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arXiv:1802.09034 · Physical review. B./Physical review. B

Resonant and off-resonant microwave signal manipulation in coupled superconducting resonators

M. Pierre, Sankar Raman Sathyamoorthy, Ida-Maria Svensson, Göran Johansson, Per Delsing

Published Mar 22, 2019• 13 citations
arXivHTMLPDF

Abstract

We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsing the frequency detuning between the two resonators. The behavior of the system, which determines how the device can be operated, is analyzed as a function of one key parameter of the system, the damping ratio of the coupled resonators. We show a good agreement between experiments and simulations, realized by solving a set of coupled differential equations.

DOI
10.1103/physrevb.99.094518

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We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsing the frequency detuning between the two resonators. The behavior of the system, which determines how the device can be operated, is analyzed as a function of one key parameter of the system, the damping ratio of the coupled resonators. We show a good agreement between experiments and simulations, realized by solving a set of coupled differential equations.
We provide a proposal to achieve single-photon router in the microwave domain based on a waveguide quantum electrodynamics structure, which consists of a double-resonator side coupled to a superconducting transmission line. A superconducting quantum interference device is used to realize tunable and switchable coupling between the resonators; thereby the transport of a single photon in the transmission line can be effectively controlled. Our calculations show that the device has high on-off ratio and is experimentally feasible in currently available superconducting quantum circuits.
In this thesis I present different types of manipulations of microwave fields using tunable superconducting resonators. A resonator is made tunable by adding one or more superconducting quantum interference devices, SQUIDs. The SQUID consists of a superconducting loop with two Josephson junctions and acts as a tunable nonlinear inductor. Modulation of the SQUID nonlinearity can be performed to induce different types of non-trivial oscillator dynamics. The first project I present is on subharmonic oscillations. Here, the SQUID in a tunable resonator is driven with an external signal at an integer multiple of the frequency w. When w is placed slightly below the first resonator mode, I show generation of radiation at w, which is known as frequency down-conversion. In my measurements, subharmonic oscillations have been detected from period doubling up to period quintupling. For the specific case of period tripling, theory is developed and I show good agreement between theory and experiments. The second project of the thesis is on a doubly tunable resonator. Here, I show creation of a superconducting resonator with two independently tunable boundary conditions. The idea with this system is to operate the resonator in a breathing or a translational mode and compare the two. For static dc magnetic flux the performance is very good. As a second step, I perform fast modulation of both SQUIDs to generate radiation. Even though some of the measurement results are promising, I also show some contradicting observations. These indicate that the actual modulation mechanism of the SQUID is not pumping of the magnetic flux in the SQUID loop as intended, but rather direct current driving of the SQUID. However, the system remains a promising idea for microwave manipulation and creation of interesting non-classical states. As a possible application of the doubly tunable resonator, I present a theory proposal on how to use it for measurements on relativistic effects. By using the tunability of the resonator boundary conditions, the resonator can simulate a space rocket and time dilation could be measured. However, due to the crosstalk problems in the doubly tunable resonator this experiment was never realized. Finally, I finish the thesis by presenting a design for a tunable microwave coupling. Papers E and F show a high on-off ratio for the coupler and demonstrate how it can be used for storage of microwave signals. Furthermore, the tunable coupler can be used to shape a microwave signal by tuning the strength of the coupling.
We propose a frequency-tunable source to emit entangled microwave photons on the platform of a superconducting circuit, in which two superconducting transmission-line resonators are coupled via a capacitor and one resonator is inserted with a superconducting quantum interference device (SQUID) in the center. By pumping the circuit appropriately with an external coherent microwave signal through the SQUID, microwave photons are emitted in pairs out of the circuit. The entanglement between the two modes is demonstrated by numerically calculating the second-order coherence function and the logarithmic negativity of the output microwave signals. Due to the tunability of SQUID’s equivalent inductance, the frequencies of the entangled microwave photons can be tuned by an external flux bias in situ. Our proposal paves a new way for obtaining entangled frequency-tunable two-mode microwave photons.
We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device. We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on resonance. The device allows capture, storage, and on-demand release of microwaves at a tunable rate.
We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum interference device that terminates one of the resonators. This produces a nonlinear interaction of the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths that should be attainable with the proposed device, and we find that the device is a promising candidate for realizing the single-photon strong-coupling regime. As a potential application, we discuss implementations of networks of nonlinearly coupled microwave resonators, which could be used in microwave-photon-based quantum simulation.
High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.