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arXiv:1003.3941 · Physical Review B

Multilevel spectroscopy of two-level systems coupled to a dc SQUID phase qubit

Tauno Palomaki, S. K. Dutta, Rupert Lewis, A. J. Przybysz, Hanhee Paik, Benjamin K. Cooper, Hyeokshin Kwon, J. R. Anderson, Christopher J. Lobb, F. C. Wellstood, Eite Tiesinga

Published Apr 7, 2010• 32 citations
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Abstract

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 $\text{Al}/{\text{AlO}}_{x}/\text{Al}$ 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 ${\text{AlO}}_{x}$ 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.

DOI
10.1103/physrevb.81.144503

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IEEE International Superconductive Electronics Conference (ISEC)•Jun 1, 2017•2 citations
We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc superconducting quantum interference device phase qubit with a 16 \ensuremathμm216\text{ }\ensuremath{\mu}{\text{m}}^{2}16 \ensuremathμm2 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.
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.
We have observed a few distinct anomalous avoided level crossings and voltage-dependent transitions in the excited-state spectrum of an Al/AlOx/Al\text{Al}/{\text{AlO}}_{x}/\text{Al}Al/AlOx​/Al Cooper-pair box (CPB). The device was measured at 40 mK in the 15--50 GHz frequency range. We find that a given level crosses the CPB spectrum at two different gate voltages; the frequency and splitting size of the two crossings differ and the splitting size depends on the Josephson energy of the CPB. We show that this behavior is not only consistent with the CPB being coupled to discrete charged ``two-level'' quantum systems, which move atomic distances in the CPB junctions, but that the spectra provide information about the fluctuators, which is not available from phase qubit spectra of anomalous avoided levels. In particular by fitting a model Hamiltonian to our data, we extract microscopic parameters for each fluctuator, including well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator. The tunneling rates range from less than 3.5--13 GHz, which represent values between 5 and 150% of the well asymmetry, and the dipole moments give a minimum hopping distance of 0.3−−0.8 A˚0.3--0.8\text{ }\text{\AA{}}0.3−−0.8 A˚. We have also found that these discrete two-level systems have a pronounced effect on the relaxation time (T1)({T}_{1})(T1​) of the quantum states of the CPB and hence can be a source of dissipation for superconducting quantum bits.
We report on the quadrupling of the transition spectrum of an Al/AlOx{}_{x}x​/Al Cooper-pair box (CPB) charge qubit in the 4.0−−7.34.0--7.34.0−−7.3 GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change (3030%--40%30) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.
The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an Al/AlOx\mathrm{Al}/{\mathrm{AlO}}_{x}Al/AlOx​/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating AlOx{\mathrm{AlO}}_{x}AlOx​ barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc superconducting quantum interference device driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge.
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 ${T}_{2}^{\ensuremath{\ast}}$ 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.
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.