PDF (double-sided) - Physics Department, UCSB - University of ...
PDF (double-sided) - Physics Department, UCSB - University of ... PDF (double-sided) - Physics Department, UCSB - University of ...
Figure 8.10: T 1 – a) Bias sequence: The qubit is excited into the | 1 〉 state with a π-pulse and measured after an increasing delay t Delay . b) T 1 : After the π-pulse, the qubit decays exponentially from the | 1 〉 state back to the | 0 〉 state. from Section 8.5. The 5% point used in the initial calibration of the measurement pulse was chosen since, from experience (and from the math describing the tunneling of the two states) the maximum visibility usually lies around the point where the ground-state tunnels about 5% of the time. All parameters describing the measure pulse can now be adjusted to maximize the visibility. 8.9 T 1 Now that we have a calibrated way to prepare the qubit in the excited state and to measure its state as accurately as possible, we can start determining the qubit’s intrinsic quality measures. The easiest quantity to measure is the qubit’s energy relaxation time T 1 . To determine it, all one needs to do is prepare the qubit in the excited state with a π-pulse and then measure its excited state population 194
as a function of the delay between the π-pulse and the measure pulse. The data will look like Figure 8.10. Fitting the decaying part of the trace to the function P (t) = P offs + V iz ∗ e −t/T 1 , gives the quantity of interest: T 1 . Since both the measurement visibility (Viz) and the ∼ 5% offset (P offs ) are free parameters in this fit, the measurement process does not affect the obtained value of T 1 . Even an imperfect π-pulse would only affect the value if part of the state is excited into the second excited state. Thus, this measurement yields a very robust number. 8.10 Ramsey Unfortunately, measuring the dephasing time T 2 is less straightforward. This is due to the fact that the phase of the qubit’s state only has meaning relative to an external clock source like the state of another quantum system. The phase of the qubit’s state can also be measured by interfering it with the microwave drive. This is done by using a pulse of half the area of the π-pulse, i.e. a π -pulse, to 2 excite the qubit into the equator of the Bloch sphere. There, the qubit is allowed to dephase for a time t Delay and finally hit with another π -pulse to complete the 2 rotation into the excited state before it is measured. As a function of t Delay , the occupation probability of the excited state looks like Figure 8.11b. The problem with this measurement is that the decay envelope only gives a correct measure 195
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Figure 8.10: T 1 – a) Bias sequence: The qubit is excited into the | 1 〉 state with<br />
a π-pulse and measured after an increasing delay t Delay . b) T 1 : After the π-pulse,<br />
the qubit decays exponentially from the | 1 〉 state back to the | 0 〉 state.<br />
from Section 8.5. The 5% point used in the initial calibration <strong>of</strong> the measurement<br />
pulse was chosen since, from experience (and from the math describing the<br />
tunneling <strong>of</strong> the two states) the maximum visibility usually lies around the point<br />
where the ground-state tunnels about 5% <strong>of</strong> the time. All parameters describing<br />
the measure pulse can now be adjusted to maximize the visibility.<br />
8.9 T 1<br />
Now that we have a calibrated way to prepare the qubit in the excited state<br />
and to measure its state as accurately as possible, we can start determining the<br />
qubit’s intrinsic quality measures. The easiest quantity to measure is the qubit’s<br />
energy relaxation time T 1 . To determine it, all one needs to do is prepare the qubit<br />
in the excited state with a π-pulse and then measure its excited state population<br />
194