Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now. In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability. We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems. We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable. Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other. We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles. In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way. In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment. The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.
In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission line resonator, quantum optical effects can be studied in these electrical circuits.The possibility of using a frequency tunable transmission line resonators for coupling of superconducting quantum bits is investigated. Tunable superconducting resonators consisting of coplanar waveguide structures, terminated to ground in one end via a superconducting quantum interference device (SQUID), are characterized. By applying a magnetic field to the SQUID loop, the boundary condition of the resonator changes leading to a change in resonance frequency.A change of the resonance frequency by more than 250 linewidths is demonstrated. It is also demonstrated that the resonator can be tune by several hundred MHz on a time scale that is much shorter than the photon lifetime of the resonator.Circuits containing both one and two transmon qubits coupled to the resonator are characterized. Quantum mechanical interactions between the resonator and the qubits, in form of vacuum Rabi splitting, are observed. Coherent control of a single qubit coupled to the resonator is demonstrated by performing Rabi oscillations of the qubit. In the two qubit case, coherent interaction between the qubits is observed in terms of a nonlinear scaling of the coupling strength between the resonator and the collective two qubit system.Measurements on a strongly driven single Cooper-pair box, using a quantum capacitance readout, are also presented. A rich structure in the response is well explained in terms of longitudinal dressed states of the single-Cooper pair box.When measuring the response of a single-electron box, a gate dependent excess dissipation is observed. The dissipation is understood by considering the internal dynamics of the single electron box. The excess dissipation is modeled as an effective resistance named the Sisyphus resistance.
Superconducting (SC) circuits can behave like atoms making transitions between a few energy levels. Such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip. This talk overviews a few of our theoretical studies on SC circuits and quantum information processing (QIP) including: SC qubits for single photon generation and for lasing; controllable couplings among qubits; how to increase the coherence time of qubits using a capacitor in parallel to one of the qubit junctions; hybrid circuits involving both charge and flux qubits; testing Bell’s inequality in SC circuits; generation of GHZ states; quantum tomography in SC circuits; preparation of macroscopic quantum superposition states of a cavity field via coupling to a SC qubit; generation of nonclassical photon states using a SC qubit in a microcavity; scalable quantum computing with SC qubits; and information processing with SC qubits in a microwave field. Controllable couplings between qubits can be achieved either directly or indirectly. This can be done with and without coupler circuits, and with and without data-buses like EM fields in cavities (e.g., we will describe both the variable-frequency magnetic flux approach and also a generalized double-resonance approach that we introduced). It is also possible to “turn a quantum bug into a feature” by using microscopic defects as qubits, and the macroscopic junction as a controller of it. We have also studied ways to implement radically different approaches to QIP by using “cluster states” in SC circuits.
This thesis presents circuit quantum electrodynamic (cQED) experiments done with artificial atoms coupled to a high quality factor superconducting microwave resonator. This work discusses the theoretical framework, design, fabrication, implementation and characterization of a multi-qubit system using superconducting persistent current qubits, often referred as flux qubits. \n \nWe developed a new type of cryogenic aid for fast turnaround microwave experiments. The minimum turnaround time to perform microwave experiments in dilution refrigerators is typically a few days, as required by cooling down and warming up the entire refrigerator. The cryogenic microwave payload and wiring needed for each qubit and resonator add a significant heat load to \nthe system which typically only has a few µW s of cooling power at millikelvin temperatures. We present a new experimental approach we developed in which a suitable sample holder is attached to a cold-insertable probe and brought in contact with transmission lines permanently mounted inside the cryostat. The total turnaround time is reduced to 8 hours if the target temperature is 80 mK. This new measurement method increased our ability to successfully identify good devices with fast design-characterization iterations, while allowing months-long measurements at 30 mK. \n \nOur device architecture uses several qubits, each of which is controlled via on-chip fast flux bias lines. Readout of the qubit’s quantum state is performed by homodyne detection of the resonator field at large driving power. We observe long coherence times at the optimal bias point of the flux qubits and present decoherence measurements around this optimal point, where the \nflux qubits couple mostly to magnetic flux noise. Dynamical decoupling techniques employing fast microwave pulses are used to protect the qubit’s coherence and allow calculating the magnetic flux noise power spectral density of the qubit’s environment. Photon-mediated interaction between distant qubits in the resonator allows the implementation of a two-qubit controlled-NOT gate \nusing the selective darkening technique. \n \nThis multi-qubit superconducting design is an interesting platform to study the decoherence properties of flux qubits, the properties of strong interaction of electromagnetic radiation with macroscopic quantum systems. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now. In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability. We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems. We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable. Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other. We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles. In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way. In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment. The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.
One of the key elements in circuit quantum electrodynamics (cQED) is the superconducting microwave resonator, which can enable strong coupling to and between nanoscale quantum systems, and as a result has emerged as an essential tool for both quantum information and quantum sensing. In this thesis, I will discuss new applications of superconducting resonators in both of these fields, which illustrates how quantum information and quantum sensing can be strongly tied together. As the field of quantum information continues to grow, various platforms for realizing a quantum computer have been proposed. One attractive platform is to control and manipulate the spin of an electron to form spin qubits, which have demonstrated a long coherence time, weak coupling to the environment, and high fidelity single- and two-qubit gates. However, scaling beyond two qubits has proven challenging, as has incorporating long-range coupling, although both are crucial for making spin qubits a scalable quantum computing platform. The confinement of electromagnetic fields in superconducting resonators enables strong coupling to small systems, such as the single electrons of a spin qubit. In the first part of this thesis, I will describe how a singlet-triplet spin qubit coupled to a high-impedance superconducting resonator constitutes a promising architecture for mediating long-ranged interactions based on a longitudinal coupling between the resonator and qubit. I will discuss the technical developments needed to successfully implement this novel type of interaction in a hybrid spin qubit-resonator device. This type of interaction has several advantages over the more commonly studied transverse coupling scheme: it does not require careful tuning of the qubit frequency to match that of the resonator, which facilitates scaling to a large number of qubits, and also avoids the loss of coherence, which is inevitable in resonant coupling. This type of interaction therefore opens promising paths for generating high-fidelity long-ranged two-qubit coupling by employing superconducting microwave resonators. By adapting techniques used in quantum information, we have also developed a new technique in quantum sensing, where we employ superconducting resonators as a probe of quantum materials such as mesoscopic systems, two-dimensional materials, and heterostructures, which are otherwise challenging to experimentally access with conventional techniques. In the second part of my thesis, I will discuss how implementing cQED techniques from quantum information allows us to probe the symmetry of the order parameter in unconventional superconductors. Unconventional superconductors are not readily available, and we therefore study an engineered system that comprises of interfacing a ferromagnet and superconductor, in which unconventional pairing can be induced into the ferromagnet. This platform allows us to simultaneously excite spin waves, a collective excitation of spins, in the ferromagnet, which opens new directions for studying interactions between coherently coupled magnons (quanta of spin waves) and unconventional superconducting states. Finally, by applying the same technique to a two-dimensional (2D) superconductor, tungsten ditelluride, we leverage this platform in an attempt to study the order parameter of its intrinsic superconducting phase. The nature of the order parameter in this material remains an open question, as both topological and superconducting phases can exist, possibly simultaneously. This work thus demonstrates a unique use of superconducting resonators beyond quantum information applications.