The quantum states of an Al/AlOx/Al Cooper pair box (CPB) qubit were measured at temperatures below 100 mK.
Detailed spectroscopic measurements of the excited state of the CPB were made along with detailed measurements of the lifetime T 1 of the first excited state. The CPB states were probed using radio-frequency (rf) techniques to read out using either an rf - single-electron transistor (rf-SET) or a low-loss superconducting resonator.
Using an rf-SET, I measured the excited state spectrum of a CPB from 15 to 50 GHz. In this spectrum, a few anomalous avoided level crossings (ALC) were observed. These ALCs exhibited a strong gate voltage dependence and Josephson energy (EJ) dependence, consistent with a charge fluctuator coupled to the CPB island. A model Hamiltonian was used to fit the measured spectrum. Fitting parameters such as the charging energy EC/h = 12.1 GHz and the Josephson energy E J/h tuned between 2 GHz and 21 GHz for the CPB, and the well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator were extracted. The tunneling rates ranged from less than 3.5 to 13 GHz, i.e. values between 5% and 150% of the well asymmetry, and the dipole moments yield a minimum hopping distance of 0.3 to 0.8 Å. I also made detailed measurements of the lifetime of the first excited state away from the CPB charge degeneracy point and found that the lifetime varied from less than 50 ns up to a few μs as the Josephson energy E J decreased, consistent with a charge noise (S q ∼ 10-11 e2/Hz around 37 GHz to Sq ∼ 10-12 e2/Hz around 27 GHz) coupled to the qubit. I also found that at frequencies where an ALC was observed in the spectrum, a decrease in T1 occurred, suggesting that the discrete charge defects are a significant source of dissipation in the CPB.
I also designed and fabricated a "quasi-lumped element" thin-film superconducting Al microwave resonator on sapphire to be used for a dispersive read-out of the CPB. The resonator consists of a meandering inductor and an interdigitated capacitor coupled to a transmission line. At T = 30 mK and on resonance at 5.578 GHz, the transmission through the transmission line decreased by 15 dB and the loaded quality factor was 60,000. I measured the temperature dependence of the resonator frequency and loss at temperatures as high as 500 mK and found reasonable agreement with the Mattis-Bardeen theory.
Finally, I coupled a "quasi-lumped element" microwave resonator ( f0 ≃ 5.443 GHz), made of superconducting Al on sapphire, to an Al/AlOx/Al CPB qubit. Most of my measurements were made in the dispersive regime where EJ – hf0 is much larger than the coupling strength. In this case, the qubit causes a small state-dependent frequency shift in the resonator's resonant frequency. By sending down a second microwave tone (the pump), I was able to excite the CPB qubit. In zero magnetic field with the CPB far detuned from the resonator, I measured a 50 kHz decrease in f 0 with the qubit in the ground state and biased near the degeneracy point of the CPB. The charging energy and Josephson energy of the CPB were determined from spectroscopy taken by saturating the CPB with a second microwave tone and measuring the transmission through the resonator. The first device had EC/h = 12.5 GHz and maximum E J/h = 9 GHz. The second device had EC/h = 6.24 GHz and EJ/h tuned between 4 GHz and 8 GHz. By changing the external magnetic field, I could decrease the effective EJ of the CPB. From modeling, I extracted coupling strengths g/2π = 11 MHz and 5 MHz for the first and second device, respectively. Finally I did single and two-tone spectroscopy, and measured the relaxation and Rabi oscillations of the CPB. From the first device, I was able to obtain relaxation times T1 of 10.3 μs at EJ/h = 7 GHz on the CPB degeneracy point and spectroscopic coherence times [special characters omitted] ∼ 100 ns. From the second device, I found relaxation times T1 of 200 μs at EJ/h = 4 GHz to 4.5 GHz decreasing down to 4 μs around 8 GHz. There was also a depression in T1 around the resonant frequency of the resonator. The Rabi decay times were found to be up to T' ∼ 330 ns.