝑓AC with 𝐵AC = 8.24, 𝜇T and 𝑁 = 4, while keeping other parameters consistent with Fig. 1C. A sharp increase in PDTC lifetime, and hence fidelity, occurs at the resonance condition 𝑓AC = 𝑓res. In contrast, the spin-lock sensing scheme introduced in [41] (grey points) lack… view at source ↗
Figure 4
Figure 4. Figure 4: Single-axis PDTC extension under AC field: (A) (i) Pro￾tocol: PDTC sequence (green) consists of a train of 𝑀 𝛾𝑦=𝜋-pulses along yˆ, spaced by 300 𝜇s, flipping the spins between +zˆ and −zˆ, robust to deviations from 𝛾𝑦=𝜋 [9]. Spin-locking trains before and after the DTC sequence read initial and final spin population ⟨𝐼𝑧 ⟩, enhancing signal-to-noise ratio. (ii) Spin motion on the Bloch sphere. PDTC oscillat… view at source ↗
read the original abstract

Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, with improvements of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50kHz range - a challenging frequency regime for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a quantum sensing protocol based on prethermal discrete time crystals (PDTCs) formed by strongly driven, dipolar-coupled 13C nuclear spins in diamond. By incorporating a time-varying AC magnetic field into the PDTC drive, the authors report an exponential extension of the PDTC lifetime by up to three orders of magnitude, reaching 44,204 cycles, accompanied by a resonant response in the time-crystalline order parameter. They claim that the sensor's linewidth is determined exclusively by the PDTC lifetime due to the stabilizing effect of strong interspin interactions, enabling operation in the 0.5-50 kHz frequency range with competitive sensitivity and robustness to drive errors and inhomogeneities.

Significance. If the central claims hold, the work would demonstrate a many-body nonequilibrium platform for AC sensing that achieves substantial lifetime extension and frequency selectivity via interaction-stabilized order, with potential advantages in robustness and applicability across platforms. The reported three-order lifetime improvement and resonant behavior would represent a notable experimental result if supported by verifiable data.

major comments (2)
  1. [Abstract] Abstract: The assertion that 'the linewidth of our sensor is limited by the PDTC lifetime alone' is central to the frequency-selectivity and sensitivity claims, yet no data, error bars, controls, or analysis are supplied to demonstrate that residual magnetic gradients, pulse-area errors, spin diffusion, or other inhomogeneities are negligible compared with the 44,204-cycle lifetime in the 13C diamond system.
  2. [Abstract] Abstract: The reported lifetime of 44,204 cycles and 'strong resonant response' are presented without accompanying experimental traces, statistical significance, or exclusion criteria for alternative decoherence channels, leaving the isolation of order-parameter susceptibility unverified and the competitive-sensitivity claim unsubstantiated.
minor comments (1)
  1. The abstract states 'competitive sensitivity' without quantitative benchmarks against existing sensors operating in the 0.5-50 kHz band.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying points that require clarification. We address each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that 'the linewidth of our sensor is limited by the PDTC lifetime alone' is central to the frequency-selectivity and sensitivity claims, yet no data, error bars, controls, or analysis are supplied to demonstrate that residual magnetic gradients, pulse-area errors, spin diffusion, or other inhomogeneities are negligible compared with the 44,204-cycle lifetime in the 13C diamond system.

    Authors: We agree that an explicit quantitative demonstration is needed to support this claim. In the revised manuscript we will add a new subsection (with associated figure or table) that compares the observed sensor linewidth against independent estimates of magnetic gradients, pulse-area errors, and spin diffusion. Error bars from repeated experimental runs will be included, together with controls that vary the interaction strength to confirm the stabilizing role of the dipolar couplings. These additions will be placed in the main text so that the abstract claim is directly substantiated. revision: yes

  2. Referee: [Abstract] Abstract: The reported lifetime of 44,204 cycles and 'strong resonant response' are presented without accompanying experimental traces, statistical significance, or exclusion criteria for alternative decoherence channels, leaving the isolation of order-parameter susceptibility unverified and the competitive-sensitivity claim unsubstantiated.

    Authors: The time traces, decay curves, and resonant response data that yield the 44,204-cycle lifetime are already shown in the main figures, with uncertainties obtained from exponential fits across multiple repetitions. To strengthen the presentation we will add, in the supplementary information, a dedicated section that (i) reproduces the raw order-parameter traces, (ii) details the statistical fitting procedure and significance tests, and (iii) explicitly compares resonant versus off-resonant and interaction-suppressed cases to exclude alternative decoherence channels. The competitive-sensitivity comparison will also be expanded with the same data set. revision: partial

Circularity Check

0 steps flagged

No significant circularity; sensor claims rest on experimental susceptibility measurements

full rationale

The paper's derivation chain consists of experimental observations of PDTC order parameter response to AC fields in the 13C diamond system, with lifetime extension and linewidth statements tied directly to measured cycle counts and interaction stabilization rather than any self-definitional equations, fitted inputs renamed as predictions, or load-bearing self-citations. The central sensing principle (susceptibility of order parameter) is presented as a physical property of the driven many-body system and does not reduce to its own inputs by construction. No uniqueness theorems or ansatzes are imported via self-citation in a manner that forces the result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, new axioms, or invented entities are introduced beyond standard assumptions of driven quantum many-body systems and prethermal physics.

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