[Show abstract][Hide abstract] ABSTRACT: We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 \mu\m2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitting sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.
[Show abstract][Hide abstract] ABSTRACT: We describe the design of an inductor-capacitor (LC) network to increase the isolation of a dc SQUID phase qubit from its current bias leads and thereby increase the relaxation time T<sub>1</sub> and coherence time T<sub>2</sub>. One junction in the SQUID acts as an ideal phase qubit while the second junction and the SQUID loop inductance act as a broadband inductive filter to isolate the first junction from the current bias leads. The LC isolation network provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. Our thin-film on-chip LC isolation network has a 10 nH inductor and an 80 pF capacitor. The combination of the broadband filter and LC filter provides a maximum nominal isolation factor of about 10<sup>8</sup> at a qubit plasma frequency of about 6.7 GHz. To reduce dielectric loss and two level systems in the qubit junction, we use a relatively small area (4 mum<sup>2</sup>) Al/AlO<sub>x</sub>/Al qubit junction built on sapphire and add an external capacitor with 100 nm thick SiN<sub>x</sub> dielectric layers. Measurements revealed Rabi oscillations with an envelope decay time constant of about 42 ns, and an energy relaxation time of 32 ns, consistent with a loss tangent tan(delta)=7times10<sup>-4</sup> in the SiN<sub>x</sub>.
[Show abstract][Hide abstract] ABSTRACT: We have investigated a dc SQUID phase qubit with LC filter, which has a relatively small (˜4 mum^2) Al/AlOx/Al Josephson junction shunted by an additional capacitor built using low-stress thin film SiNx. The LC isolation provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. We report Rabi oscillations with a 42 ns envelope decay time (T'), and a 32 ns energy relaxation time (T1), consistent with a loss tangent of about 7 x 10-4 in the loss-stress SiNx. We also report on progress towards getting longer coherence times using a high-stress SiNx with a lower loss tangent.
[Show abstract][Hide abstract] ABSTRACT: We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states. Comment: 14 pages, 9 figures; minor corrections, updated references
[Show abstract][Hide abstract] ABSTRACT: 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 T2* varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant T' = 25 ns on average at 80 mK. The three Nb devices also showed T2* in the range of 4 to 6 ns, but T' was 9 to 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. Comment: 5 figures. Accepted to Physical Review B
[Show abstract][Hide abstract] ABSTRACT: We performed measurements of a Nb/AlOx/Nb dc--SQUID phase qubit at 100 mK by monitoring the plasma frequency, fp, of the readout/isolation junction. This qubit contains two Josephson junctions (JJ) separated by a 1.3 nH inductance; one JJ operates as a pure phase qubit, the second JJ isolates and reads out the qubit junction. When driving the isolation junction at 1.5 GHz, near fp, current fluctuations in the SQUID loop cause fluctuations in fp which appear in the sidebands of the reflected microwave power. At 100 mK we find an effective flux noise, Sphi^0.5 of 50 muphi0/ Hz^0.5 at 1 Hz. The measurement bandwidth is about 10 MHz, the upper limit being set by the Q of the readout junction. We will discuss how the measurement performance depends on biasing parameters of each junction.
[Show abstract][Hide abstract] ABSTRACT: We examine microwave reflectometry readout of a dc SQUID phase qubit. Our device is a Nb/AlOx/Nb SQUID fabricated by Hypres with loop inductance of 1.3 nH and symmetric junction critical currents of approximately 5 muA. The SQUID is current and flux biased, with one junction used as the qubit and the other used to provide isolation. The isolation junction is shunted by a large capacitor to depress its plasma frequency to about 1.5 GHz. This frequency can be shifted by flux-induced circulating current in the SQUID loop, allowing us to determine which flux state we are in by making reflectometry measurements of the resonant behavior of the isolation junction. The utility of this measurement for qubit state readout is discussed.
[Show abstract][Hide abstract] ABSTRACT: We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a 6-turn Nb loop, the second had a single-turn Al loop, and the third was a first order gradiometer formed from 6-turn wound and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6-7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogeneous broadening in these devices.
[Show abstract][Hide abstract] ABSTRACT: We have used 2 ns pulses of current to read out the states of a Nb/AlO<sub>x</sub>/Nb dc SQUID phase qubit at 25 mK. Plotting the number of escape events that occur versus the size of the current pulse reveals a series of steps corresponding to the occupancy of different energy levels. After calibrating the measurement pulses, we fit these steps to determine the population in each level. Rabi oscillations were viewed using this technique. The single-shot measurement fidelity was theoretically analysed and the optimal single pulse in our device was determined.
[Show abstract][Hide abstract] ABSTRACT: We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a single-turn Al loop, the second had a 6-turn Nb loop, and the third was a first order gradiometer formed from 6-turn wound and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogenous broadening in these devices.
[Show abstract][Hide abstract] ABSTRACT: We present measurements of the spectroscopic coherence time, T<sub>2</sub>* of a Nb-AlOx-Nb dc SQUID phase qubit. T<sub>2</sub>* is calculated from the spectroscopic width of the |0rang to |1rang transition measured at 25 mK. We find that T<sub>2</sub>*increases at higher transition frequencies corresponding to measurements deeper in the potential well. The measured are consistent with root mean square current noise saturating at 4 nA.
[Show abstract][Hide abstract] ABSTRACT: Rabi oscillations have been observed in many superconducting devices, and
represent prototypical logic operations for quantum bits (qubits) in a quantum
computer. We use a three-level multiphoton analysis to understand the behavior
of the superconducting phase qubit (current-biased Josephson junction) at high
microwave drive power. Analytical and numerical results for the ac Stark shift,
single-photon Rabi frequency, and two-photon Rabi frequency are compared to
measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions.
Good agreement is found between theory and experiment.
[Show abstract][Hide abstract] ABSTRACT: We report on rf-reflectometry measurements on a Nb/AlOx/Nb Josephson junction tank circuit. The junction has nominal critical current of 5 muA and is loaded with an on chip capacitance of 50 pF to suppress the plasma frequency to fp 2 GHz. Measurements were performed at temperature T 100 mK in a dilution refrigerator. Reflection data show a clear rf absorption resonance and concomitant phase change about the resonant frequency. We will discuss use of this circuit for state readout of a phase qubit and as a device for measuring critical current noise in Josephson junctions. I. Siddiqi et al., Phys. Rev. Lett.,207002 (2004).
[Show abstract][Hide abstract] ABSTRACT: In dc SQUID phase qubit, one junction (Al/Al2O3/Al or Nb/Al2O3/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>. 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 > to |1> resonance frequency ( 10 to 15 GHz) of the isolation junction equaled the |0> to |2> or the |1> to |3> transition frequency of the qubit junction.  J. M. Martinis, et al. Phys. Rev. Lett. 89, 117901 (2002)
[Show abstract][Hide abstract] ABSTRACT: 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 muA 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.
[Show abstract][Hide abstract] ABSTRACT: We have investigated the fidelity and speed of single-shot current-pulse measurements of the three lowest energy states of the dc SQUID phase qubit. We apply a short (2ns) current pulse to one junction of a Nb/AlOx/Nb SQUID that is in the zero voltage state at 25 mK and measure if the system switches to the finite voltage state. By plotting the switching rate versus pulse size we can determine average occupancy of the levels down to 0.01%, quantify small levels of leakage, and find the optimum pulse condition for single-shot measurements. Our best error rate is 3% with a measurement fidelity of 94%. By monitoring the escape rate during the pulse, the pulse current in the junction can be found to better than 10 nA on a 0.1 ns time scale. Theoretical analysis of the system reveals switching curves that are in good agreement with the data, as well as predictions that the ultimate single-shot error rate for this technique can reach 0.4% and the fidelity 99.2%.
[Show abstract][Hide abstract] ABSTRACT: We describe a technique for initializing the flux state of an
inductively isolated Josephson junction, fulfilling an essential
requirement for using the device as a qubit. By oscillating the applied
magnetic flux with a specified amplitude and offset, we can select any
of the allowed long-lived metastable flux states. We applied this
technique to Nb-Al2O3-Nb and
Al-Al2O3-Al devices with from 10 to over 100
distinct flux states at temperatures as low as 25mK . In a ten-state
system with an initial probability p=0.13 to be in the desired flux
state, we achieved p=0.99996 after 50 oscillations at 22.6kHz . The
technique is generally applicable to other systems with multiple
metastable wells (including rf SQUIDs), requires no additional readout
or bias lines, involves minimal energy dissipation, and appears to scale
favorably with the number of qubits.
Physical Review B 01/2006; 73(1):14520-. DOI:10.1103/PhysRevB.73.014520 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present measurements of an inductively-isolated current-biased Nb/AlOx/Nb Josephson junction quantum bit at 20 mK. Density matrix fits of Rabi oscillations in our system suggest that the tunneling rate (gamma1) from the first excited state is an order of magnitude lower than expected from a single current-biased junction. Furthermore, measurements of the energy relaxation time, T1, through both pulse/decay and thermal population techniques only agree if gamma1 is approximately an order of magnitude lower than our single junction model predicts. To test for low gamma1, we use a fast-ramp technique (alpha= d(ln gamma)/dt > 1/T1) to directly measure gamma1. We propose that an increase in the Josephson inductance of the qubit junction when in the excited state causes this effective reduction in gamma1. S. K. Dutta et al. , Phys. Rev. B 70 140502(R) (2004).
[Show abstract][Hide abstract] ABSTRACT: Martinis et al.  first proposed a technique for inductively isolating a Josephson junction qubit from the bias leads. It involves using one junction of a dc SQUID as a qubit, and the SQUID inductance and second junction of the SQUID as an inductance divider. This arrangement allows for isolation from current bias lines but potentially introduces greater sensitivity to flux noise. By introducing counterwound inductors on the qubit arm of the SQUID, we can reduce spatially uniform flux noise. We compare experimental coherence times for a Nb/Al2O3/Nb qubit in such gradiometer designs to similar devices lacking the counterwound inductors. No significant difference is seen, suggesting that uniform flux noise is not the major source of decoherence in our system.  J. M. Martinis et al., PRL 89, 117901
[Show abstract][Hide abstract] ABSTRACT: We have experimentally studied asymmetric Nb/AlOx/Nb dc SQUID qubits at 25 mK. The two lowest metastable levels localized within a single well of the complex two-dimensional potential of the device can serve as qubit states, if they are not unduly perturbed by resonant coupling to higher states of the full potential. Rabi oscillations between the qubit states can be driven with a microwave bias current. State readout is performed by measuring the tunneling rate from all energy levels with non-zero occupation probability to the finite voltage state. To interpret the results of our Rabi oscillation measurements, we have used a multi-level density matrix simulation to extract the populations of the individual quantum states from this total rate. We can then calculate the visibility of the oscillations and determine the effects of the higher levels and multi-photon transitions.