INTERACTIVE QUANTUM SENSING LAB

See magnetic noise change NV T₁

Move the controls to explore how fluctuating nanoparticle magnetization produces magnetic noise near the NV resonance, increases spin relaxation, and changes optical readout.

NV ground-state resonance
D ≈ 2.87 GHz
γ/2π ≈ 28 GHz/T

01 · Particle near a diamond NV

SCHEMATIC · NOT TO SCALE

The arrow represents a fluctuating magnetic moment. Nearby NV spins respond to its transverse magnetic noise at their resonance frequency.

NV center Diamond lattice NanoparticleFluctuating moment magnetic field noise near-surface sensing
● magnetic nanoparticle   ● NV center
schematic B⊥ fluctuations

02 · Tune the physics

LIVE MODEL
1 ps → 10 ns. Controls how quickly the particle's magnetic noise fluctuates.
Noise amplitude at the NV; stronger coupling increases relaxation.
Splits the ms = ±1 transitions, moving the NV's spectral filters.
Background relaxation from lattice, defects, and other environmental noise.
TRY A SCENARIO
NV transition frequencies
2.87 GHz
Both transitions overlap
Particle-induced ΔΓ₁
0 s⁻¹
Added longitudinal relaxation rate
Intrinsic T₁
1.20 ms
Diamond without magnetic noise
Effective T₁
0.44 ms
Shorter than baseline

03 · Which noise frequencies can the NV detect?

FREQUENCY DOMAIN

This Lorentzian shows relative magnetic noise power. Vertical markers show the NV transitions. The particle changes T₁ only when it supplies noise near these frequencies.

Noise spectral shapeNV transition(s)
Moving τc changes how much fluctuation power reaches ~2.87 GHz.

04 · What does the optical T₁ experiment measure?

TIME DOMAIN

Green light prepares ms ≈ 0. A variable dark period follows. Early fluorescence in the readout pulse reveals the spin polarization remaining.

NV aloneNV + particle noiseReadout time
Decay is shown as normalized spin-polarization contrast, not absolute fluorescence intensity.

05 · Experiment with the dark time

τ = 0.60 ms
LASER ONInitialize
LASER OFFWait for τ
LASER ONRead out
The detector samples early readout fluorescence, before the laser repolarizes the NV.
Difference in remaining spin polarization
0.0 percentage points

At this delay, the nanoparticle's added magnetic noise reduces the retained NV spin polarization.

01 / STATIC FIELD
ODMR measures average fields.

A stable nearby magnetic dipole can shift NV transition frequencies but need not produce additional T₁ relaxation. Static shifts and fluctuations are distinct observables.

02 / DYNAMIC FIELD
T₁ detects noise near the NV resonance.

Slow Brownian rotation alone generally has little noise power at GHz frequencies. Internal magnetization and spin dynamics may provide faster fluctuations.

03 / BIOSENSING
More noise is not automatically more particles.

Relaxation depends on spectral dynamics, distance, magnetic moment, and background noise. Controls and calibration are essential to interpret a T₁ change.

ΔΓ₁ ∝ γ² Brms,⊥² τc / [1 + (2π fNV τc)²]

Illustrative single-correlation-time (Lorentzian) noise model. Peak coupling for a single NV transition occurs near 2π fNV τc ≈ 1. At 2.87 GHz this is about 55 ps. The word “resonant-like” in the preset refers to spectral overlap, not microwave driving.

Physics and limitations: The displayed rate uses ΔΓ₁ = ½ γ² B² τc [1/(1+(2πf+τc)²) + 1/(1+(2πf−τc)²)], with γ = 2π × 28 GHz/T. This fixes a simple illustrative coupling convention, not a quantitatively calibrated prediction for a given particle or NV depth. It approximates optical relaxation by a single exponential. Real spin-1 NV systems may need a multi-level rate model, and actual magnetic nanoparticles can have non-Lorentzian, multi-timescale fluctuations. The animated dipole and noise trace are time-scaled teaching illustrations, not GHz-resolved physical motion. Changes in T₁ can also arise from surface spins, paramagnetic molecules, heating, defects, and other environmental effects.
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