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arXiv:0804.4430 · Physical Review B

Decoherence in dc SQUID phase qubits

Hanhee Paik, S. K. Dutta, Rupert Lewis, Tauno Palomaki, Benjamin K. Cooper, Roberto Ramos, Haitan Xu, Alex J. Dragt, J. R. Anderson, Christopher J. Lobb, F. C. Wellstood

Published Jun 13, 2008• 18 citations
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Abstract

We report measurements of Rabi oscillations and spectroscopic coherence times in an $\text{Al}/{\text{AlO}}_{x}/\text{Al}$ and three $\text{Nb}/{\text{AlO}}_{x}/\text{Nb}$ 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.

DOI
10.1103/physrevb.77.214510

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IEEE Transactions on Applied Superconductivity•Jun 1, 2009•3 citations
We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al\text{Al}/{\text{AlO}}_{x}/\text{Al}Al/AlOx​/Al and three Nb/AlOx/Nb\text{Nb}/{\text{AlO}}_{x}/\text{Nb}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\ensuremath∗{T}_{2}^{\ensuremath{\ast}}T2\ensuremath∗​ varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant T\ensuremath′=25ns{T}^{\ensuremath{'}}=25\phantom{\rule{0.3em}{0ex}}\text{ns}T\ensuremath′=25ns on average at 80 mK. The three Nb devices also showed T2\ensuremath∗{T}_{2}^{\ensuremath{\ast}}T2\ensuremath∗​ in the range of 3--8 ns, but T\ensuremath′{T}^{\ensuremath{'}}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.
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.
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 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.
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.
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.
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 T1and coherence time T2. 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 108at 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 mum2) Al/AlOx/Al qubit junction built on sapphire and add an external capacitor with 100 nm thick SiNxdielectric 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)=7times10-4in the SiNx.