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Short answer: T1 is the population-relaxation time, T2* is the unrefocused (Ramsey) phase-dephasing time, and T2 is the phase-coherence time measured after refocusing. In most experiments they follow T2* ≤ T2 ≤ 2T1. T2* is usually shortest because it includes reversible frequency offsets and inhomogeneous broadening; a Hahn-echo pulse removes much of that contribution, revealing the longer T2.
These are not universal constants for a defect. Temperature, crystal host, isotope purification, impurity density, magnetic-field orientation, charge state and pulse sequence can change a reported value by orders of magnitude. The number is meaningful only with those conditions attached.
What T1, T2 and T2* measure
T1: longitudinal or spin-lattice relaxation
T1 describes how quickly a disturbed spin population returns toward thermal equilibrium. The spin exchanges energy with phonons or other environmental degrees of freedom, changing the populations of its energy levels. For a nitrogen-vacancy (NV) center, a T1 experiment follows recovery among the ground-state populations ms = 0 and ms = ±1.
Do these 3 things before closing this tab:
1Repair Windows errors before they cause bigger problems2Scan for outdated or missing drivers - takes under a minute3Clear out junk files and repair common Windows errorsT1 is therefore a population time, not a direct measure of how long a superposition retains phase. A long T1 means that energy relaxation is slow, but other noise can still destroy phase coherence much sooner.
T2*: raw free-induction or Ramsey coherence
T2* is the dephasing time observed without a refocusing pulse. A Ramsey experiment creates a superposition, allows it to evolve freely, and then reads the resulting oscillation. The decaying envelope reflects both irreversible noise and static or slowly drifting frequency offsets from local magnetic fields, electric fields, strain, nearby spins and ensemble frequency variations.
Because those offsets differ from one location or shot to the next, T2* is especially sensitive to inhomogeneous broadening and slow drift. It is the quantity most closely related to the linewidth seen in an unrefocused free-induction measurement.
T2: homogeneous coherence after refocusing
T2 is the phase-coherence time that remains after a refocusing sequence. In a Hahn echo, a π pulse halfway through the evolution reverses phase accumulated from a static frequency offset: spins that moved ahead of the reference begin to lag, and vice versa. The echo-envelope decay therefore suppresses much of the reversible broadening present in T2*.
The remaining decay comes from fluctuations that the sequence cannot refocus, including noise that changes during the evolution and truly irreversible processes. Multipulse dynamical-decoupling sequences can filter additional noise and produce a longer apparent coherence time, but that value belongs to the specified sequence and pulse spacing rather than being a sequence-independent material constant.
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Why T2* is usually shorter than T2
The practical hierarchy is:
T2* ≤ T2 ≤ 2T1
The first inequality reflects reversible inhomogeneous broadening. Ramsey interferometry leaves static and slowly varying frequency offsets in the signal, while a Hahn echo cancels much of them. The second inequality follows because population relaxation removes the energy-level information that carries phase; even in the ideal limit, longitudinal relaxation places a ceiling of 2T1 on transverse coherence.
This is a guide rather than a promise that every data set will fit the same mathematical form. A measured envelope can be exponential, stretched or otherwise non-single-exponential when several noise sources and timescales contribute. Comparing values is valid only when the definitions, fit window, pulse sequence and sample conditions are also compared.
How each time is measured
Optically detected magnetic resonance (ODMR) supplies spin-selective initialization and readout in the commonly studied color centers. The optical pulse prepares or interrogates the spin, while microwaves perform rotations between spin states.
Measuring T1 with pump–wait–read
- Initialize or perturb: use an optical pump (or another preparation step) to place the spin population in a known, non-equilibrium state.
- Wait: leave the spin undriven for a variable delay. During this interval, energy exchange with phonons and the environment drives the populations toward thermal equilibrium.
- Read: apply the optical readout and record the spin-dependent fluorescence or ODMR signal.
- Fit recovery: plot the measured population signal against the wait time and fit its return toward equilibrium. The fitted recovery time is T1 under those temperature, field and sample conditions.
A T1 measurement is affected by optical repumping, microwave leakage and other preparation errors, so the pulse sequence and readout conditions should accompany the quoted value.
Measuring T2* with a Ramsey sequence
- Apply a π/2 microwave pulse to create a coherent superposition.
- Allow free evolution for a variable interval, with no refocusing π pulse.
- Apply a second π/2 pulse and read the resulting population through ODMR.
- Fit the oscillation envelope as the free-evolution time increases. That decay gives T2* for the measured detuning distribution and drift environment.
The Ramsey signal contains both irreversible dephasing and reversible frequency offsets. Changing the magnetic field, sample position, isotope composition or averaging time can therefore change T2* even when the underlying defect is nominally the same.
Measuring T2 with a Hahn echo
- Apply a π/2 pulse to create the superposition.
- Wait for a time τ.
- Apply a π pulse to exchange the phase trajectories of the two components.
- Wait another τ so the trajectories rephase at the echo.
- Apply a final π/2 pulse and perform optical readout.
- Repeat for increasing total evolution time and fit the echo envelope. The resulting decay time is T2 for that Hahn-echo protocol.
For longer apparent coherence, add multiple refocusing pulses in a dynamical-decoupling sequence. Such sequences act as noise filters: they remove fluctuations in a frequency band selected by the pulse spacing, so the reported time must state the sequence and number of pulses.
Representative published values—and what they do (and do not) show
The following figures come from different defects, hosts, temperatures and control protocols. They illustrate the scale of the quantities, not a universal leaderboard.
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|---|---|---|---|---|
| NV center in diamond | Room temperature; multiple decoupling pulse sequences | ≈ 6 ms | Not stated in the cited figure (Frontiers in Quantum Science and Technology, 2023) | ≈ 3.3 ms |
| Neutral divacancy in isotopically purified 4H-SiC | 5 K; microwave dressing | Not stated in the cited figure (Frontiers in Quantum Science and Technology, 2023) | Not stated in the cited figure (Frontiers in Quantum Science and Technology, 2023) | 5 s |
| Negatively charged silicon-vacancy center in diamond | 100 mK; value reported by Sukachev et al. (2017) | > 1 s | Not stated in the cited report | 13 ms |
| Single silicon-vacancy center in diamond | 3.6 K; Ramsey interferometry, Nature Communications (2017) | Not stated in the cited report | 115 ± 9 ns | Not stated in the cited report |
The 5-second T2 for the neutral divacancy is the longest T2 among these representative figures, but it was obtained at 5 K in isotopically purified 4H-SiC with microwave dressing. It cannot be used to claim that every divacancy, every temperature or every pulse sequence outperforms an NV or silicon-vacancy center. Conversely, the 115 ± 9 ns Ramsey value for a silicon-vacancy center at 3.6 K is a T2* result; it should not be compared directly with a Hahn-echo T2.
Which spin defect has the longest coherence?
There is no single answer without specifying the metric and conditions. If “coherence” means the longest reported Hahn-echo or dynamically protected T2 in the figures above, the neutral divacancy in isotopically purified 4H-SiC reaches 5 s at 5 K with microwave dressing. If the question instead means room-temperature operation, raw Ramsey T2*, optical performance or compatibility with a particular magnetic field, a different platform may be preferable.
Use a comparison that keeps these axes together:
- Defect and host: the electronic structure and surrounding lattice set the available transitions and noise channels.
- Temperature: cooling generally changes phonon-mediated relaxation and can greatly increase T1 and T2.
- Measurement metric: T2* (Ramsey), Hahn-echo T2 and multipulse T2 answer different questions.
- Isotopic and impurity concentration: nuclear-spin and paramagnetic impurities create fluctuating fields and inhomogeneous broadening.
- Magnetic-field magnitude and orientation: the field selects quantization axes and can alter sensitivity to nearby noise.
- Charge state and optical cycle: charge stability, initialization fidelity and readout contrast determine whether a long intrinsic time is usable in an experiment.
- Control overhead: microwave dressing and dynamical decoupling can extend the measured envelope but require additional pulses, calibration and available optical or microwave power.
A Nature Reviews Materials review emphasizes that defect, host, optical, charge and material properties jointly determine suitability for sensing, communication and computing. A platform with the largest T2 is not automatically the best device platform if it is difficult to initialize, read out or operate at the required temperature.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What changes the measured times
Temperature and phonons
Phonons provide a pathway for energy exchange, so temperature directly affects T1 and can indirectly limit T2. The same defect can show very different times at room temperature, a few kelvin and millikelvin temperatures.
Host isotope and impurity environment
Isotopic purification reduces some nuclear-spin noise, while lower concentrations of paramagnetic impurities reduce fluctuating magnetic fields. These changes can lengthen both the unrefocused and refocused measurements, although the improvement depends on which noise source dominates.
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Magnetic field and orientation
The field magnitude and its orientation relative to the defect axis alter transition frequencies and the way environmental fields project onto the qubit. Two laboratories can therefore obtain different T2* values from nominally similar material if their field geometry differs.
Charge state, strain and local fields
Defect charge stability, local strain and electric or magnetic fields shift the transition frequency. A static shift may be largely removed by a Hahn echo, while a fluctuating shift during the sequence contributes to the measured T2.
Pulse sequence and fit convention
Ramsey, Hahn echo and multipulse decoupling sample different portions of the environmental noise spectrum. Pulse errors, finite pulse widths and the chosen fit model also affect the extracted number. Always report the sequence, pulse count, evolution-time range and fit convention with T1, T2* or T2.
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Use T1 when population reset or thermal stability matters
T1 sets how quickly a spin naturally forgets its population state and how rapidly it can return to equilibrium. It is central to reset protocols, repetition rates and understanding phonon-induced relaxation.
Use T2* when you need unrefocused sensing or frequency resolution
Ramsey T2* includes the static and slowly varying fields that an unrefocused sensor actually experiences. It is the relevant baseline for a simple free-induction measurement and for estimating how quickly an ensemble loses phase without active correction.
Use T2 when refocusing is available
Hahn-echo T2 is the appropriate measure when your experiment includes a refocusing pulse. It estimates the coherence that survives after reversible offsets are canceled, while multipulse T2 indicates performance under a specific dynamical-decoupling filter.
Common interpretation mistakes
- Calling T1 a coherence time: T1 measures population recovery; T2 and T2* measure transverse phase information.
- Comparing T2* with T2 as if they were identical tests: the former is Ramsey and unrefocused, while the latter includes a π refocusing pulse.
- Ignoring temperature and material: a millikelvin silicon-vacancy result and a room-temperature NV result answer different engineering questions.
- Reporting a decoupled value without the sequence: pulse number and spacing determine which noise is filtered.
- Treating the 2T1 limit as a guaranteed result: it is an upper bound imposed by relaxation, not a promise that a sample will approach it.
- Using one record value as a platform ranking: defect species, host crystal, isotope purity, impurity density, field orientation and optical practicality all matter.
For a reproducible report, state the defect and charge state, host and isotope composition, temperature, impurity concentration when known, magnetic-field magnitude and orientation, optical and microwave sequence, fit model and whether the quoted value is T1, Ramsey T2* or Hahn-echo/multipulse T2.
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