T1 Relaxation

T1​ relaxation times represent the time scale over which the NV center(s) spin state returns to thermal equilibrium with its surroundings. This is also known as spin-lattice relaxation. This process is influenced by the local magnetic noise in the environment, which can be caused by unpaired electronic spins, paramagnetic impurities, or other defects in the diamond lattice. Such imperfections are often introduced during the manufacturing of diamond and the creation of NV centers. These interactions between the NV center and its noisy surroundings lead to energy dissipation, making T1 ​a valuable measure of the magnetic environment at the nanoscale. Fig. 4a and Fig. 4b shows the T1 protocol and a typical T1 decay trace, correspondingly. The T1 relaxation data acquisition protocol involves a series of light pulses structured as follows: an initialization pulse of length ∆tP is applied to establish a polarized state. This pulse is characterized by a rapid fluorescence signal jump, followed by a slower exponential build-up, typically occurring on a millisecond timescale. After a sufficiently long initialization period, typically 10 ms, a dark interval is introduced to allow for relaxation. Following the dark interval, a short detection pulse is applied with a controlled variable delay, typically ∆tD ranging from 100 μs to 200 μs. The signal is recorded during this period. The detection pulse signal undergoes processing through extrapolation fitting to a linear or exponential curve, enabling extraction of a signal value at the beginning of the pulse. This value represents a point in the T1 relaxation time at the specific detection pulse delay time. After a brief dark reset time, the sequence is repeated either for averaging purposes with the same delay time or to acquire the next relaxation point at successively increasing delay increments. There is a choice between keeping the reset time constant or the repetition period (T) constant between relaxation points. Keeping the reset time constant enables faster data collection by dynamically adjusting the repetition time short enough to accommodate the current delay sequence. Conversely, maintaining a constant repetition time requires accommodating all pulse sequences and is limited by the longest delay time. While keeping the repetition time constant necessitates long reset times even for short delays, it is the best approach to ensure that the initialization states reach the same level of polarization for each sequence. This method is often the best way to prevent unwanted baseline drifts in the relaxation curve.

A typical relaxation curve follows approximately an exponential decay dependence of fluorescence signal on delay time between initialization and detection pulses. The curve can be modeled using a stretched exponential function of the form A × exp[-(delay/T1)ᵖ] + offset. Here, offset is the fluorescence signal level in the relaxed state, i.e., delay → ∞, A is the maximum increase of fluorescence level due to light polarization at the end of the initialization pulse, i.e., at the delay time zero, T1 is the relaxation constant, and ρ is the stretching exponent. Parameters are obtained by fitting a series of discrete points. It is advantageous to collect these data points with a parametric sampling scheme, where distance is kept constant along the relaxation curve instead of equidistant sampling on the delay axes. Such sampling provides a more accurate representation of the decay process and saves data acquisition time. If data are normalized so that the signal maximum at delay zero equals 100%, then parameter A equals the T1 contrast. More generally T1 contrast = A / (A + offset) x 100 in %.

Fig. 4. Schematic of T1 relaxation pulse protocol (a) and a typical T1 relaxation decay trace demarked with characteristic parameters (b)