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Item Decoherence And Defects In Cooper-Pair Boxes(2013) Zaretskey, Vitaley; Wellstood, Fred; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation describes my detailed investigation of decoherence and defects in two Al/AlOx/Al Cooper-pair box (CPB) charge qubits. Both devices were coupled to thin-film lumped-element superconducting aluminum LC resonators at a temperature of 25 mK. Device 1 was previously found to have an exceptionally long energy relaxation time of T1=205 μs and a strong correlation between the lifetime T1 and the decoupling from the microwave drive line dVg,rms/dΩR,0. I determined the dephasing properties of this CPB though a series of experiments. I measured Ramsey fringes, extracted dephasing times Tφ in the range200-500 ns, and determined a corresponding bound of Sq(f=1 Hz)≤(3×10-3)2 e2/Hz on the amplitude of the 1/f charge noise affecting the qubit. I then carried out a spin echo experiment and found echo decay times Techo in the 2.4-3.3 μs range, implying a high frequency 1/f charge noise cutoff of ωc/2π≈0.2 MHz. I followed this up by fabricating and characterizing a nearly identical Device 2. This CPB had a reasonably long relaxation time T1≈4-30 μs and again the lifetime T1 and decoupling dVg,rms/dΩR,0 were correlated. Although the lifetime of Device 2 was shorter than that of Device 1, the results suggest that the exceptional relaxation time was somewhat reproducible and that this approach may lead to further improvements in qubit coherence. During my initial characterization of Device 2, I discovered that it displayed an anomalously twinned transition spectrum. I studied this feature in detail in parallel with my decoherence experiments. I found that above the resonator resonance at ω/2π=5.472 GHz the system spectrum was twinned but below it was quadrupled. This behavior was consistent with a pair of two-level systems (TLS) coupled non-resonantly to the CPB via both charge and critical current. I developed a model that matched this scenario and successfully fit the predicted spectrum to my data. Both the coherent non-resonant interaction and joint charge and critical current CPB-TLS coupling are novel observations. From the fits I extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a minimum hopping distance of 0.2-0.45 Å. I also found a large fractional change of the Josephson energy ΔEJ,k/EJ≈30-40%, consistent with a non-uniform tunnel barrier containing a few dominant conduction channels and a defect that modulates one of them.Item Reducing Decoherence in dc SQUID Phase Qubits(2010) Przybysz, Anthony Joseph; Wellstood, Frederick C.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis examines sources of dissipation and dephasing in a dc SQUID phase qubit. Coupling of the qubit to the bias lines and lossy dielectrics causes the qubit to lose quantum information through a process known generally as decoherence. Using knowledge of the possible sources of decoherence, a dc SQUID phase qubit is designed with parameters that should have made it resistant to dissipation and dephasing from those sources. Device PB9 was a dc SQUID with one small area 0.23 (μm)2 Josephson junction with a critical current of 130 nA, which was meant to be the qubit junction, and a larger area 5 (μm)2 junction with a critical current of 8.6 μA, which acted as part of an inductive isolation network. The qubit junction was shunted by a 1.5 pF low-loss interdigitated capacitor. The dc current bias line had an on-chip LC filter with a cutoff frequency of 180 MHz. The other control lines were also designed to minimize coupling of dissipative elements to the qubit. According to a theoretical model of the dissipation and dephasing, the qubit was expected to have an energy relaxation T1 ≤ 8.4 μs and dephasing time Tphi ~ 1 μs. Because of the relatively high Josephson inductance of the qubit junction, the device did not act perform like a conventional isolated single-junction phase qubit. Instead, the resonant modes that I observed were the normal modes of the entire SQUID. At 20 mK and a frequency of 4.047 GHz, the maximum energy relaxation time of the device was found to be 350 ± 70 ns, despite the optimized design. Through a study of T1 versus applied flux, T1 was found to depend on the strength of the coupling of the microwave drive line to the qubit. When the line was more coupled, T1 was shorter. This was evidence that the microwave line was overcoupled to the qubit, and was limiting the lifetime of the excited state T1. Through a study of the spectroscopic coherence time T2*, which measured the effects of low-frequency inhomogeneous broadening and higher frequency dephasing from noise, I discovered that device PB9 has several sweet spots. In particular, the presence of a sweet spot with respect to critical current fluctuations allowed me to identify critical current noise as a major source of broadening and dephasing in the qubit. From the spectroscopy I estimated the 1/f critical current noise power density at 1 Hz was and the 1/f flux noise power spectral density at 1 Hz was . Both of these values were quite high, possibly due to switching of the device between measurements.Item DISSIPATIVE AND DISPERSIVE MEASUREMENTS OF A COOPER PAIR BOX(2010) Kim, Zaeill; Wellstood, Frederick C.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)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 T1 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 Ej/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 Angstroms. 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 us as the Josephson energy Ej decreased, consistent with a charge noise (Sq~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 f0 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 Ej/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/2&pi = 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 us at Ej/h = 7 GHz on the CPB degeneracy point and spectroscopic coherence times T2 *~ 100 ns. From the second device, I found relaxation times T1 of 200 us at Ej/h = 4 GHz to 4.5 GHz decreasing down to 4 us 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.Item Coherence in dc SQUID phase qubits(2007-09-17) Paik, Hanhee; Lobb, Christopher J; Wellstood, Frederick C; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)I report measurements of energy relaxation and quantum coherence times in an aluminum dc SQUID phase qubit and a niobium dc SQUID phase qubit at 80 mK. In a dc SQUID phase qubit, the energy levels of one Josephson junction are used as qubit states and the rest of the SQUID forms an inductive network to isolate the qubit junction. Noise current from the SQUID's current bias leads is filtered by the network, with the amount of filtering depending on the ratio of the loop inductance to the Josephson inductance of the isolation junction. The isolation unction inductance can be tuned by adjusting the current, and this allows the isolation to be varied in situ. I quantify the isolation by the isolation factor rI which is the ratio of the current noise power in the qubit junction to the total noise current power on its bias leads. I measured the energy relaxation time T1, the spectroscopic coherence time T2* and the decay time constant T' of Rabi oscillations in the Al dc SQUID phase qubit AL1 and the Nb dc SQUID phase qubit NBG, which had a gradiometer loop. In particular, I investigated the dependence of T1 on the isolation rI . T1 from the relaxation measurements did not reveal any dependance on the isolation factor rI. For comparison, I found T1 by fitting to the thermally induced background escape rate and found that it depended on rI . However, further investigation suggests that this apparent dependence may be due to a small-noise induced population in j2i so I cannot draw any firrm conclusion. I also measured the spectroscopic coherence time T2* , Rabi oscillations and the decay constant T' at significantly different isolation factors. Again, I did not observe any dependence of T2* and T' on rI , suggesting that the main decoherence source in the qubit AL1 was not the noise from the bias current. Similar results were found previously in our group's Nb devices. I compared T1, T2* and T0 for the qubit AL1 with those for NBG and a niobium dc SQUID phase qubit NB1 and found significant differences in T2* and T' among the devices but similar T1 values. If flux noise was dominant, NBG which has a gradiometer loop would have the longest Rabi decay time T'. However, T' for NBG was similar to NB1, a Nb dc SQUID phase qubit without a gradiometer. I found that T' = 28 ns for AL1, the Al dc SQUID phase qubit, and this was more than twice as long as in NBG (T' ~ 15 ns) or NB1 (T' ~ 15 ns). This suggests that materials played an important role in determining the coherence times of the different devices. Finally, I discuss the possibility of using a Cooper pair box to produce variable coupling between phase qubits. I calculated the effective capacitance of a Cooper pair box as a function of gate voltage. I also calculated the energy levels of a Josephson phase qubit coupled to a Cooper pair box and showed that the energy levels of the phase qubit can be tuned with the coupled Cooper pair box.Item On the Typical and Average Contributions to the Persistent Current in Mesoscopic Rings(2004-07-27) Jariwala, E. Manher Q.; Webb, Richard A; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Low-temperature measurements of the magnetic response of one or more electrically-isolated, micron-sized metallic rings yield an unexpected yet unequivocal result: the presence of equilibrium persistent currents, with nanoampere-sized amplitudes and either h/e- or h/2e-periodicity in the applied magnetic flux. This effect follows from the extended phase coherence of the conduction electrons in this disordered mesoscopic system. As with transport phenomena, this thermodynamic effect demonstrates sample-specific as well as ensemble-averaging qualities common to mesoscopic physics. With few exceptions, however, there is strong disagreement between the different theoretical calculations and the few successful experiments to date. For this thesis work, we have designed and executed a unique and unprecedented new experiment: the measurement of the sign, amplitude, and temperature dependences of both the typical and average current contributions to the h/e- and h/2e-periodic magnetic response of the same sample of thirty mesoscopic Au rings. Of particular interest here is the innovative design of our custom SQUID-based detector as well as the unusually long phase coherence of electrons in our lithographically-patterned Au sample. Remarkably, both the typical and average contributions are diamagnetic in sign near zero field, over multiple cooldowns, and comparable in magnitude per ring to the Thouless scale Ec of energy level correlations. Taken in conjunction with earlier experiments, the new data strongly challenge conventional theories of the persistent current.