Fig. 2.
Thermal echo (TE) and thermal CPMG-N (TCPMG-N) pulse sequences in finite magnetic fields. (A) Diagram showing the pulse sequences. Here a π pulse has a duration such that it will invert the spin population between the two sublevels that are resonantly addressed. The subscripts indicate the spin transition being addressed. (B) Hahn echo measurement (mS = 0 to mS = −1 transition) at Bz = 30 G showing IPL as a function of the free evolution time (2τ for the Hahn echo and TE, 4τ for TCPMG, and 8τ for TCPMG-2). The measurement demonstrates the coherence collapse caused by the incoherent precession of the 13C spin bath. The width of the shaded gray region represents T2*. C, D, and E show TE, TCPMG, and TCPMG-2 measurements, respectively, performed at 297.00 K (SI Appendix). The uncertainties in IPL, estimated from the photon shot noise, are ∼0.005. To induce oscillations in IPL to clearly observe the signal envelope, the average microwave carrier frequency (ΩREF) was detuned from D by ∼0.5 MHz. The solid red lines are best fits to the data and the 1/e decay times (τ1/e) are noted on the plots. The observed coherences are in good agreement with numerical modeling (solid green lines). For the TCPMG-2 sequence the coherence time is ninefold greater than T2*. For these experimental conditions we infer the thermal sensitivity (η) is 54 ± 1 mK⋅Hz−1/2. Enhancements in the photon collection efficiency could improve η to ∼15 mK⋅Hz−1/2 (Methods).