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Physics Procedia

Quantum Interference in DC-SQUIDs Comprising Two Sub-Micron Aluminum Josephson Junctions: Deviation from Classical Model

Kōji Miura, Kento Kikuchi, Hiroshi Shimada, Yoshinao Mizugaki

Published Jan 1, 2015• 0 citations
Publisher

Abstract

In a small Josephson junction, the critical current is often found experimentally to be smaller than the value expected fromthe Ambegaokar-Baratoff theory because of the quantum phase fluctuations. We also observed in our previous study that the quantum interference in a dc-SQUID comprising sub-micron Al junctions deviated from the classical model. In this work, we have fabricated 13devices having different values of maximal critical currents, and evaluated their quantum interference patterns.The quantum interference of 12among 13 devices has deviated from the classical model. It is confirmed that their maximal critical currents(Icsq,max) are reduced from the values (Icsq0) predicted by the Ambegaokar-Baratofftheory. Besides, the quantum interference for Icsq,max / Icsq0< 0.4 agrees with themodified quantum-interference model.

DOI
10.1016/j.phpro.2015.05.104

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In a small Josephson junction, the critical current is often found experimentally to be smaller than the value expected fromthe Ambegaokar-Baratoff theory because of the quantum phase fluctuations. We also observed in our previous study that the quantum interference in a dc-SQUID comprising sub-micron Al junctions deviated from the classical model. In this work, we have fabricated 13devices having different values of maximal critical currents, and evaluated their quantum interference patterns.The quantum interference of 12among 13 devices has deviated from the classical model. It is confirmed that their maximal critical currents(Icsq,max) are reduced from the values (Icsq0) predicted by the Ambegaokar-Baratofftheory. Besides, the quantum interference for Icsq,max / Icsq0< 0.4 agrees with themodified quantum-interference model.
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 investigate critical current (Ic) modulation of stacked Josephson junctions (SJJs) dc superconducting quantum interference device ( dc SQUID) on a Bi 2 Sr 2 CaCu 2 O 8+δ ( Bi -2212) whisker. A coupled SJJs with a completely perforated hole of 0.1 μ m × 0.2 μ m were fabricated by using a 3-D focused-ion-beam (FIB) etching method. Those dc SQUIDs exhibited uniform multi-branch structures and clearly oscillated critical current under external magnetic fields (He). With applying He, the clear periodic modulation patterns of Ic are obtained and well fitted to the calculated value from the loop area of 0.02 μm2.
The experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.
The optimal design of a direct current superconducting quantum interference device (DC-SQUID) with high sensitivity requires two identical Josephson junctions, which is difficult to achieve. The design of a DC-SQUID using controlled Josephson junction technology provides a mechanism for modifying the characteristics of the device. Here we report on the nano-fabrication and measurement of a DC-SQUID utilizing two Dayem bridge weak-link Josephson junctions fabricated with a width ∼100 nm and a length of ∼200 nm. These junctions are controlled via the irradiation of hot phonons from nearby titanium/chromium normal metal constrictions which are current biased. The devices were measured at a temperature of 4.2 K and control over the critical current oscillations was observed.
We have measured the switching current versus applied magnetic flux of a highly asymmetric, hysteretic dc superconducting quantum interference device (SQUID) from 30 mK to 400 mK. The SQUID loop had an inductance of 1 nH, and the capacitances of the two Al-Al2O3-Al Josephson junctions comprising the SQUID were 100 fF and 5 fF. As expected, the switching current of the SQUID displayed a small, periodic modulation with applied flux, from which the switching currents of the large and small junctions at 30 mK were determined to be 846.3 ± 0.1 nA and 0.7 ± 0.08 nA, respectively. Measurements of an identically prepared small junction exhibited a highly suppressed switching current (IS < 10 pA), consistent with phase diffusion in this device. The observed modulation in the SQUID thus demonstrates that the quantum mechanical uncertainty in the phase difference across the small junction was significantly reduced by coupling to the large junction through the loop inductance. We discuss the sensitivity of this technique for determining the gauge-invariant phase difference of small Josephson junctions, and the implications for imaging the phase of superconductors at the atomic scale using scanning tunneling microscopy.