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Clear out junk files and repair common Windows errorsFree Scan →Scan for outdated or missing drivers - takes under a minuteDriver Scan →Repair Windows errors before they cause bigger problemsFix Now →T1 is the population-relaxation time, T2* is the unrefocused (Ramsey) dephasing time, and T2 is the phase-coherence time measured after refocusing. In most experiments they follow T2* ≤ T2 ≤ 2T1. The exact values are not universal: temperature, host crystal, defect species and charge state, isotopic purity, impurity density, magnetic field, and pulse sequence can change them by orders of magnitude.
What T1, T2 and T2* mean
Spin-defect qubits store information in quantum states associated with an atomic-scale defect in a solid. Experiments usually address the spin with microwaves, initialize and read it optically, and monitor how population or phase information decays. The three time constants describe different ways that information is lost.
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T1: longitudinal or spin-lattice relaxation
T1 is the time scale for a disturbed spin population to return toward thermal equilibrium. A spin exchanges energy with phonons and other environmental degrees of freedom; in a magnetic resonance picture this is called spin-lattice relaxation. For an NV center in diamond, a typical T1 experiment prepares a particular mixture of the ground-state ms = 0 and ms = ±1 levels, waits, and then measures how the populations recover.
A simple population-recovery trace is fitted to an exponential or, where several mechanisms contribute, to a more appropriate multi-component model. The fitted T1 is therefore a property of both the defect and the local environment, not a fixed constant for every sample of a named qubit.
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T2*: free-induction or inhomogeneous dephasing
T2* describes how an ensemble of phase-coherent spins loses its collective signal during free evolution, with no refocusing pulse. It is commonly measured with a Ramsey sequence: a π/2 pulse creates a superposition, the spin evolves freely for a variable time, and a second π/2 pulse converts phase into a population that can be read optically.
The Ramsey signal oscillates at the detuning frequency while its envelope decays. That envelope contains irreversible noise, but also reversible effects such as static magnetic or electric-field offsets, slow drift, strain variation, and a distribution of resonance frequencies across defects. Because those offsets differ from one location or experimental shot to the next, T2* is especially sensitive to inhomogeneity.
T2: refocused transverse coherence
T2 is the transverse phase-coherence time extracted after refocusing. In the standard Hahn-echo sequence, a π/2 pulse creates a superposition, the system evolves for a time τ, a π pulse reverses phase accumulation, and a final π/2 pulse converts the recovered phase into a measurable population. Static or slowly varying frequency offsets accumulate before the π pulse and are largely unwound afterward. The decay of the echo envelope therefore emphasizes fluctuations that the sequence cannot refocus.
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Multipulse dynamical-decoupling sequences can extend the apparent coherence beyond a Hahn-echo T2 by applying several π pulses. That longer value is sequence-dependent: it reflects the noise frequencies filtered by the chosen pulse spacing and number of pulses, rather than a new material constant.
Why the usual hierarchy is T2* ≤ T2 ≤ 2T1
Ramsey evolution includes reversible frequency spread as well as irreversible dephasing, so it normally gives the shortest time. A Hahn echo removes some of that spread, making T2 longer than or equal to T2*. Population relaxation also destroys phase information. In the idealized limit, the relaxation contribution alone gives the bound T2 = 2T1; additional dephasing makes the measured T2 smaller. The practical guide is therefore:
T2* ≤ T2 ≤ 2T1.
This is a physical constraint and a diagnostic, not a promise that every data fit will obey the relation exactly. Different experiments may use stretched exponentials, oscillatory envelopes, or multi-component fits; finite measurement windows and pulse errors can also bias a fitted value. If a reported T2 appears to exceed 2T1, check whether T1 and T2 were measured under the same temperature, field, sample, readout model, and time interval, and whether the quoted T1 is the relevant relaxation channel.
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How each time is measured in practice
ODMR provides the readout
Optically detected magnetic resonance (ODMR) supplies spin-selective initialization and readout in many color-center experiments. A laser prepares the defect in a preferred spin state; microwave pulses manipulate the state; fluorescence changes reveal the final population. The optical contrast, laser power, microwave frequency and power, and collection efficiency all affect signal quality, even though they do not define T1, T2, or T2* themselves.
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Measuring T1 with pump–wait–read
- Initialize: apply the optical pump (or another preparation operation) to create a known population.
- Wait: turn off or separate the pump and allow the spin to evolve for a variable delay t.
- Read: apply the optical readout and record the population-sensitive fluorescence or ODMR contrast.
- Fit: plot the recovered signal versus t and fit the appropriate relaxation model. The characteristic delay at which the perturbation has decayed by the model’s defined fraction is reported as T1.
The waiting period must be long enough to reach the equilibrium baseline. Optical leakage, heating, laser-induced charge conversion, and nearby paramagnetic impurities can create extra recovery components, so a single-exponential fit should not be treated as automatic.
Measuring T2* with Ramsey interferometry
- First π/2 pulse: place the spin in a coherent superposition of the chosen qubit states.
- Free evolution: wait for a variable time t while the relative phase accumulates at the detuning frequency.
- Second π/2 pulse: map phase to population.
- Read and fit: record the oscillating signal and fit its envelope, including the detuning and any decay model, to obtain T2*.
Because no refocusing pulse is used, Ramsey data expose static frequency offsets and slow drift. Repeating the sequence at different locations or after retuning the microwave frequency can reveal whether the apparent limit is dominated by inhomogeneous broadening rather than fast, irreversible noise.
Measuring T2 with a Hahn echo
- Prepare: use a π/2 pulse to create transverse coherence.
- Accumulate phase: evolve for τ.
- Refocus: apply a π pulse that reverses the sign of phase accumulation from quasi-static offsets.
- Accumulate again: evolve for another τ, giving a total evolution time of 2τ.
- Read and fit: apply the final π/2 pulse, measure the echo, and fit its envelope versus 2τ.
Changing the interpulse delay or adding further π pulses implements dynamical decoupling. Comparing Hahn echo with multipulse results is useful for identifying the environmental noise spectrum, but the values must always be labeled with the sequence used.
What controls the measured times
Temperature and phonons
Phonon populations and defect orbital dynamics change with temperature. Lowering the temperature can suppress some relaxation channels and substantially increase T1 or T2, while other mechanisms may become dominant. A value measured at 5 K should not be presented as representative of a room-temperature device.
Host crystal, defect species and charge state
The lattice determines strain, vibrational modes, nuclear-spin environment, and optical properties. Even within diamond, an NV center and a silicon-vacancy center have different orbital and spin physics. In silicon carbide, neutral divacancies in different polytypes can have distinct coherence behavior. Charge-state stability also matters: unwanted conversion changes the optical signal and can interrupt a nominally identical sequence.
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Isotopic purity and impurity concentration
Nuclear spins from host isotopes and electron spins from substitutional impurities produce fluctuating magnetic fields. Isotopic purification reduces one source of magnetic noise; lower impurity density reduces another. The benefit is sample-specific, and material processing can introduce strain or additional defects that offset the gain.
Magnetic-field orientation and operating point
The field magnitude and direction set the transition frequencies, mixing of spin states, and sensitivity to noise. Aligning a field with a defect’s symmetry axis can produce a different T2* or T2 from a misaligned field. Reporting a coherence number without the field orientation is therefore incomplete.
Control sequence and pulse imperfections
Hahn echo, Carr–Purcell-style sequences, and other decoupling protocols filter different noise frequencies. More pulses do not automatically mean a better qubit: finite pulse width, detuning, microwave amplitude errors, and pulse-induced heating can create a shorter apparent decay. A published “T2” is meaningful only when its sequence and pulse conditions are specified.
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The following examples illustrate the range of reported times under their stated conditions. They are not an apples-to-apples league table: the samples, temperatures, charge states, magnetic environments, and control protocols differ.
| Defect and host | Conditions and protocol | Reported value | What it shows |
|---|---|---|---|
| NV center in diamond | Room temperature; Frontiers in Quantum Science and Technology (2023); measurements using multiple decoupling sequences | T1 ≈ 6 ms; T2 ≈ 3.3 ms | A room-temperature NV can have millisecond-scale relaxation and echo coherence, with sequence choice affecting T2. |
| Neutral divacancy in isotopically purified 4H-SiC | 5 K; microwave dressing; Frontiers in Quantum Science and Technology (2023) | T2 = 5 s | Low temperature, isotope purification and dressed control can produce multi-second coherence. |
| Negatively charged silicon-vacancy center in diamond | 100 mK; Sukachev et al. (2017) | T2 = 13 ms; T1 > 1 s | Cryogenic operation can give a long relaxation time, while residual dephasing still limits T2 far below 2T1. |
| Single silicon-vacancy center in diamond | 3.6 K; Ramsey interferometry; Nature Communications (2017) | T2* = 115 ± 9 ns | Unrefocused single-defect coherence can be much shorter than an echo value because static and slowly varying frequency offsets remain visible. |
These data do not establish which defect has the longest coherence in every application. A five-second T2 obtained with microwave dressing at 5 K answers a different engineering question from a room-temperature T2* needed for a compact sensor. Comparisons should include at least the defect and host, temperature, T1 mechanism, Ramsey T2*, Hahn-echo or decoupled T2, isotopic and impurity concentrations, field orientation, noise environment, and optical initialization/readout practicality.
Which spin defect has the longest coherence?
There is no single winner independent of conditions. Among the representative figures above, the longest quoted coherence is T2 = 5 s for a neutral divacancy in isotopically purified 4H-SiC at 5 K with microwave dressing. That result should be read as a conditional record for that material and protocol, not as a universal ranking of all spin defects.
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For a practical choice, define the operating requirements first:
- Room-temperature sensing: prioritize the coherence available without cryogenics, the optical signal, and tolerance to nearby materials.
- Quantum memory or networking: compare low-temperature T1 and T2, optical linewidth and stability, charge-state control, and compatibility with photonic interfaces.
- High-bandwidth sensing: a shorter T2* may still be useful because Ramsey measurements can be repeated rapidly; the relevant figure is sensitivity in the intended bandwidth, not the largest published T2.
- Processor-style control: compare gate times and pulse errors with T1 and sequence-specific T2, rather than selecting on a long idle-time value alone.
How to read a coherence claim critically
- Check whether the number is T1, Ramsey T2*, Hahn-echo T2, or a multipulse-decoupling value.
- Record the temperature, host polytype or crystal, defect charge state, isotope composition, impurity density, and magnetic-field orientation.
- Ask whether the result is from a single defect or an ensemble; ensemble inhomogeneity often shortens T2*.
- Check the fit function, confidence interval, and total observation window.
- Look for optical pumping, microwave dressing, dynamical decoupling, or other controls that may not be available in the intended device.
- Compare the reported T1 and T2 against the 2T1 ceiling under matching conditions.
Common mistakes and troubleshooting
Calling every decay “T2”
A Ramsey envelope is T2*, not Hahn-echo T2. Label the sequence in figures, notes, and device specifications so a refocused value is not mistaken for free-induction performance.
Comparing unlike temperatures
A cryogenic result cannot be used to predict room-temperature operation. Repeat the measurement at the intended operating temperature or state clearly that the value is a low-temperature benchmark.
Ignoring reversible broadening
If T2* is much shorter than T2, first investigate static field gradients, strain, charge noise, and slow frequency drift. Better frequency stabilization or a refocusing sequence may recover coherence without changing the material.
Assuming more decoupling pulses always help
If T2 stops increasing or decreases as pulses are added, inspect pulse calibration, detuning, finite pulse duration, and heating. The sequence may be moving the experiment into a control-error-limited regime.
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Fitting away multiple physical processes
A poor single-exponential fit can hide optical repumping, charge conversion, several impurity baths, or temperature drift. Examine residuals and repeat measurements at different laser powers, microwave powers, delays, and locations before assigning a single mechanism.
Why the distinction matters for qubit design
T1 sets how long energy populations survive and places a hard ceiling on phase coherence. T2* determines how quickly an unrefocused Ramsey signal disappears and therefore affects calibration, spectroscopy, and sensing bandwidth. T2 determines the usable interval for operations protected by a chosen refocusing sequence. A device that advertises only one time constant leaves out the information needed to estimate gate depth, sensing sensitivity, memory lifetime, or communication fidelity.
The most informative specification reports all three times with their measurement sequences and environmental conditions. That makes it possible to separate material limitations from reversible inhomogeneity and from control-engineering choices.
Frequently Asked Questions
Can T2 ever be longer than 2T1?
For the same transition and consistent definitions, energy relaxation imposes the ideal upper bound T2 ≤ 2T1. An apparent violation usually indicates that T1 and T2 were measured under different conditions, that different fit definitions were used, or that the quoted relaxation channel is incomplete.
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Ramsey measurements retain static and slowly drifting frequency offsets from magnetic fields, electric fields, strain and charge noise. Those reversible shifts can dominate the free-induction envelope even when a Hahn echo recovers a much longer T2.
Does a longer T2 always make a better sensor?
No. The useful metric depends on bandwidth, readout contrast, repetition rate and noise. A sensor may benefit from rapid Ramsey cycles with a modest T2* or from long decoupled T2, depending on the signal being measured.
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