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Nature Communications

Quantum interference of currents in an atomtronic SQUID

Changhyun Ryu, E. Carlo Samson, M. G. Boshier

Published Jul 3, 2020• 80 citations
Publisher

Abstract

Quantum interference of currents is the most important and well known quantum phenomenon in a conventional superconducting quantum interference device (SQUID). Here, we report the observation of quantum interference of currents in an atomtronic SQUID. Analogous to a conventional SQUID, currents flowing through two junctions in an atomtronic SQUID interfere due to the phase difference from rotation. This interference results in modulation of critical currents. This modulation was observed for three different radii with clear modulation periods which were measured to be consistent with fundamental rotation rates. This observation shows the possibility of studying various interesting SQUID physics with an atomtronic SQUID and especially, macroscopic quantum phenomena with currents may be realized with an atomtronic SQUID toward the goal of quantum metrology of rotation sensing.

DOI
10.1038/s41467-020-17185-6

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Quantum interference of currents is the most important and well known quantum phenomenon in a conventional superconducting quantum interference device (SQUID). Here, we report the observation of quantum interference of currents in an atomtronic SQUID. Analogous to a conventional SQUID, currents flowing through two junctions in an atomtronic SQUID interfere due to the phase difference from rotation. This interference results in modulation of critical currents. This modulation was observed for three different radii with clear modulation periods which were measured to be consistent with fundamental rotation rates. This observation shows the possibility of studying various interesting SQUID physics with an atomtronic SQUID and especially, macroscopic quantum phenomena with currents may be realized with an atomtronic SQUID toward the goal of quantum metrology of rotation sensing.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.
We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.
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.
Abstract We directly observed π-leaps of superconducting phase differences in π-junction-based superconducting quantum interference devices (SQUIDs). The SQUIDs studied here are formed by introducing a π-junction to a conventional-junction (0-junction)-based direct current (DC)-SQUID, which is referred to as the 0-0-π SQUID. Either clockwise or counter-clockwise-circulating currents flow spontaneously in the 0-0-π SQUID because of a π-phase shift of the π-junction. In other words, the 0-0-π SQUID has a bistable state corresponding to the directions of circulating currents. π-leaps are generated by transiting between the two states of the bistable state. π-leaps are an ultra-fast phenomenon and are difficult to observe as they are. We prepared a half-flux quantum (HFQ)-SQUID that comprised two 0-0-π SQUIDs. π-leaps are reflected in a static characteristic, that is, a modulation pattern of the critical current in the HFQ-SQUID. We formed π-junctions with the PdNi layer on 0-junction-based circuits supplied by the National Institute of Advanced Industrial Science and Technology. The modulation pattern of the HFQ-SQUID had a period corresponding to π-leaps as expected, although some microstructures were observed. We demonstrated that the microstructures originated from the asymmetry inside each 0-0-π SQUID by analyzing the relationship between the phase change of 0-0-π SQUIDs and the modulation patterns.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
We investigate the dynamics of an atomtronic superconducting quantum interference device (SQUID) created by two mobile barriers, moving at two different, constant velocities in a quasi-one-dimensional toroidal condensate. We implement a multiband truncated Wigner approximation numerically to demonstrate the functionality of a SQUID reflected in the oscillatory voltage-flux dependence. The relative velocity of the two barriers results in a chemical potential imbalance analogous to a voltage in an electronic system. The average velocity of the two barriers corresponds to a rotation of the condensate, analogous to a magnetic flux. We demonstrate that the voltage equivalent shows characteristic flux-dependent oscillations. We point out the parameter regime of barrier heights and relaxation times for the phase slip dynamics, resulting in a realistic protocol for atomtronic SQUID operation.