Abstract Solid state quantum devices, operated at dilution cryostat temperatures, are relying on microwave signals to both drive and read-out their quantum states. These signals are transmitted into the cryogenic environment, out of it towards detection devices, or even between quantum systems by well-designed waveguides , almost lossless when made of superconducting materials. Here we report on the quantum theory that describes the simplest Cartesian-type geometries: parallel plates, and rectangular tubes. The aim of the article is twofold: first on a technical and pragmatic level, we provide a full and compact quantum description of the different traveling wave families supported by these guides. Second, on an ontological level, we interpret the results and discuss the nature of the light fields corresponding to each mode family. The concept of potential difference is extended from transverse electric-magnetic (TEM) waves to all configurations, by means of a specific gauge fixing . The generalized flux φ ^ introduced in the context of quantum electronics becomes here essential: it is the scalar field, conjugate of a charge Q ^ , that confines light within the electrodes, let them be real or virtual . The gap in the dispersion relations of non-TEM waves turns out to be linked either to a potential energy necessary for the photon confinement , or to a kinetic energy arising from a photon mass . We finally compute the field zero-point fluctuations in every configuration. The theory is predictive: the lowest transverse magnetic modes should have smaller quantum noise than the higher ones, which at large wavevectors recover a conventional value similar to TEM and transverse electric ones. Such low-noise modes might be particularly useful for the routing of quantum information.
Abstract Solid state quantum devices, operated at dilution cryostat temperatures, are relying on microwave signals to both drive and read-out their quantum states. These signals are transmitted into the cryogenic environment, out of it towards detection devices, or even between quantum systems by well-designed waveguides , almost lossless when made of superconducting materials. Here we report on the quantum theory that describes the simplest Cartesian-type geometries: parallel plates, and rectangular tubes. The aim of the article is twofold: first on a technical and pragmatic level, we provide a full and compact quantum description of the different traveling wave families supported by these guides. Second, on an ontological level, we interpret the results and discuss the nature of the light fields corresponding to each mode family. The concept of potential difference is extended from transverse electric-magnetic (TEM) waves to all configurations, by means of a specific gauge fixing . The generalized flux φ ^ introduced in the context of quantum electronics becomes here essential: it is the scalar field, conjugate of a charge Q ^ , that confines light within the electrodes, let them be real or virtual . The gap in the dispersion relations of non-TEM waves turns out to be linked either to a potential energy necessary for the photon confinement , or to a kinetic energy arising from a photon mass . We finally compute the field zero-point fluctuations in every configuration. The theory is predictive: the lowest transverse magnetic modes should have smaller quantum noise than the higher ones, which at large wavevectors recover a conventional value similar to TEM and transverse electric ones. Such low-noise modes might be particularly useful for the routing of quantum information.
Abstract We present a canonical quantization of electromagnetic modes in cylindrical waveguides, extending a gauge-based formalism previously developed for Cartesian geometries (Collin and Delattre 2025 New J. Phys. 27 093502). By introducing the two field quadratures X , Y of transverse electric–magnetic, but also of TM (transverse magnetic) and TE (transverse electric) traveling modes, we identify for each a characteristic one-dimensional scalar field (a generalized flux φ ) governed by a Klein–Gordon type equation. The associated Hamiltonian is derived explicitly from Maxwell’s equations, allowing the construction of bosonic ladder operators. The generalized flux is directly deduced from the electromagnetic potentials A , V by a proper gauge choice , generalizing Devoret’s approach (Devoret 1997 Les Houches, Session LXIII). Our analysis unifies the treatment of cylindrical and Cartesian guided modes under a consistent and generic framework, ensuring both theoretical insight and experimental relevance. Especially, we find out that TE n = 0 modes break a fundamental gauge symmetry that is observed by all other families. We derive mode-specific capacitance and inductance from the field profiles and express voltage and current in terms of the canonical field variables. Measurable quantities are therefore properly defined from the mode quantum operators, especially for the non-trivial TM and TE ones. The formalism shall extend in future works to any other type of waveguides, especially on-chip coplanar geometries particularly relevant to quantum technologies.
We report on the mapping of classical microwave transmission line theory onto the quantum scattering matrix description. By means of a generalized flux formalism a la Devoret, we derive a charge-current vector living on the confining electrodes, to which a Hodge-like decomposition is applied. The presented theory holds equally well for all types of waves traveling within Cartesian and cylindrical guide geometries (the usual Transverse Electric Magnetic, but also Transverse Magnetic and Transverse Electric ones). We then demonstrate how a generic load decomposes into a series of complex coefficients Zload(α), for each mode α propagating along the line. This decomposition leads to a particular classification of traveling waves: gradient-type and curl-type charge-currents. This distinction shines a new light on a broken gauge symmetry exhibited by a class of Transverse Electric modes. Our results provide a universal theoretical framework, which finds a direct usage in microwave-based quantum information transfer.
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.
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.
Most of the publications on Quantum Computing and its main building block; the Qubit, rely on the Quantum Theory and use its terminologies. It is therefore not an easy task for the Electrical Engineers to fully understand the concept of the qubits, and how they are designed, controlled, readout, and used for computation. The primary aim of this paper is to show that the physical quantities describing the superconducting Transmons-the microwave realizations of the qubits-are just noisy signals similar to those encountered in e.g. Mobile and Satellite Communications. The nature of the noise in the qubit case, which will be simply called Quantum Noise, is essentially different from that of e.g. the thermal one. Contrary to the well-studied Thermal Noise, the Quantum one enjoys precise probability distributions and can interfere coherently. In particular, the so-called Stationary States resemble individually pure noise. However, a superposition of at least two of them results in a noisy signal, whose signal-to-noise ratio improves (goes higher) as more stationary states enter the superposition. Furthermore, the excitation (control) and readout of the qubits will be treated from the perspectives of the Electrical Engineering.
The study of light-matter interaction in superconducting quantum circuits has seen remarkable progress over the last 20 years. By engineering artificial atoms, novel quantum phenomena have been demonstrated, and old ideas have come into a new light. Beyond their application to basic science, the prospect of implementing large-scale quantum information processing with superconducting circuits has fueled a rapid development of surrounding technologies, with ever-increasing control over their behavior as a result. The field's success stems primarily from the flexible design and strong non-linearity of the artificial atom, whose coherent interaction with both electrical and mechanical degrees of freedom has opened many doors for science. This thesis deals with the interaction between artificial atoms and quantum fields in one-dimensional waveguides. The waveguide represents a one-dimensional environment for the atom, which we use to study the properties of open quantum systems. All quantum systems are, in fact, open, and interactions between the system and its environment lead inevitably to a loss of energy and quantum coherence. A continuous loss of information into the environment is called a Markovian process. The work contained in this thesis indicates that deviations from a Markovian process can be detected in the steady state of driven systems. This could simplify the detection of non-Markovianity in open quantum systems, as no information about the system's transient dynamics would be necessary.Specifically, this thesis considers both electromagnetic fields in microwave transmission lines and acoustic fields in the form of surface acoustic waves (SAWs) traveling on the surface of solids. The recent realization of artificial atoms interacting with acoustic waves has opened up a new research field called quantum acoustics. We have built a model of the interaction between atoms and SAWs that predicts the existence of a new regime where the atom forms its own cavity. Additionally, we have considered synthesizing electromagnetically induced transparency, a quantum optics phenomena in opaque media where the absorption of photons is canceled, in waveguides using multiple closely spaced two-level systems. Some of the work in this thesis represents experimental work done in collaboration. In the first experiment, we studied the routing of acoustic waves at the quantum level. In the other experiment, we demonstrated electromagnetically induced transparency by creating an effective Lambda system using a giant artificial atom. This thesis reviews the numerical techniques used to model these experiments.