This thesis examines the behavior of dc SQUID phase qubits in terms of their proposed use in a quantum computer. In a phase qubit, the two lowest energy states (n=0 and n=1) of a current-biased Josephson junction form the qubit states, with the gauge invariant phase difference across the junction being relatively well defined. In a dc SQUID phase qubit, the Josephson junction is isolated from the environment using an inductive isolation network and Josephson junction, which are connected across the phase qubit junction to form a dc SQUID. Five dc SQUID phase qubits were examined at temperatures down to 25 mK. Three of the devices had qubit junctions that were Nb/AlOx/Nb junctions with critical currents of roughly 30 microamps. The other two had Al/AlOx/Al junctions with critical currents of roughly 1.3 microamps. The device that had the best performance was an Al/AlOx/Al device with a relaxation time of 30 ns and a coherence time of 24 ns. The devices were characterized using microwave spectroscopy, Rabi oscillations, relaxation and Ramsey fringe measurements. I was also able to see coupling between two Nb/AlOx/Nb dc SQUID phase qubits and perform Rabi oscillations with them. The Nb/AlOx/Nb devices had a relaxation time and coherence time that were half that of the Al/AlOx/Al device. One of the goals of this work was to understand the nature of parasitic quantum systems (TLSs) that interact with the qubit. Coupling between a TLS and a qubit causes an avoided level crossing in the transition spectrum of the qubit. In the Al/AlOx/Al devices unintentional avoided level crossings were visible with sizes up to 240 MHz, although most visible splittings were of order ~20 MHz. The measured spectra were compared to a model of the avoided level crossing based on the TLSs coupling to the junction, through either the critical current or the voltage across the junction.
This thesis examines the behavior of dc SQUID phase qubits in terms of their proposed use in a quantum computer. In a phase qubit, the two lowest energy states (n=0 and n=1) of a current-biased Josephson junction form the qubit states, with the gauge invariant phase difference across the junction being relatively well defined. In a dc SQUID phase qubit, the Josephson junction is isolated from the environment using an inductive isolation network and Josephson junction, which are connected across the phase qubit junction to form a dc SQUID. Five dc SQUID phase qubits were examined at temperatures down to 25 mK. Three of the devices had qubit junctions that were Nb/AlOx/Nb junctions with critical currents of roughly 30 microamps. The other two had Al/AlOx/Al junctions with critical currents of roughly 1.3 microamps. The device that had the best performance was an Al/AlOx/Al device with a relaxation time of 30 ns and a coherence time of 24 ns. The devices were characterized using microwave spectroscopy, Rabi oscillations, relaxation and Ramsey fringe measurements. I was also able to see coupling between two Nb/AlOx/Nb dc SQUID phase qubits and perform Rabi oscillations with them. The Nb/AlOx/Nb devices had a relaxation time and coherence time that were half that of the Al/AlOx/Al device. One of the goals of this work was to understand the nature of parasitic quantum systems (TLSs) that interact with the qubit. Coupling between a TLS and a qubit causes an avoided level crossing in the transition spectrum of the qubit. In the Al/AlOx/Al devices unintentional avoided level crossings were visible with sizes up to 240 MHz, although most visible splittings were of order ~20 MHz. The measured spectra were compared to a model of the avoided level crossing based on the TLSs coupling to the junction, through either the critical current or the voltage across the junction.
We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al and three Nb/AlOx/Nb dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear isolating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit, a spectroscopic coherence time ${T}_{2}^{\ensuremath{\ast}}$ varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant ${T}^{\ensuremath{'}}=25\phantom{\rule{0.3em}{0ex}}\text{ns}$ on average at 80 mK. The three Nb devices also showed ${T}_{2}^{\ensuremath{\ast}}$ in the range of 3--8 ns, but ${T}^{\ensuremath{'}}$ was 9--15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening.
A dc SQUID phase qubit consists of two Josephson junctions in a loop. One junction acts as a qubit with two lowest energy levels forming the |0> and |1> status. The second junction and the loop inductance act to isolate the qubit junction from noise. In this thesis, I report on the improvement of the relaxation time and the coherence time in a dc SQUID phase qubit that used an LC filter. I also report the measurement of anomalous switching curves. In order to improve the relaxation and coherence times, I used two isolation networks, an LC isolation network and an inductive isolation network, to decouple the device from the current bias lines. This produced a very large total effective resistance of the input leads that increases the relaxation time of the qubit. In addition, I connected a low-loss SiNx shunting capacitor across the qubit junction to reduce dielectric losses. I measured two dc SQUID phase qubits. Device DS6 had a 4 (μm)2 Al/AlOx/Al qubit junction with a critical current of 0.5 μA and a 1 pF shunting capacitor. It used an LC filter made from a 10 nH inductor and a 145 pF capacitor. The capacitors contained N-H rich SiNx which produced a loss tangent of about 7×10 -4 . Device DS8 had a 2 (μm)2 Al/AlOx/Al qubit junction with a critical current of 77 nA and an LC filter similar to the first one. The shunting capacitor contained Si-H rich SiNx. Using a pulse readout technique, I measured the characteristics of the qubits, including the transition spectrum, Rabi oscillations, relaxation, Ramsey fringes and state tomography. The best relaxation time T1 for device DS6 was 32 ns and 280 ns for device DS8. The best Rabi decay time T' for DS6 was 42 ns while for device DS8 it was 120 ns. From these and other data I obtained estimates for the best coherence time T2 in device DS6 of 61 ns and 76 ns in device DS8. In DS8, I observed anomalous switching curves; i.e. switching curves which were qualitatively different from conventional switching curves. In the conventional case, the switching curve for the superposition state is the weighted sum of the |0> and |1> curves, but it was not in device DS8. Instead, the switching curve shifted along the current axis as the exited state probability increased. I present a model for understanding the behavior and use this model to extract the probability to be in the excited state.
This thesis examines Josephson tunnel junctions as candidate qubits for quantum computation. A large area current-biased junction, known as a phase qubit, uses the two lowest energy levels in a tilted washboard potential as the qubit states |0> and |1>. I performed experiments with 10 x 10 um^2 Nb/AlOx/Nb qubit junctions, with critical currents of roughly 30 uA. The state of a device was initialized by cooling below 50 mK in a dilution refrigerator. In order for quantum mechanical superpositions to be long-lived, it is necessary to isolate the junction from noisy bias leads that originate at room temperature. I studied two types of isolation: an LC filter, and a broadband scheme that used an auxiliary junction, resulting in a dc SQUID. One of the main goals of this work was to determine how well a simple Hamiltonian, derived assuming just a few lumped elements, describes the observed behavior of a macroscopic Josephson device, including coherent dynamics such as Rabi oscillations. I did this by comparing results to the expected behavior of ideal two-level systems and with more detailed master equation and density matrix simulations. I performed state manipulation by applying dc bias currents and resonant microwave currents, and through temperature control. The tunneling escape rate of the junction from the states |0> and |1> (zero voltage) to the running state (finite voltage) depends on the occupation probability of the energy levels and served as state readout. Experiments to measure the relaxation time T1 between |1> and |0> were performed by examining the dependence of the escape rate with temperature, yielding a maximum T1 = 15 ns. Measuring the decay to the ground state after applying a microwave pulse revealed at least two time constants, one of about 10 ns and another as long as 50 ns. The spectroscopic coherence time T2* was estimated to be roughly 5 ns by measuring resonance widths and the decay envelope of coherent Rabi oscillations was found to have a time constant T' = 10 ns over a wide range of conditions.
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 Tø ∼ 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 SI01 (1Hz) ≈ 10 (nA) 2/Hz and the 1/f flux noise power spectral density at 1 Hz was SΦ (1Hz) ≈ (110 μΦ 0)2/Hz. Both of these values were quite high, possibly due to switching of the device between measurements.
We have fabricated and tested an Al/AlOx/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area 0.17 μm2and critical current I0,J1= 1.4 μA. The qubit is shunted by an interdigitated capacitor and isolated from the bias leads by an inductive isolation network using a larger Josephson junction with area 2 μm2and critical current I0,J2= 29 μA. Additional high-frequency filtering is provided by an on-chip LC filter, which consists of square spiral inductors and parallel plate SiNxcapacitors. From detuned Rabi oscillation measurements, we estimate a relaxation time T1≈ 400 ns and dephasing time TΦ1700 ns. Additionally, we observe that the qubit transition spectrum has multiple equally spaced subpeaks. These subpeaks are caused by coupling between the phase qubit and the LC filter, forming a Jaynes-Cummings system. Each individual subpeak corresponds to transitions with different photon numbers in the LC filter.
This work concerns the study of Josephson junction circuits in the context of their usability for quantum computing. The zero-voltage state of a current-biased Josephson junction has a set of metastable quantum energy levels. If a junction is well isolated from its environment, it will be possible to use the two lowest states as a qubit in a quantum computer. I first examine the meaning of isolation theoretically. Using a master equation, I analyzed the effect of dissipation on escape rates and suggested a simple method, population depletion technique, to measure the relaxation time. Using a stochastic Bloch equation to analyze microwave resonance shapes, I found a relation between current noise induced decoherence and the noise spectrum. I then analyze and test a few qubit isolation schemes, including resistive isolation, inductor-capacitor (LC) isolation, and inductor-junction (LJ) isolation. I found the resistive isolation scheme has a severe heating problem. Macroscopic quantum tunneling and energy level quantization were observed in the LC isolated junction qubits at 25 mK. Relaxation times of 4-12 ns and spectroscopic coherence times of 1-3 ns were obtained for these LC isolated qubits. I measured a relaxation time of 50 ns and a spectroscopic coherence time of 5-8 ns for the LJ isolated junction qubit. Both times are much longer than those of the LC isolated qubits. Rabi oscillations were also observed on this sample with a decay time of around 10 ns. Using microwave spectroscopy techniques, I probed quantum phenomena in a coupled macroscopic three-qubit system that is comprised of two Nb/AlOx/Nb Josephson junctions and an LC resonator. The measured spectrum at 25 mK in the frequency range 4-15 GHz agrees well with quantum mechanical calculations, consistent with the existence of entangled states between the three degrees of freedom. These entangled states and a first-order strong coupling between two junction qubits open the possibility of using a resonator as a data bus for information storage and manipulation in a multi-qubit system. The measurements also demonstrate spectroscopy is a powerful tool and can be used to study a composite system with many qubits.