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arXiv:1203.4431 · Applied Physics Letters

A Josephson junction defect spectrometer for measuring two-level systems

M. J. A. Stoutimore, M. S. Khalil, Christopher J. Lobb, Kevin D. Osborn

Published Aug 6, 2012• 27 citations
arXivHTMLPDF

Abstract

We have fabricated and measured Josephson junction (JJ) defect spectrometers, which are frequency-tunable, nearly harmonic oscillators that probe strongly coupled two-level systems (TLSs) in the barrier of a JJ. The JJDSs accommodate a wide range of junction inductances, LJ, while maintaining a resonance frequency, fres, in the range of 4–8 GHz. By applying a magnetic flux bias to tune fres, we detect strongly coupled TLSs in the junction barrier as splittings in the device spectrum. JJDSs fabricated with a via-style Al/thermal AlOx/Al junction and measured between 30–45 mK with single-photon excitation levels show a density of TLSs in the range σTLSh≈0.4-0.5/GHzμm2, and a junction loss tangent of tanδJ≈2.9×10−3.

DOI
10.1063/1.4744901

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We have fabricated and measured Josephson junction (JJ) defect spectrometers, which are frequency-tunable, nearly harmonic oscillators that probe strongly coupled two-level systems (TLSs) in the barrier of a JJ. The JJDSs accommodate a wide range of junction inductances, LJ, while maintaining a resonance frequency, fres, in the range of 4–8 GHz. By applying a magnetic flux bias to tune fres, we detect strongly coupled TLSs in the junction barrier as splittings in the device spectrum. JJDSs fabricated with a via-style Al/thermal AlOx/Al junction and measured between 30–45 mK with single-photon excitation levels show a density of TLSs in the range σTLSh≈0.4-0.5/GHzμm2, and a junction loss tangent of tanδJ≈2.9×10−3.
The high-Q harmonic oscillator mode of a Josephson junction can be used as a novel probe of spurious two-level systems (TLSs) inside the amorphous oxide tunnel barrier of the junction. In particular, we show that spectroscopic transmission measurements of the junction resonator mode can reveal how the coupling magnitude between the junction and the TLSs varies with an external magnetic field applied in the plane of the tunnel barrier. The proposed experiments offer the possibility of clearly resolving the underlying coupling mechanism for these spurious TLSs, an important decoherence source limiting the quality of superconducting quantum devices.
The dominant contribution to the energy relaxation of state-of-the-art superconducting qubits is often attributed to their coupling to an ensemble of material defects which behave as two-level systems. These defects have varying microscopic characteristics which result in a wide range of observable defect properties such as resonant frequencies, coherence times, and coupling rates to qubits ggg. Here, we investigate strategies to mitigate losses to the family of defects that strongly couple to qubits ($g/2\ensuremath{\pi}\ensuremath{\ge}0.5\mathrm{M}\mathrm{Hz}$). Such strongly coupled defects occur more rarely and are particularly detrimental to the qubit coherence when resonant with the qubit, and to the fidelities of operations relying on frequency excursions, such as flux-activated two-qubit gates. To assess their impact, we perform swap spectroscopy on 92 frequency-tunable qubits and quantify the spectral density of these strongly coupled modes. We show that the frequency configuration of the defects is rearranged by warming the sample to room temperature, whereas the total number of defects on a processor tends to remain constant. We then explore methods for fabricating qubits with a reduced number of strongly coupled defect modes by systematically measuring their spectral density for decreasing Josephson junction dimensions and for various surface cleaning methods. Our results provide insights into the properties of strongly coupled defect modes and show the benefits of minimizing Josephson junction dimensions to improve qubit properties.
We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc superconducting quantum interference device phase qubit with a $16\text{ }\ensuremath{\mu}{\text{m}}^{2}$ area Al/AlOx/Al\text{Al}/{\text{AlO}}_{x}/\text{Al}Al/AlOx​/Al junction. Applying microwaves in the 10--11 GHz range, we found eight avoided level crossings with splitting sizes from 10 to 200 MHz and spectroscopic lifetimes from 4 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 noninteracting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx{\text{AlO}}_{x}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.
The superconducting Josephson phase qubit device was fabricated by a NbN/AlN-based technology with the goal to carry out the spectroscopy of parasitic quantum two-level systems (TLSs) in the AlN tunnel barrier by combining qubit spectroscopy with mechanical strain tuning. So far all existing results on TLS spectroscopy have been obtained on Al-based Josephson qubits and thus only TLSs in amorphous aluminum oxide barriers were studied. Understanding the physics of TLS and TLS-induced decoherence requires a study of individual TLSs in tunnel barriers made from different materials. The layout of the NbN/AlN device was optimized to improve the magnetic flux coupling between the flux bias coil and the qubit loop and to minimize the unwanted coupling to the dc-readout SQUID. The area of the SiO insulation under wiring layer was made as small as possible in order to decrease the number of TLSs which can contribute to the suppression of the coherence time. The NbN/AlN Josephson phase qubit was tested in a 3He/4He dilution refrigerator at a temperature of about 60 mK by measuring Rabi oscillations and the energy relaxation time TD. Rabi oscillations had a mean decay time of about of 3-5 ns. We performed systematic studies of TD by varying the power and duration of a resonant microwave pulse. We observe a large enhancement of the qubit's relaxation time for longer microwave pulses. We explain this effect by microwave induced suppression of spontaneous qubit emission.
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.
We have fabricated and measured a high-Q Josephson junction resonator with a tunable resonance frequency. A dc magnetic flux allows the resonance frequency to be changed by over 10%. Weak coupling to the environment allows a quality factor of ~7000 when on average less than one photon is stored in the resonator. At large photon numbers, the nonlinearity of the Josephson junction creates two stable oscillation states. This resonator can be used as a tool for investigating the quality of Josephson junctions in qubits below the single photon limit, and can be used as a microwave qubit readout at high photon numbers.