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IEEE Transactions on Applied Superconductivity

An On-Chip Mach-Zehnder Interferometer in the Microwave Regime

Steven Schuermans, Michaël Simoen, Martin Sandberg, Philip Krantz, Christopher M. Wilson, Per Delsing

Published Nov 18, 2010• 5 citations
Publisher

Abstract

The design, simulation and measurements of an on-chip Mach-Zehnder interferometer operating in the microwave regime are described. Using microwave signals in microfabricated superconducting Al waveguides, the concept of an interferometer is transferred from optics to on-chip. Tuning of the path length of one of the interferometer arms is executed through the tunable inductance of a SQUID. By placing one or more SQUIDs in the waveguide structure and by varying the magnetic flux through the SQUID loop, the total SQUID inductance can be tuned. In this way, a phase difference leading to destructive or constructive interference at the interferometer output can be achieved. Thorough software simulations were performed to determine the different design parameters, assign a desired working frequency and provide a reference for comparison with experimental results. Measurements at 300 mK show an effective working frequency close to the simulations, with a deviation smaller than 0.05 GHz. The behavior of the interferometer is very similar to the simulations as well. The on-off ratio exceeds 40 dB.

DOI
10.1109/tasc.2010.2088354

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The design, simulation and measurements of an on-chip Mach-Zehnder interferometer operating in the microwave regime are described. Using microwave signals in microfabricated superconducting Al waveguides, the concept of an interferometer is transferred from optics to on-chip. Tuning of the path length of one of the interferometer arms is executed through the tunable inductance of a SQUID. By placing one or more SQUIDs in the waveguide structure and by varying the magnetic flux through the SQUID loop, the total SQUID inductance can be tuned. In this way, a phase difference leading to destructive or constructive interference at the interferometer output can be achieved. Thorough software simulations were performed to determine the different design parameters, assign a desired working frequency and provide a reference for comparison with experimental results. Measurements at 300 mK show an effective working frequency close to the simulations, with a deviation smaller than 0.05 GHz. The behavior of the interferometer is very similar to the simulations as well. The on-off ratio exceeds 40 dB.
We implement a broadly tunable phase shifter for microwaves based on superconducting quantum interference devices (SQUIDs) and study it both experimentally and theoretically. At different frequencies, a unit transmission coefficient, |S21| = 1, can be theoretically achieved along a curve where the phase shift is controllable by the magnetic flux. The fabricated device consists of three equidistant SQUIDs interrupting a transmission line. We model each SQUID embedded at different positions along the transmission line with two parameters, capacitance and inductance, the values of which we extract from the experiments. In our experiments, the tunability of the phase shift varies from 0.07 × π to 0.14 × π radians along the full-transmission curve with the input frequency ranging from 6.00 GHz to 6.28 GHz. The reported measurements are in good agreement with simulations, which is promising for future design work of phase shifters for different applications.
We have created a doubly tunable resonator, with the intention to simulate relativistic motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide microwave resonator, with fundamental resonant frequency ω 1 / (2 π ) ~ 5 GHz. Both of its ends are terminated to ground via dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows the tuning of ω 1 / (2 π ) by approximately 700 MHz. Using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to 2 ω 1 . We observe photon generation, at ω 1 , above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control this threshold, in good agreement with a theoretical model. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings resulting in current driving of the SQUIDs.
Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics.To this end, the strong nonlinearities of superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain.In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task.In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters.By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment.For frequencies near the qubit transition frequency, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit.At low frequencies 0 w  , we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators.Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.
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We have succeeded in the first demonstration of a simple and accurate resonator-superconducting quantum interference device (SQUID) coupling for microwave SQUID multiplexers. A simple theory shows our direct coupling with adjustable fractional inductance in the SQUID loop can decrease the deviation of resonance frequencies from designed values in contrast to a conventional inductive coupling. Our direct coupling provides the individual coupling that can be optimized with keeping identical structure, shape, and dimension of the SQUID among all pixels on the same chip. It covers experimentally three or potentially more factors of a frequency band that is larger than that of cryogenic high electron mobility transistor amplifiers. The deviation of experimental fractional inductance from the designed one is less than −3/+10%.
Predictable frequency trimming of superconducting resonators at liquid-helium temperatures requires a tuning element whose usable range remains well defined despite screening currents and hysteresis. Here, we realize flux-controlled λ/4 coplanar-waveguide resonators terminated by two-junction DC superconducting quantum interference devices (SQUIDs) fabricated in a standard Nb/Al-AlOx/Nb multilayer process. Integrated on-chip flux-bias lines allow the resonant frequency to be controlled at 4.2 K. RF measurements show periodic frequency modulation with applied flux, with a maximum shift of δfr=8.63 MHz and a single-valued tuning interval of δfr0=2.85 MHz. Near half-integer flux quanta, the response exhibits hysteretic jumps caused by the finite SQUID loop inductance, so that the usable single-valued tuning interval is smaller than the full modulation range. We develop a semi-analytical model of the frequency–flux response, supported by numerical simulations and 3D electromagnetic extraction of the device parameters, which reproduces the measured hysteretic branches and identifies the SQUID loop inductance and junction critical current as the main parameters limiting the usable tuning range. These results provide a quantitative design framework for MHz-scale frequency trimming of Nb superconducting resonators in 4 K cryogenic readout circuits.