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Feasibility study of HTS flux qubit read-out using aluminium dc-SQUID

Johansson, Jesper

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

This thesis for the degree of Master of Science studies and tests the feasibility of HTS flux qubit read-out using an aluminium dc-SQUID. The feasibility is studied on a device consisting of an YBCO dc-SQUID surrounded by an aluminium dc-SQUID separated by an intermediate layer. The intermediate layer acts as insulator between the YBCO and the aluminium and as capping layer for the underlying YBCO. Each part of the device has been studied within this project.\n\nAluminium dc-SQUIDs for flux qubit read-out have been fabricated using electron beam lithography and shadow evaporation. A typical SQUID had a critical current of 56 nA and was highly under-damped. The SQUIDs were characterized below 300 mK. An intermediate layer consisting of amorphous STO, deposited at room temperature, and thermally evaporated silicon dioxide has been studied. The roughness, peak-to-valley, was found to be approximately 10 nm and the resistance was 9 k$\\Omega$ for an 360 nm thick layer of silicon dioxide and 12 k$\\Omega$ for a 500 nm thick layer at 4.2 K. YBCO SQUIDs were fabricated on STO 0$^o$/30$^o$ bi-crystals using electron beam lithography and ion milling through a mask of amorphous carbon. The properties of the grain boundary junctions in the SQUIDs were unchanged when a multi-layer of amorphous STO and silicon dioxide was deposited on top of them. A SQUID that consists of 3 $\\mu$m wide junctions typically had a critical current of 1.5 mA. It was found that the insulating properties, the adhesion and the smoothness of the intermediate layer has to be improved in order to get the proposed device working.

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This thesis for the degree of Master of Science studies and tests the feasibility of HTS flux qubit read-out using an aluminium dc-SQUID. The feasibility is studied on a device consisting of an YBCO dc-SQUID surrounded by an aluminium dc-SQUID separated by an intermediate layer. The intermediate layer acts as insulator between the YBCO and the aluminium and as capping layer for the underlying YBCO. Each part of the device has been studied within this project.\n\nAluminium dc-SQUIDs for flux qubit read-out have been fabricated using electron beam lithography and shadow evaporation. A typical SQUID had a critical current of 56 nA and was highly under-damped. The SQUIDs were characterized below 300 mK. An intermediate layer consisting of amorphous STO, deposited at room temperature, and thermally evaporated silicon dioxide has been studied. The roughness, peak-to-valley, was found to be approximately 10 nm and the resistance was 9 kOmega\\OmegaOmega for an 360 nm thick layer of silicon dioxide and 12 kOmega\\OmegaOmega for a 500 nm thick layer at 4.2 K. YBCO SQUIDs were fabricated on STO 0o^oo/30o^oo bi-crystals using electron beam lithography and ion milling through a mask of amorphous carbon. The properties of the grain boundary junctions in the SQUIDs were unchanged when a multi-layer of amorphous STO and silicon dioxide was deposited on top of them. A SQUID that consists of 3 mu\\mumum wide junctions typically had a critical current of 1.5 mA. It was found that the insulating properties, the adhesion and the smoothness of the intermediate layer has to be improved in order to get the proposed device working.
Most proposed realizations of a high temperature superconductor (HTS) qubit require the use of very small Josephson junctions. The properties of bicrystal junctions are especially interesting since they make it possible to implement several types of flux qubits in a relatively simple way. We have developed a technique that allows us to produce high quality sub-micrometer junctions in a reproducible way using bicrystal technology. We have successfully fabricated and characterized a large number of YBCO junctions and SQUIDs with bridge width as small as 0.2 micrometer on 0/spl deg/-3/spl deg/, 0/spl deg/-40/spl deg/ and 0/spl deg/-45/spl deg/ bicrystal STO substrates. The properties of these junctions have been extensively examined at temperatures down to 20 mK. The effects of external magnetic fields on these structures have been investigated. Figures of merit for the proposed qubits were also extracted from these measurements.
The characteristics of a simple logic gate which consists of an rf-Superconducting QUantum Interference Device (SQUID) and dc-SQUID has been investigated in connection with the Single-Flux-Quantum (SFQ) logic operation and Josephson junction characteristics. The Josephson junctions were made of Neodymium Barium Copper Oxide thin film employing Focused Ion Beam technology. We confirmed the generating SFQ in the rf-SQUID and simultaneous read-out by the dc-SQUID up to 50 K. It has been found that the temperature dependence of output voltage level decreased more rapid than that of critical current normal resistance product. The origin of the discrepancy was studied using a phenomenological model of the Josephson junction and numerical simulation.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
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.
In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.
Autonomous single-layer dc superconducting quantum interference devices (SQUIDs) have been prepared from epitaxial, laser-deposited YBa2Cu3Ox films on step edge SrTiO3 and LaAlO3 substrates. For device patterning, a SiOx inhibit technique as well as conventional ethylenediaminetetraacetic wet etch was used. The Josephson junctions are of grain boundary type. Their widths are 5 μm. The SQUID hole is a square of about 5 μm; the SQUID inductance is estimated to be about 20 pH. We obtained a very regular, nonhysteretic flux to voltage modulation over more than 100 flux quanta (Φ0). The maximum voltage signal is of the order of 15 μV peak to peak and the maximum transfer function dV/dΦ at the appropriate flux bias is 50 μV/Φ0 at 77 K. The best value of the equivalent flux noise as measured in the flux locked loop mode is 1.4×10−5 Φ0/Hz1/2 at 1 Hz and 1×10−5 Φ0/Hz1/2 in the white noise region for f≳5 Hz. This results in an energy resolution εn,w(f≳5 Hz)=1×10−29 J/Hz in the white noise region and 2×10−29 J/Hz at 1 Hz.