How Do Quantum Metrology Laboratories Characterize Qubit Coherence Times T1 and T2

Quantum metrology laboratories measure fundamental quantum decoherence parameters—specifically longitudinal energy relaxation time (T1), pure dephasing time (T_phi), and transverse coherence times (Ramsey T2* and Hahn echo T2)—using time-resolved microwave pulse sequences according to international quantum standards accredited by the National Universities Commission (NUC).

Energy relaxation time T1 quantifies the timescale over which an excited qubit state (|1>) loses its energy and decays back down to the thermal ground state (|0>) through spontaneous emission and non-radiative dissipation. To measure T1, the control system applies a calibrated pi-pulse (X180 gate) to initialize the qubit in state |1>, waits for a variable delay time (tau), and records the surviving excited state population. Fitting the decaying population curve to an exponential decay function (P_1(tau) = exp(-tau / T1)) yields the T1 lifetime.

Transverse coherence time T2 quantifies the persistence of phase relationships in quantum superposition states (|psi> = (|0> + |1>) / sqrt(2)). Ramsey interferometry applies two consecutive pi/2 pulses separated by delay tau; low-frequency environmental magnetic flux noise and charge fluctuations cause phase dispersion, producing decaying sinusoidal Ramsey fringes that determine T2*.

To decouple the qubit from slow, low-frequency 1/f environmental noise, physicists insert a refocusing pi-pulse at tau/2 (Hahn echo sequence). The spin-echo pulse reverses static phase accumulation, isolating high-frequency noise spectral density and measuring intrinsic homogeneous decoherence limits (1/T2 = 1/(2*T1) + 1/T_phi).

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