PDF (double-sided) - Physics Department, UCSB - University of ...
PDF (double-sided) - Physics Department, UCSB - University of ... PDF (double-sided) - Physics Department, UCSB - University of ...
phase shift into the middle of the delay time. This pulse effectively inverts the accumulated phase of the qubit state in the equator, such that any precession in the first half of the delay time undoes itself in the second half of the delay time. This removes the effect of a potential microwave detuning onto the data and yields a better estimate of T 2 if the data is fit to the function P (t) = P offs +V iz ∗e −t/T 2 . Even if the qubit’s resonance frequency was perfectly stable, the trace measured in this experiment would still decay to around 50% due to the fact that T 1 decays the qubit state from the equator back into the ground-state. Since the groundstate does not have any phase associated with it, this decay also erases phase information. T 2 is defined as the timescale on which the qubit loses its phase information and thus, this T 1 effect does not need to be removed from the fit, but instead does contribute to the real value of T 2 . This leads to the fact that T 2 can never be larger than 2T 1 . There also exists a quantity that measures the loss of phase information due to only the instability in the qubit’s resonance frequency. This quantity is called T ϕ and can be calculated from: 1 = 1 + 1 . (8.3) T 2 2 T 1 T ϕ 198
Figure 8.13: Fine Spectroscopy – a) High power: The | 0 〉 ↔ | 1 〉 and the | 0 〉 ↔ | 2 〉 transition are visible. This qubit couples to very few two-level states. b) Low power: Only the | 0 〉 ↔ | 1 〉 transition is visible. This qubit couples to more two-level states. 8.12 2D-Spectroscopy The final scan that is part of our standard qubit bringup sequence is called “2D-Spectroscopy”. It is probably the single most useful calibration scan we do due to the large amount of information it provides. The scan is simply the 2D extension of the above mentioned spectroscopy scan as a function of operating bias. The data is usually drawn as a 2D color plot and should resemble Figure 8.13a or b depending on whether the microwave pulse power is high enough to excite the two-photon | 0 〉 → | 2 〉 transition. The dependence of the response frequency ω 01 on the operating bias follows a quadratic equation almost exactly. The two- 199
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Figure 8.13: Fine Spectroscopy – a) High power: The | 0 〉 ↔ | 1 〉 and the | 0 〉 ↔<br />
| 2 〉 transition are visible. This qubit couples to very few two-level states. b)<br />
Low power: Only the | 0 〉 ↔ | 1 〉 transition is visible. This qubit couples to more<br />
two-level states.<br />
8.12 2D-Spectroscopy<br />
The final scan that is part <strong>of</strong> our standard qubit bringup sequence is called<br />
“2D-Spectroscopy”. It is probably the single most useful calibration scan we do<br />
due to the large amount <strong>of</strong> information it provides. The scan is simply the 2D<br />
extension <strong>of</strong> the above mentioned spectroscopy scan as a function <strong>of</strong> operating bias.<br />
The data is usually drawn as a 2D color plot and should resemble Figure 8.13a<br />
or b depending on whether the microwave pulse power is high enough to excite<br />
the two-photon | 0 〉 → | 2 〉 transition. The dependence <strong>of</strong> the response frequency<br />
ω 01 on the operating bias follows a quadratic equation almost exactly. The two-<br />
199
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