We study the metastable response of a highly hysteretic DC-SQUID made of a Niobium loop interrupted by two nano-bridges. We excite the SQUID with an alternating current and with direct magnetic flux, and find different stability zones forming diamond-like structures in the measured voltage across the SQUID. When such a SQUID is embedded in a transmission line resonator similar diamond structures are observed in the reflection pattern of the resonator. We have calculated the DC-SQUID stability diagram in the plane of the exciting control parameters, both analytically and numerically. In addition, we have obtained numerical simulations of the SQUID equations of motion, taking into account temperature variations and non-sinusoidal current-phase relation of the nano-bridges. Good agreement is found between experimental and theoretical results.
This paper presents the analytical and numerical analysis of fluctuational dynamics of ac hysteretic SQUID. It has been demonstrated, that the most important parameter for the improvement of the hysteretic SQUID sensitivity is the ratio between the pump and the characteristic frequencies but not their absolute values. The resonant behavior of signal-to-noise ratio as function of the pump frequency has been observed and the narrow area for the optimal pump frequency range is indicated.
We have measured and propose a model for switching rates in hysteretic DC-SQUID in the regime where phase diffusion processes start to occur. We show that the switching rates in this regime are smaller than the rates given by Kramers' formula due to retrapping of Josephson phase. The retrapping process, which is affected by the frequency dependent impedance of the environment of the DC-SQUID, leads to a peaked second moment of the switching distribution as a function of temperature. The temperature where the peaks occur are proportional to the critical current of the DC- SQUID.
In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic SQUID ring, coupled to an rf tank circuit resonator, display relaxation oscillations. We demonstrate that the the overall form of these characteristics, together with the relaxation oscillations, can be modelled accurately by solving the quasi-classical non-linear equations of motion for the system. We suggest that in these very strongly hysteretic regimes SQUID ring-resonator systems may find application in novel logic and memory devices.
Micron-sized superconducting interference devices ($μ$-SQUIDs) based on constrictions optimized for minimizing thermal runaway are shown to exhibit voltage oscillations with applied magnetic flux despite their hysteretic behavior. We explain this remarkable feature by a significant supercurrent contribution surviving deep into the resistive state, due to efficient heat evacuation. A resistively shunted junction model, complemented by a thermal balance determining the amplitude of the critical current, describes well all experimental observations, including the flux modulation of the (dynamic) …
In this paper we study numerical solutions to the quasi-classical equations of motion for a SQUID ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g. 10…
We discuss heat transport in a thermally-biased SQUID in the presence of an external magnetic flux, when a non-negligible inductance of the SQUID ring is taken into account. A properly sweeping driving flux causes the thermal current to modulate and behave hysteretically. The response of this device is analysed as a function of both the hysteresis parameter and degree of asymmetry of the SQUID, highlighting the parameter range over which hysteretic behavior is observable. Markedly, also the temperature of the SQUID shows hysteretic evolution, with sharp transitions characterized by temperature…
Highly reproducible Nb/Al(AlOx)/Nb Josephson junction based direct current superconducting quantum interference devices (DC SQUID) were fabricated by three dimensional etching using focused ion beam. Hysteretic and non-hysteretic DC SQUID with critical current ranging from 25 to 1100 microampere were fabricated by varying the Al barrier and oxygen exposure time. The fabricated DC SQUIDs have shown periodic flux dependence with high modulation factor reaching a value of 92% at 4.2 K.
We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box (CPB) and the measuring device is a two junction superconducting quantum interference device (dc-SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final read-out. We test the feasibility of our idea against realistic experimental circuit parameters an…
We studied thermal and dynamic history effects in the vortex lattice (VL) near the order-disorder transition in clean NbSe$_2$ single crystals. Comparing the evolution of the effective vortex pinning and the bulk VL structure, we observed metastable superheated and supercooled VL configurations that coexist with a hysteretic effective pinning response due to thermal cycling of the system. A novel scenario, governed by the interplay between (lower) elastic and (higher) plastic energy barriers, is proposed as an explanation for our observations: Plastic barriers, which prevent the annihilation o…
We study voltage response of nano-bridge based DC-SQUID fabricated on a Si\_{3}N\_{4} membrane. Such a configuration may help in reducing 1/f noise, which originates from substrate fluctuating defects. We find that the poor thermal coupling between the DC-SQUID and the substrate leads to strong hysteretic response of the SQUID, even though it is biased by an alternating current. In addition, when the DC-SQUID is biased near a threshold of spontaneous oscillations, the measured voltage has an intermittent pattern, which depends on the applied magnetic flux through the SQUID.
Thermal hysteresis in a micron-size Superconducting Quantum Interference Device ($μ$-SQUID), with weak links as Josephson junctions, is an obstacle for improving its performance for magnetometery. Following the "hot-spot" model of Skocpol et al. [J. Appl. Phys. {\bf 45}, 4054 (1974)] and by incorporating the temperature dependence of thermal conductivity of superconductor using a linear approximation, we find a much better agreement with the observed temperature dependence of the retrapping current in short superconducting Nb-based weak links and $μ$-SQUIDs. In addition, using the temperature …
We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. From the mode distance observed in spectroscopy experiments, we derive a coupling strength ranging between -320MHz and 37 MHz. In the case where the coupling strength is about zero, the microwave power cross transmission between the two resonators can be reduced by almost four orders of magnitude compared to the case where the coupling is switched on. In addition, we observe parametric ampl…
In this paper we present experimental data on the frequency domain response of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency (rf) tank circuit resonator. We show that with the ring weakly hysteretic the resonance lineshape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off lineshapes exist as solutions of the non-linear equations of motion for the system.
We present a hybrid microwave SQUID multiplexer that combines two frequency-division multiplexing techniques to allow multiplexing a given number of cryogenic detectors with only a fraction of frequency encoding resonators. Similar to conventional microwave SQUID multiplexing, our multiplexer relies on inductively coupling non-hysteretic, unshunted rf-SQUIDs to superconducting microwave resonators as well as applying flux ramp modulation for output signal linearization. However, instead of utilizing one resonator per SQUID, we couple multiple SQUIDs to a common readout resonator and encode the…
The escape probability out of the superconducting state of a hysteretic DC-SQUID has been measured at different values of the applied magnetic flux. At low temperature, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional (1D) Macroscopic Quantum Tunneling (MQT) law but are perfectly accounted for by the two-dimensional (2D) MQT behaviour as we propose here. Near zero flux, our data confirms the recent MQT observation in a DC-SQUID \cite{Li02}.
An overview of several dynamic properties of SQUID metamaterials is given in the presence of both constant and alternating magnetic field. The total current as a function of the driving frequency exhibits hysteretic effects which are favored by low levels of disorder. Multistability in the current states leads to multiple magnetic responses with different value of magnetic permeability. SQUID metamaterials exhibit wide-band tuneability which is periodic with the applied constant magnetic field; the numerical calculations reproduce fairly well recent experimental results. Current work also reve…
We report on the development of an analytical model describing the readout power and SQUID hysteresis parameter dependence of the resonator characteristics used for frequency encoding in microwave SQUID multiplexers. Within the context of this model, we derived the different dependencies by analyzing the Fourier components of the non-linear response of the non-hysteretic rf-SQUID. We show that our model contains the existing model as a limiting case, leading to identical analytical expressions for small readout powers. Considering the approximations we made, our model is valid for rf-SQUID hys…
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), whi…
We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an $N$-qubit adiabatic quantum optimization system comprises $N$ hysteretic dc SQUIDs and $N$ rf SQUID latches controlled by $2\sqrt{N} + 2$ bias…
We fabricated an asymmetric nanoscale SQUID consisting of one nanobridge weak link and one Dayem bridge weak link. The current phase relation of these particular weak links is characterized by multivaluedness and linearity. While the latter is responsible for a particular magnetic field dependence of the critical current (so-called vorticity diamonds), the former enables the possibility of different vorticity states (phase winding numbers) existing at one magnetic field value. In experiments the observed critical current value is stochastic in nature, does not necessarily coincide with the cur…
We show a novel method for controlling the coupling of flux-based qubits by means of a superconducting transformer with variable flux transfer function. The device is realized by inserting a small hysteretic dc SQUID with unshunted junctions, working as a Josephson junction with flux controlled critical current, in parallel to a superconducting transformer; by varying the magnetic flux coupled to the dc-SQUID, the transfer function for the flux coupled to the transformer can be varied. Measurements carried out on a prototype at 4.2 K show a reduction factor of about 30 between the 'on' and the…
Modern Superconducting QUantum Interference Devices (SQUIDs) are commonly fabricated from either Al or Nb electrodes, with an in-situ oxidation process to create a weak link between them. However, common problems of such planar nano- and micro-SQUIDs are hysteretic current-voltage curves, and a shallow flux modulation depth. Here, we demonstrate the formation of both Josephson junctions and SQUIDs using a dry transfer technique to stack and deterministically misalign flakes of NbSe$_{2}$; allowing one to overcome these issues. The Josephson dynamics of the resulting twisted NbSe$_{2}$-NbSe$_{2…
By scanning with a $30\, \mathrm{keV}$ focused He ion beam (He-FIB) across YBa$_2$Cu$_3$O$_7$ (YBCO) thin film microbridges, we create Josephson barriers with critical current density $j_\mathrm{c}$ adjustable by irradiation dose $D$. The dependence $j_\mathrm{c} (D)$ yields an exponential decay. At $4.2\, \mathrm{K}$, a transition from flux-flow to Josephson behavior occurs when $j_\mathrm{c}$ decreases below $\approx 2\, \mathrm{MA/cm^2}$. The Josephson junctions exhibit current-voltage characteristics (IVCs) that are well described by the resistively and capacitively shunted junction model,…
We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence,…
We present measurements obtained on a bulk cylinder of lead with a SQUID picovoltmeter. A distinctive hysteretic step structure is observed. It is washed out on increasing the current and reinforced in higher field. Classical models for the dissipation mechanisms in the intermediate state are briefly reviewed and used to give a first interpretation of these results, although a complete understanding is not reached yet.
We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped element resonator. The coupling strength is mediated by a flux-biased RF SQUID operated in the non-hysteretic regime. By tuning the applied flux bias to the RF SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator . We verify the modulation of coupling strength from 0 to $100 MHz$ by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillatio…
