UMD Theses and Dissertations
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Item TUNNELING PROPERTIES AND ELECTROMAGNETIC RESPONSE IN IRON BASED SUPERCONDUCTORS AND OTHER SYSTEMS(2023) Barik, Tamoghna; Sau, Jay JS; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An iron-based chalcogenide compound, $\text{FeTe}_{1-x}\text{Se}_{x}$ (FTS), has recently attracted attention as a potential candidate for a readily available platform for hosting the exotic topological superconducting (TSC) phase on its surface. In its 3D sample the co-existence of the strong topological insulating (TI) phase and cylindrical Fermi sheets provide the two necessary ingredients for the TSC phase on its surface - i) the topologically protected helical surface states and ii) the intrinsically induced s-wave pairing from the bulk superconductivity. The strong TI phase in the FTS alloy is crucially dependent on the relative composition ratio between Te and Se atoms. The topological FTS sample, $\text{FeTe}_{.55}\text{Se}_{.45}$, that is widely studied for having the highest critical temperature ($T_c$) in this class, interestingly, lies close to the topological-trivial phase boundary (estimated to be close to $x=.5$ as observed by a recent experiment \cite{Brookhaven}). Furthermore, due to its alloy nature a typical sample of FTS suffers from spatial inhomogeneity in Te/Se composition at multiple length scales ranging from few nm to 100 $\mu \text{m}$. Thus, in a topological FTS sample there might be patches where the phase is driven out of its topological natures due to the local deficit of Te composition induced by Te/Se fluctuations. Such trivial domains would be scattered throughout the sample - hence, we call such a phase a topological domain disordered phase. The trivial domains in such a disordered sample would inflict inhomogeneity in the topological surface state (TSS) density distribution which we study in Chapter \ref{chap:chapter_2} of this thesis. After carefully exploring the effects of topological domain disordered phase in an effective model of FTS, we conclude that the non-topological domains on the surface are characterized by suppressed local density of states (LDOS) surrounded by ridges of enhanced LDOS throughout the energy range of the Dirac dispersion of the TSS. Moreover, the appropriately scaled LDOS at various energies within the Dirac window collapse on each other for a given disordered sample which, as we show, is in stark contrast to the case of conventional chemical potential disorder. Hence, these features are expected to appear in measurements of tunneling conductance such as in scanning tunneling spectroscopy (STS) of the FTS surface when the sample is not in the superconducting phase. Another kind of exotic modes, namely the helical Majorana modes, appear in the 2D TSC phase at a linear defect when the TSC gap on either side differs by a phase difference of $\pi$ from the other side - thus, forming a $\pi$ shifted Josephson junction (JJ) on the TSC surface. Signatures of such helical Majorana modes have been observed by a recent tunneling experiment on the surface of FTS. In FTS such signatures are characterized by the non-zero flat density of states (DOS) in an STS measurement at a crystalline domain wall (DW) which is associated with the in-plane half-unit-cell-shift (HUCS) of the lattice. Such non-zero flat DOS within the SC gap which is consistent with the existence of linearly dispersing 1D modes is absent in the non-topological $\text{FeSe}$ sample - hinting towards the topological origin of the same in FTS. Even though the TSC phase on the surface is expected in FTS, the origin of a $\pi$ shifted order parameter that is crucial to accommodate the helical Majorana modes at the DW, is yet to be fully understood. In chapter \ref{chap:chapter_3} of this thesis we propose a mechanism that stabilizes a $\pi$-junction at the HUCS domain wall when the intrinsic superconducting pairing is of $s_{\pm}$ character as is the case for bulk FTS superconductivity that consists of hole-like pockets around $\Gamma$ and electron-like pockets around $M$ point of the Brillouin zone (BZ). We argue that if the DW induces inter-pocket transmission between the $\Gamma$ and $M$ pockets strongly enough, the coupling between the order parameters (OPs) of the two pockets ($\Gamma$ and $M$) is also enhanced. Since the $s_{\pm}$ nature of the pairing implies an intrinsic $\pi$-phase difference between the OPs associated with the $\Gamma$ and $M$ pockets, strong DW-induced coupling between them can stabilize a Josephson junction with $\pi$-phase shift. We explore the possibility of such $\pi$-junction in FTS by constructing an effective model of the Fermi surface of FTS and computing the Bogoliubov-de-Gennes (BdG) spectrum with $s_{\pm}$ pairing at the HUCS DW. Varying our model parameters within the regime of the observed FTS Fermi surface we find that for a wide range of parameters the $\pi$-junction accommodates Andreev bound states (ABSs) that have lower occupied energies than those for trivial 0-phase shifted junction. Simultaneous numerical computation of the DW-induced scattering problem reveals that the strong inter-pocket transmission strength is positively correlated with the stability of the $\pi$-junction, supporting our proposed mechanism for the $\pi$-junction stability as described earlier. Such $\pi$-Josephson junctions can in principle be detected using superconducting quantum interference device (SQUID) using either a mesoscopic device or corner junction. In the next chapter \ref{chap:chapter_4} of the thesis we consider another setup of Josephson junction (JJ) consisting of an interacting one-dimensional quantum wire sandwiched between two semi-infinite SC leads of conventional s-wave pairing. The low energy Physics of such interacting 1D system which is known as Luttinger liquid (LL) is controlled by the two decoupled sets of eigen modes - namely, the charge and spin density waves. The SC leads in such a JJ thus allow easy access to the charge degrees of freedom in the LL - also known as plasmons which can also be probed optically using near field optical microscopy \cite{Wang2015,Wang2020}. An interesting aspect of an S-LL-S setup is that the NS interface blocks the flow of spin current due to the perfect Andreev reflection at low energies. Hence, the spin modes of the LL would typically be obscure to a transport measurement due to the aforementioned spin-charge decoupling. Hence, a conductivity measurement would not be able to detect the spin degrees of freedom if they are separated from the charge modes. However, we note that the impurity induced back-scattering processes which involve low energy but large momentum transfer can couple the spin and charge densities in the LL and we study the signatures of such spin-charge coupling in the electromagnetic (EM) response measurements. In our numerical evaluation which incorporates the impurity potential perturbatively and we calculate the resultant EM absorption spectrum using linear response theory which is measurable in a similar S-LL-S setup. We find that the signatures of back-scattering induced spin-charge coupling appear in the absorption spectrum as excitation peaks at the energies that are associated with the spin excitations of the LL. Tuning the total density of the 1D system and hence the Fermi momentum we find a regime where the spin peaks are roughly of equal amplitude as that of the charge peaks. Since in a 1D wire the density can be tuned by means of gating \cite{Wang2020}, such regime is accessible to a transport measurement. In that regime tuning the Coulomb interaction strength one can distinguish the charge peaks as they shift on the energy axis whereas the spin peaks are insensitive to such interaction strength variation. We conclude that such impurity induced signatures of spin modes can thus be probed in an S-LL-S setup by investigating the EM response of the sample in a conductivity measurement. In the last chapter \ref{chap:chapter_5} of the thesis we go beyond the regime of linear response formalism that is discussed in relation to the EM response of the S-LL-S setup in the previous paragraph and consider the optical response up to second order in the applied EM field. A fundamental feature of non-linear response is its non-equilibrium nature which is absent in linear responses. Such non-equilibrium character is manifested as the out-of-time-ordered correlators (OTOC) in response theory associated with the second power of the applied EM field magnitude. Such correlators for a generic interacting system cannot be described using the standard Feynman diagrams, rather one requires its non-equilibrium extension which is known as the Keldysh formalism. We focus on this non-equilibrium nature of the response by considering the bulk photovoltaic effect (BPVE) in a non-centrosymmetric system where we include electron-phonon (e-ph) coupling as the mode of relaxation. Considering the semi classical limit where the e-ph scattering is stronger than the applied field strength we show how the contribution of the OTOC appears in the BPVE induced DC current measurement when the system is illuminated by an inhomogeneous profile of optical intensity similar to the case of a irradiation on a finite portion of the sample. We also introduce the Floquet master equation approach to treat the e-ph coupling quantum mechanically and demonstrate a shift in the scaling of the DC response from quadratic to linear in the limit of the e-ph coupling strength being much smaller than the applied EM field.Item Ultra-high impedance superconducting circuits(2023) Mencia, Raymond; Manucharyan, Vladimir E; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Chains of Josephson junctions are known to produce some of the largest kinetic per unit-length inductance, which can exceed the conventional geometric one by about 104. However, the maximum total inductance is still limited by the stray capacitance of the chain, which results in parasitic self-resonances. This stray capacitance is unnecessarily large in most circuits due to the high dielectric constant of silicon or sapphire substrates used. Here, we explore a regime of ultra-high impedance superconducting circuits by introducing the technique of releasing the Josephson chain off the substrate. The ultra-high impedance regime (Z > 4xRQ ~ 25.8 kOhms) is realized by combining a maximal per-unit-length inductance with a minimal stray capacitance and demonstrating the highest impedance electromagnetic structures available today. We begin with suspended “telegraph” transmission lines, composed of 30,000+ junctions, and show that the wave impedance can exceed 5 x RQ (33 kOhms) while the line still maintains a negligible DC resistance. To quantify the effects of parasitic chain modes in ultra-high impedance circuits, we use high-inductance fluxonium qubits. We show that chain modes are ultra-strongly coupled to the qubit but can be moved to a higher frequency with the Josephson chain releasing technique. Finally, we create a superconducting quasicharge qubit (blochnium), dual of transmon, whose impedance reaches over 30 x RQ (200 kOhms) with no evidence of parasitic modes below 10 GHz. This qubit completes the periodic table of superconducting atoms and demonstrates the dual nature of a small Josephson junction in ultra-high impedance circuits, which we probe in a DC experiment in the final chapter.Item Supercurrent and Andreev bound states in multi-terminal Josephson junctions(2022) Lee, Hanho; Manucharyan, Vladimir; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A Josephson junction (JJ) is known as a weak link connecting two superconductors, in which the non-dissipative supercurrent flows. More than two superconductors also can form a single composite JJ, called a “multi-terminal JJ”, by being connected through a common weak link. The supercurrent in multi-terminal JJs may depend on multiple superconducting phase differences defined across the junction. The multi-phase-dependence of the supercurrent is attributed to the sub-gap quasiparticle bound states, called Andreev bound states (ABSs), which carry the supercurrent across the junction. First, we investigate the supercurrent of three- and four-terminal JJs fabricated on hybrid two-dimensional Al/InAs (superconductor/semiconductor) heterostructures. The critical current of an N-terminaljunction is given as a (N-1)-dimensional hypersurface of the DC bias currents, which can be reduced to a set of critical current contours (CCCs) in low dimensional space. Non-trivial modifications of the geometry of the CCCs in response to magnetic field, electrical gating and phase biasing can be understood in the presence of the multi-phase-dependent ABSs. Second, we demonstrate the multi-phase-dependent ABSs in three-terminal JJs by tunneling spectroscopy measurements. Multi-loop superconducting quantum interference devices (SQUIDs) are realized to detect the multi-phase-dependence. The ABS energy spectrum mimics electronic band structure in solid, which makes multi-terminal JJs provide a new platform to study band topology in higher dimensional parameter space. Moreover, spin-splitting of ABS energies induced by the multi-phase and gapless energy spectrum facilitated by the presence of a discrete vortex, a nonzero winding of the superconducting phases, are investigated.Item On the nature of the Josephson effect in topologically nontrivial materials(2021) Trimble, Christie Jordan; Williams, James R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a tunnel barrier, giving rise to a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. Here, I experimentally investigate three such cases. In the first part of the thesis, I fabricate JJs with weak links made of the topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te and compare them with JJs made from its topologically trivial cousin, PbTe. I find that measurements of the AC Josephson effect reveal a stark difference between the two: while the PbTe JJs exhibit Shapiro steps at the expected values of $V=nhf/2e$, Pb$_{0.5}$Sn$_{0.5}$Te JJs show more complicated subharmonic structure. I present the skewed sinusoidal CPR necessary to reproduce these measurements and discuss a potential origin for this alteration. Next, I investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in Josephson junctions. I report indications of an unexpected breaking of time-reversal symmetry in these devices, including observations of an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. I analyze how multiband effects and the experimentally visualized ferroelectric domain walls may give rise to a nonstandard CPR in the junction. Finally, I measure JJs with weak links made of the topological insulator (BiSb)$_2$Te$_3$. Under low frequency RF radiation, I observe suppression of the first and third Shapiro steps, consistent with the fractional AC Josephson effect. This could indicate a 4$\pi$ periodic component in the junction's CPR, potentially implying the presence of Majorana bound states. However, not all of the devices showed this behavior; some devices show suppression of only the first step, while others show distortions to the AC Josephson effect which differ upon repeated measurements, possibly indicating other nonequilibrium effects at play. I discuss this behavior and possible topologically trivial sources of step suppression found in the literature.Item INTERACTING PHOTONS IN CIRCUIT QUANTUM ELECTRODYNAMICS: DECAY OF THE COLLECTIVE PHASE MODE IN ONE-DIMENSIONAL JOSEPHSON JUNCTION ARRAYS DUE TO QUANTUM PHASE-SLIP FLUCTUATIONS(2020) Grabon, Nicholas Christopher; Manucharyan, Vladimir; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Light does not typically scatter light, as witnessed by the linearity of Maxwell’s equations. In this work, we demonstrate two superconducting circuits, in which microwave photons have well-defined energy and momentum, but their lifetime is finite due to decay into lower energy photons. The circuits we present are formed with Josephson junction arrays where strong quantum phase-slip fluctuations are present either in all of the junctions or in only a single junction. The quantum phase-slip fluctuations are shown to result in the strong inelastic photon-photon interaction observed in both circuits. The phenomenon of a single photon decay provides a new way to study multiple long-standing many-body problems important for condensed matter physics. The examples of such problems, which we cover in this work include superconductor to insulator quantum phase transition in one dimension and a general quantum impurity problem. The photon lifetime data can be treated as a rare example of a verified and useful quantum many-body simulation.Item SUPERCONDUCTING RADIO FREQUENCY MATERIALS SCIENCE THROUGH NEAR-FIELD MAGNETIC MICROSCOPY(2020) Oripov, Bakhrom Gafurovich; Anlage, Steven M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Superconducing Radio-Frequency (SRF) cavities are the backbone of a new generation of particle accelerators used by the high energy physics community. Nowadays, the applications of SRF cavities have expanded far beyond the needs of basic science. The proposed usages include waste treatment, water disinfection, material strengthening, medical applications and even use as high-Q resonators in quantum computers. A practical SRF cavity needs to operate at extremely high rf fields while remaining in the low-loss superconducting state. State of the art Nb cavities can easily reach quality factors Q>2x10^10 at 1.3 GHz. Currently, the performance of the SRF cavities is limited by surface defects which lead to cavity breakdown at high accelerating gradients. Also, there are efforts to reduce the cost of manufacturing SRF cavities, and the cost of operation. This will require an R&D effort to go beyond bulk Nb cavities. Alternatives to bulk Nb are Nb-coated Copper and Nb3Sn cavities. When a new SRF surface treatment, coating technique, or surface optimization method is being tested, it is usually very costly and time consuming to fabricate a full cavity. A rapid rf characterization technique is needed to identify deleterious defects on Nb surfaces and to compare the surface response of materials fabricated by different surface treatments. In this thesis a local rf characterization technique that could fulfill this requirement is presented. First, a scanning magnetic microwave microscopy technique was used to study SRF grade Nb samples. Using this novel microscope the existence of surface weak-links was confirmed through their local nonlinear response. Time-Dependent Ginzburg-Landau (TDGL) simulations were used to reveal that vortex semiloops are created by the inhomogenious magnetic field of the magnetic probe, and contribute to the measured response. Also, a system was put in place to measure the surface resistance of SRF cavities at extremely low temperatures, down to T=70 mK, where the predictions for the surface resistance from various theoretical models diverge. SRF cavities require special treatment during the cooldown and measurement. This includes cooling the cavity down at a rate greater than 1K/minute, and very low ambient magnetic field B<50 nT. I present solutions to both of these challenges.Item Topological Superconductivity and Majorana Zero Modes(2017) Setiawan, FNU; Das Sarma, Sankar; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Recent years have seen a surge interest in realizing Majorana zero modes in condensed matter systems. Majorana zero modes are zero-energy quasiparticle excitations which are their own anti-particles. The topologically degenerate Hilbert space and non-Abelian statistics associated with Majorana zero modes renders them useful for realizing topological quantum computation. These Majorana zero modes can be found at the boundary of a topological superconductor. While preliminary evidence for Majorana zero modes in form of zero-bias conductance peaks have already been observed, confirmatory signatures of Majorana zero modes are still lacking. In this thesis, we theoretically investigate the robustness of several signatures of Majorana zero modes, thereby suggesting improvement and directions that can be pursued for an unambiguous identification of the Majorana zero modes. We begin by studying analytically the differential conductance of the normal-metal--topological superconductor junction across the topological transition within the Blonder-Tinkham-Klapwijk formalism. We show that despite being quantized in the topological regime, the zero-bias conductance only develops as a peak in the conductance spectra for sufficiently small junction transparencies, or for small and large spin-orbit coupling strength. We proceed to investigate the signatures of Majorana zero modes in superconductor--normal-metal--superconductor junctions and show that the conductance quantization in this junction is not robust against increasing junction transparency. Finally, we propose a dynamical scheme to study the short-lived topological phases in ultracold systems by first preparing the systems in its long-lived non-topological phases and then driving it into the topological phases and back. We find that the excitations' momentum distributions exhibit Stuckelberg oscillations and Kibble-Zurek scaling characteristic of the topological quantum phase transition, thus provides a bulk probe for the topological phase.Item Superconducting Logic Circuits Operating With Reciprocal Magnetic Flux Quanta(2011) Oberg, Oliver Timothy; Wellstood, Frederick; Herr, Anna; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Complimentary Medal-Oxide Semiconductor (CMOS) technology is expected to soon reach its fundamental limits of operation. The fundamental speed limit of about 4 GHz has already effectively been sidestepped by parallelization. This increases raw processing power but does nothing to improve power dissipation or latency. One approach for increasing computing performance involves using superconducting digital logic circuits. In this thesis I describe a new kind of superconducting logic, invented by Quentin Herr at Northrop Grumman, which uses reciprocal pairs of quantized single magnetic flux pulses to encode classical bits. In Reciprocal Quantum Logic (RQL) the data is encoded in integer units of the magnetic flux quantum. RQL gates operate without the bias resistors of previous superconducting logic families and dissipate several orders of magnitude less power. I demonstrate the basic operation of key RQL gates (AndOr, AnotB, Set/Reset) and show their self-resetting properties. Together, these gates form a universal logic set and provide memory capabilities. Experiments measuring the bit error rate of the AndOr gate extrapolated a minimum BER of 10-480 and a BER of 10-44 with 30% margins on flux biasing. I describe an analytic timing model for RQL gates which demonstrates the self-correcting timing features. From this model I derive equations for the timing behavior and operating limits. Using this timing model I ran simulations to determine correction factions for more accurate predictions at higher frequencies. Using these results, I also develop Very High Speed Integrated Circuit (VHSIC) Hardware Description Language (VHDL) models to describe the combinational logic of RQL gates. To test the timing predictions of the timing model, I performed three experiments on Nb/AlOx/Nb circuits at 4.2 K. The first measured the time of output. The second measured the operating margins of the circuit. The third measured the maximum frequency of operation for RQL circuits. Together, these three experiments showed quantitative agreement with the model for the timing output, qualitative agreement with the limits of operation, and a projected speed limit of 50 GHz for the Hypres 4.5 kA/cm2 process. To power RQL circuits I describe a new design for power splitters and combiners which minimize standing waves. I describe a new kind of Wilkinson power splitter which required numerical optimization but proved to be adequate. I experimentally tested two new designs of the power splitter. Both showed less than 10% variation in standing waves between power splitter and combiner, making it adequate for RQL circuits. I also compared these results with the S-parameters of the power network, which also indicated that the design was adequate for RQL circuits. Finally, I tested an 8-bit Kogge-Stone architecture carry-look ahead adder designed using VHDL models. The adder contained 815 Josephson junctions and was fully functional at 6.21 GHz with a latency of 1.25 clock cycles. The adder produced the correct logical output, had a measured optimal operating point within 8% of the optimal simulated operating point, and measured power margins of 1 dB. It operated best at the designed clock amplitude of 0.88Ic and dissipated 0.570 mW of power.Item dc SQUID Phase Qubit(2008-08-06) palomaki, tauno; Wellstood, Frederick C; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)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.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.