Session L33: Focus Session: Superconducting Qubits III

Novel quantum transport in superconducting phase-qubit arrays.

The dramatic increase of coherence times in superconducting phase qubit experiments allows the exploration of multi-qubit quantum dynamics. In this talk I theoretically explore the controlled propagation of excitations in capacitively-coupled phase qubits. By exploiting the tunability and flexible topology of phase-qubit arrays, this artificial solid can demonstrate novel quantum transport effects such as perfect state transfer. These ideas are confirmed by multi-qubit, multi-level simulations including the effects of long-range couplings, disorder, and decoherence.   

Josephson Phase Qubits with Hydrogenated Amorphous Silicon Dielectric

The lifetime of Josephson phase qubits is limited by the presence of two-level defect states in the dielectric material of the qubit. Improvements in the loss tangents of dielectric materials have resulted in substantial gains in qubit lifetime by reducing the number of such defects. Measurements of the loss tangent of hydrogenated amorphous silicon indicate at least a five-fold decrease in the loss tangent compared to our current SiN dielectric, making a-Si:H a promising candidate dielectric for use in phase qubits. We discuss the incorporation of a-Si:H dielectric into our qubit fabrication process, and present measurements of the energy decay and dephasing lifetimes of qubits made with this material.   

Reducing defects in Josephson phase qubits -- interdigitated capacitors and microbridges

Josephson phase qubits have recently demonstrated increased coherence times, setting them as a serious option for scalable quantum computing. This has been made possible by identifying dielectric two-level defect states in the Josephson junction and in any additional capacitance in the circuit as a major source of decoherence. We show that by fabricating an external, high quality interdigitated capacitor the lifetime of the qubit is increased to at least half a microsecond. Further reduction in decoherence is expected by completely removing the dielectric of the tunnel junction and replacing it with a superconducting microbridge. Some preliminary results for MBE grown Rhenium microbridge qubits will be presented.   

Precise measurements of single gate errors in Josephson phase qubits

As Josephson phase qubits continue to improve, the accuracy of qubit manipulations become increasingly important. We have built a new generation of control electronics to generate microwave pulses with an accurate Gaussian-envelope for single qubit logic gates, using a modular and card-rack design to promote scalability. To understand the tradeoff between accuracy and speed, we plan to present an experiment that measures gate errors versus the width of the applied pulses. We intend to more precisely measure the accuracy of single qubit rotations using multi-pulse sequences, similar to that already done for ion-trap qubits.   

Attempt to Violate the CHSH Bell Inequality in Josephson Phase Qubits

The violation of Bell's inequality is the primary argument against the possible existence of a hidden-variable-theory as an alternative to quantum mechanics. It also often serves as a convincing demonstration that a given system behaves in a truly non-classical way. There have been many proposals of different classically binding inequalities that quantum mechanics can violate. The most widely accepted forms follow closely along a correlation measurement proposed by Clauser, Horne, Shimony and Holt (CHSH) in 1969. Here we present our attempt to implement the CHSH Bell test using Josephson phase qubits. The nature of this experiment places high demands –-- compared to the current state of the art in solid state qubits –-- on qubit performance measures such as the energy relaxation time T1, the decoherence time T2, measurement fidelities, and the quality of single and two qubit operations. We will examine these demands and position our past and current qubit designs against them.   

Quantum kinetics of a Josephson phase qubit continuously monitored for escape.

Inspired by recent experiment [1] on partial measurement of a Josephson phase qubit, we consider evolution of a qubit in a metastable potential being continuosly monitored for escape. Assuming that the continuous measurement may induce incoherence both in the tunneling reservoir and in the tunneling matrix elements but not in the qubit itself, we discuss the conditions for the qubit to retain coherence. We argue that qubit state remains pure as long as the tunneling event is never reverted, that is, the tunneling from the reservoir back to qubit state is suppressed. Such a suppression may happen due to the choice of system parameters (e.g., for nearly continuous spectrum in the tunneling reservoir), or dynamically due to the properties of coherent or incoherent evolution in the reservoir. We illustrate these scenarios by numerical simulations and with an analytical model where the exact solution of the master equation gives no decoherence of the qubit over a finite time interval. \medskip\par\noindent [1] N. Katz {\it et al.}, Science {\bf 312}, 1498 (2006).   

Crossover of phase qubit dynamics in presence of negative-result weak measurement

Coherent dynamics of a superconducting phase qubit is considered in the presence of both unitary evolution due to microwave driving and continuous non-unitary collapse due to negative-result measurement. In the case of a relatively weak driving, the qubit dynamics is dominated by the non-unitary evolution, and the qubit state tends to an asymptotically stable point on the Bloch sphere. This dynamics can be clearly distinguished from conventional decoherence by tracking the state purity and the measurement invariant (``murity''). When the microwave driving strength exceeds certain critical value, the dynamics changes to non-decaying oscillations: any initial state returns exactly to itself periodically in spite of non-unitary dynamics. The predictions can be verified using a modification of a recent experiment.   

Temperature Dependence of Rabi Oscillations in Phase Qubits

Using the experimental setup in Erlangen, we compared aluminum-based phase qubits with SiN$_x$ shunting capacitors made at UCSB with similarly designed circuits fabricated at HYPRES foundry using a standard niobium-based fabrication process with SiO$_2$ insulation. Measured decoherence times are about 100 ns and 5 ns, respectively. In both types of circuits, energy relaxation time $T_1$ scales inversely proportional to the area of the qubit junction, which agrees with earlier data. Rabi oscillations remain visible up to the temperature $T$ of about 400 mK (UCSB) and 800 mK (HYPRES), where the energy level separation becomes comparable with $k_{\rm B}T$. The current pulse readout in the upper temperature range is dominated by thermal escape rather then tunneling. Temperature dependence data for the decoherence time and oscillations contrast will be presented and discussed.   

A dc-SQUID phase qubit

A current and flux biased dc-SQUID behaves as a quantum particle trapped in a cubic-quadratic potential well. Resonant transitions between the ground and first excited states are induced by the application of microwave current or flux pulses. Measurement is performed by an adiabatic nanosecond flux pulse which projects the excited levels of the quantum particle onto the voltage state of the SQUID. Rabi-like coherent oscillations have been observed with a decay time $\tau \simeq 20$ ns [PRL 93, 187003]. The dominant source of this decoherence was thermal current fluctuations [PRB 73, 180502]. We propose operation of this circuit as a qubit at an optimal point where it is insensitive to these current fluctuations to first order. Preliminary measurements show an increase in $\tau$ by a factor of 5.   

Quantum Behavior of the dc SQUID phase qubit.

We analyze the quantum behavior of a SQUID phase qubit in which one junction acts as a qubit while the other filters out any external low frequency bias current noise. We solve Schr\"{o}dinger's equation for the two dimensional Hamiltonian of the system at zero temperature assuming no dissipation. We obtain the states and from these the energy levels, tunneling rates, and expectation values of the currents in the junctions. We use these results to show how this design isolates the system from noise without affecting the essential nature of the qubit. This work is funded by the NSA, NSF Grant EIA 0323261, and the Center for Superconductivity Research.   

Strong Field Effects in Rabi Oscillations of the dc SQUID Phase Qubit

In the phase qubit, Rabi oscillations between the two lowest metastable zero-voltage states can be driven with a microwave current. At the high microwave powers needed to perform fast single-qubit operations, multilevel and multiphoton effects lead to an ac Stark shift of the resonant drive frequency and modification of the Rabi frequencies. We have observed these effects in an asymmetric Nb/AlOx/Nb dc SQUID at 25 mK, where one junction (with a roughly 20 $\mu$A critical current) behaves as a phase qubit and the other provides isolation from the bias line. We found quantitative agreement between experimental results and theoretical predictions obtained with a three-level multiphoton analysis.   

Evidence of Microstates in dc SQUID Phase Qubits

We report experimental results consistent with external quantum systems coupling to a Josephson junction phase qubit. When the energy level spacing for the qubit is made equal to that of the fixed external system the coupling lifts the degeneracy. By applying microwaves to excite transitions in the qubit, we are able to map out the splittings in the spectrum due to the coupling. This effect has been seen in both an Al/AlOx/Al and a Nb/AlOx/Nb dc SQUID phase qubit. This work is supported by the NSA, NSF Grant EIA 0323261, and the Center for Superconductivity Research.   

In situ variation of the coupling of a dc SQUID phase qubit to its bias leads

In dc SQUID phase qubit[1], one junction (Al/Al$_2$O$_3$/Al or Nb/Al$_2$O$_3$/Nb) acts as an ideal phase qubit and the rest of the SQUID which includes a second junction acts as an inductive isolation network. The Josephson inductance of the isolation junction was varied by changing its bias current, allowing in situ control of the coupling between the qubit junction and the leads. Measurements of the tunneling escape rate showed excess tunneling events due to high-frequency noise exciting the qubit junction out of the ground state $|0\rangle$. The impedance of the isolation junction becomes infinite at its resonance frequency where the isolation fails and the isolation network lets noise in to the qubit junction. Analysis of the data taken at 80 mK reveals that excess tunneling was largest when the $|0 \rangle$ to $|1\rangle$ resonance frequency (~10 to 15 GHz) of the isolation junction equaled the $|0\rangle$ to $|2\rangle$ or the $|1\rangle$ to $|3\rangle$ transition frequency of the qubit junction. [1] J. M. Martinis, et al. Phys. Rev. Lett. 89, 117901 (2002)   

Improving Superconducting Phase Qubits with Low-Loss Vacuum-Gap Capacitors

Significant progress has been made in eliminating sources of decoherence in superconducting qubits by carefully selecting, manipulating and engineering materials used in fabrication. Dielectrics in and around a qubit remain a major source of decoherence. By decreasing the size of a Josephson junction (JJ) one can reduce the number of decoherence-causing spurious two level systems. However, in order to maintain a typical phase qubit operation frequency, one has to shunt the JJ with a capacitor. We have fabricated structurally robust parallel plate capacitors in which lossy dielectrics are replaced by vacuum. Our LC oscillator measurements show that the loss tangent of the vacuum-gap capacitor is significantly lower than that of SiO2 and SiNx capacitors. Vacuum-gap capacitor fabrication has been integrated with phase qubit fabrication. We also show that our vacuum-gap technology can be used to fabricate on-chip wiring crossovers without dielectrics and vacuum suspended qubit junctions.   

Optimization of Silicon Nitride Films For Use in Phase Qubits

The lifetime (coherence time) of superconducting phase qubits is currently severely limited by lossy materials used in standard fabrication techniques. In particular, the insulator material - typically Silicon Nitride - used to isolate and physically separate different layers of the qubit is of interest. We have conducted a fractional factorial design experiment to optimize SiNx loss properties with respect to several deposition parameters in an Electron Cyclotron Resonance (ECR) Plasma-Enhanced Chemical Vapor Deposition (PECVD) reactor. Our experimental design included a three-level, four-parameter matrix with N2/SiH4 ratio, microwave power, rf power, and pressure as the parameters. The test-bed for these films is a low temperature microwave LC resonator circuit in which the various insulator films are used as the dielectric between a parallel plate capacitor and the Q (Quality Factor) of the circuit gives the relevant loss information for qubit operations.