Microkelvin resolution thermometry at the nanometre scale

AI summary

Overview

Research area: Nanoscale quantum thermometry using nitrogen-vacancy (NV) centres in diamond, with applications spanning quantum sensing, biology and catalysis.

Technical level: Advanced. The paper assumes familiarity with NV spin physics, optically detected magnetic resonance (ODMR), coherence times and sensitivity metrics, although the core result — a tiny thermometer with microkelvin resolution — is conceptually accessible.

Scope: The paper demonstrates that isotopically purified dual-NV nanodiamonds combined with a bespoke quantum sensing chip deliver temperature sensitivities and resolution previously achievable only in bulk diamond, and applies this capability to laser-induced heating and to a chemical mixing experiment.

What This Paper Is About

Measuring temperature accurately at the nanometre scale is hard because existing nanoscale sensors are insensitive, especially for fast or transient events. Nanodiamonds containing NV centres are biocompatible and can be placed inside living cells, but their thermometry performance has been limited by short coherence times and low photon counts. This paper shows that isotopically purified nanodiamonds containing two aligned NV centres, read out with a thermal echo protocol on a custom chip, reach sub-millikelvin resolution and sensitivities competitive with bulk diamond.

Key Contributions

1. A dual-NV nanodiamond thermometry platform. The authors use nanodiamonds ball-milled from isotopically purified ¹²C diamond that contain two NV centres oriented in the same direction, giving double the photon counts without degrading coherence. They report an approximately 30% improvement in temperature sensitivity compared with an equivalent single-NV nanodiamond.

2. Sensitivity and resolution at bulk-diamond levels in a nanoscale sensor. They report an experimental sensitivity of 48.2 mK/√Hz under real operating conditions, a shot-noise-limited sensitivity of 9.6 mK/√Hz, and a temperature noise floor (resolution) of 682 μK. The abstract frames this as an order of magnitude improvement in temperature measurement sensitivity compared with previous reports.

3. Quantification of probe-induced heating. Using the thermal echo protocol, they measure how the 532 nm excitation laser used for NV readout heats the nanodiamond itself, reaching a maximum temperature rise of 224 mK at 0.63 mW incident power, with a linear dependence of 337 mK mW⁻¹.

4. Direct nanoscale observation of exothermic mixing. They observe a 1.5 K transient temperature rise when 10 μL of 1 mM FCCP dissolved in DMSO is added to 200 μL of deionized water, decaying over 180 seconds — a chemical artefact that could be mistaken for biological thermogenesis.

Main Findings

• Dual-NV identification: A normalized correlation of g⁽²⁾(t_delay = 0) = 0.592 ± 0.004 indicates two NV centres in the selected nanodiamond. CW-ODMR and magnetic field alignment indicate both NVs share the same lattice orientation.

• Spin properties: With an external field of approximately 5 mT producing a 140 MHz Zeeman splitting, Rabi rates of approximately (2π) 10.5 MHz are achieved. Ramsey measurements give T₂* = 11.7 ± 1.6 μs, Hahn echo gives T₂,HE = 102.6 ± 0.9 μs, and spin-lattice relaxation gives T₁ = 5.2 ± 0.3 ms.

• Sensor size: Atomic force microscopy and dynamic light scattering give a major axis diameter of approximately 280 nm, consistent with the original nanodiamond work and within the size range reported to be taken up by cells.

• Thermal echo performance: The thermal echo coherence envelope time constant is T_TE = 34.4 ± 0.2 μs, with measured photon detection probabilities p₀ = 0.151 and p₁ = 0.112, yielding a shot-noise-limited sensitivity of 9.6 mK/√Hz.

• Comparison of protocols on the same nanodiamond: Shot-noise-limited sensitivities are 1.013 K/√Hz for continuous-wave ODMR, 102 mK/√Hz for pulsed ODMR, and 9.6 mK/√Hz for thermal echo — an improvement of two orders of magnitude over CW-ODMR.

• Controls and variants: The thermal echo protocol applied to an ensemble bulk diamond sample gave a worse sensitivity of 266 mK/√Hz, and a zero-field variant on the same nanodiamond gave 284 mK/√Hz.

• Robustness to detuning and field misalignment: Deliberate microwave detuning in 50 kHz steps over a ±3.2 MHz range (approximately ±33 °C) reproduces the applied detuning exactly, with errors growing at large detuning due to reduced contrast and undersampling. A misaligned external field at a polar angle of 78° relative to the NV axis produces only an approximately 20% decrease in temperature resolution and sensitivity.

• In situ calibration: Cross-referenced against an on-chip resistance temperature detector (RTD), the temperature coefficient is −95.7 kHz/K — larger than typical bulk diamond values but similar to previous nanodiamond reports.

• Agreement with an independent thermometer: During on-chip heating pulses of 50–500 ns, nanodiamond readout closely matches the on-chip RTD, with an offset attributed to the nanodiamond sitting closer to the heater than the comparatively macroscopic RTD. The average error on a temperature measurement taking 83 seconds was 11.9 mK.

• Laser heating is modest: Heating scales linearly with incident laser power at 337 mK mW⁻¹, reaching 224 mK at 0.63 mW. The authors attribute this partly to poor thermal conductivity of the glass substrate and surrounding air, and conclude that their quantum sensing experiments do not produce detrimental heating in living systems.

• Chemical heating control: No significant transient temperature change appears for the other solution additions tested; only the 10 μL addition of 1 mM FCCP in DMSO produces the 1.5 K rise. Thermal echo measurements were accumulated every 14 seconds, except when positional optimization occurred. The observed heating is similar in magnitude to reported mitochondrial uncoupling measurements but persists for a shorter time.

Methodology in Plain English

The sensor is a tiny diamond crystal, roughly 280 nm across, containing two atomic-scale defects called NV centres. These defects emit light in a way that depends on their spin state, and their spin behaviour depends subtly on temperature.

The team first confirmed the crystal contained two NV centres by measuring the correlation between photon arrivals. They then applied a small magnetic field to separate the spin transitions and used microwaves to manipulate the spins. Rather than simply sweeping microwave frequency and watching for a dip in fluorescence (the standard CW-ODMR approach), they used a "thermal echo" sequence: the spins are placed in a superposition, allowed to evolve for a time τ, and then recombined. A change in temperature shifts the microwave frequency that the spins respond to, which shows up as a change in the oscillation frequency of the measured signal. By fitting those oscillations, the team extracts temperature. Because they compare two spin-state readouts and take the difference divided by the sum, common-mode noise cancels.

The chip is custom-built and includes both the microwave delivery and a resistance temperature detector for independent calibration. The authors calibrated the conversion between frequency shift and temperature in place, because strain in nanodiamonds makes the coefficient sample-specific. They then tested the sensor against known perturbations: deliberate microwave detuning, a heater on the chip, and a laser whose power was ramped. Finally, they submerged the nanodiamond in water and added small volumes of a DMSO solution to watch heat release from mixing in real time.

Why This Matters

This work moves nanodiamond thermometry from a technique with roughly kelvin-scale sensitivity into the regime previously reserved for bulk diamond, while keeping the sensor small enough to sit inside a cell. It also addresses a credibility problem in the field: the paper explicitly measures how much the measurement itself heats the sample, and shows that adding DMSO-borne compounds produces its own transient heating that could be misread as biological heat generation. That kind of control matters for the ongoing controversy over whether mitochondria produce temperature gradients larger than theory predicts.

Real-world applications:

• Intracellular and mitochondrial thermogenesis studies: providing the resolution needed to test theoretical predictions of small temperature perturbations in live cells.
• Quantifying laser-induced heating in biological imaging: the same protocol can characterise thermal load during sustained illumination such as super-resolution microscopy.
• Catalyst assessment: measuring heat produced by nanoscale chemical and biological catalysts to gauge reaction efficacy and inform catalyst design.
• Chemical assay controls: distinguishing genuine biological heating from solvent mixing artefacts such as DMSO in water.

Industry relevance: the results are relevant to quantum sensing hardware developers building chip-integrated nanoscale metrology, to biomedical instrument makers concerned with photothermal damage, and to the catalysis and pharmaceutical sectors, where local heat production is a diagnostic of reaction performance and where solvent-mixing artefacts can confound assays.

Future Directions

• Live-cell mitochondrial thermogenesis: applying the platform to sub-millikelvin-resolution measurements inside living cells, where temperature perturbations consistent with theoretical models are now within reach of the technique.
• Catalyst screening at the nanometre scale: using the sensor to assess heat production from individual catalytic nanostructures and to guide the design of more efficient catalysts.
• Disentangling thermal sources: exploiting the temporal resolution and millikelvin resolution to separate biological heating from chemical or optical artefacts in complex experiments.
• Extending operating conditions: building on the demonstrated robustness to field misalignment and the zero-field and bulk-diamond comparison variants to make the protocol practical in less controlled environments.

Target Audience

Researchers in quantum sensing and NV-centre physics, biophysicists and cell biologists interested in intracellular temperature, physical chemists studying catalysis and solvation thermodynamics, and instrument developers working on chip-integrated quantum sensors. Readers new to NV thermometry will find the introduction and protocol comparison useful, while specialists will focus on the sensitivity accounting in Appendix 1 and the controls around laser heating and DMSO mixing.

Authors’ abstract

Accurate temperature readings of transient events at the nanometer scale are challenging due to the low sensitivity of available sensors. Nanodiamonds containing nitrogen-vacancy (NV) centers have been used for nanoscale thermometry in complex environments, including inside living cells. However, their performance has been limited by short coherence times and low photon counts. In this work, we use isotopically-purified dual-NV nanodiamonds and a bespoke quantum sensing chip to showcase an order of magnitude improvement in temperature measurement sensitivity compared with previous reports. We demonstrate robust temperature measurements with an error of 682 $μ$K, experimental sensitivities below 50 mK/$\surd \text{Hz}$ and a shot-noise limited sensitivity of 9.6 mK/$\surd \text{Hz}$. To confirm the utility of these high-performance nanothermometers, we quantify the temperature change induced by the thermometry measurement itself, specifically the optical excitation laser used to probe the NV spin state. In addition, we observe directly at the nanometre scale the transient heating caused by the exothermic mixing of dimethyl sulfoxide in water. Sub-millikelvin resolution and millikelvin sensitivity thermometry unlock the possibility of monitoring minute thermal fluctuations in living systems and assessing catalyst performance at the nanometre scale.