Quantum technology stands at the forefront of a technological revolution and has become a central focus of modern physics in recent decades. By exploiting the principles of quantum mechanics, such as superposition and entanglement, it enables capabilities beyond the reach of classical devices. These include enhanced computational power (quantum computing), secure information transfer (quantum communication), and high-precision measurements (quantum sensing and metrology). These capabilities often rely on the precise generation, control, and conversion of microwave photons. However, many aspects of their manipulation remain unexplored and require further study to uncover new possibilities. This thesis focuses on one class of devices known as the Josephson parametric converter (JPC). In its conventional implementation, the JPC leverages three-wave mixing to realize quantum-limited amplification and noiseless frequency conversion. Since these applications have been extensively studied, this work considers a modified variant with one junction removed, thereby enabling four-wave mixing. The aim is to analyze this variant to determine whether photon doubling can be achieved with such a relatively simple circuit. Using the normal-mode formalism, the analysis shows that the photon-doubling coefficients are maximized when the junction is biased at half a flux quantum. Numerical simulations relied on a Floquet approach and Suzuki-Trotter decomposition to model the time evolution of the circuit and verify the occurrence of photon doubling. The simulations indicate that the minimal three-junction JPC can theoretically achieve unity conversion for photon doubling, as verified for initial photon populations $n=1$ and $n=2$. However, achieving full conversion requires accounting for Stark shifts, conversion speed, and drive frequency precision. Since this device now employs four-wave mixing, its potential should be further explored. With these new capabilities, it is worth investigating whether it can support operations beyond photon doubling, such as the generation of multiphoton states and squeezed states.
Quantum technology stands at the forefront of a technological revolution and has become a central focus of modern physics in recent decades. By exploiting the principles of quantum mechanics, such as superposition and entanglement, it enables capabilities beyond the reach of classical devices. These include enhanced computational power (quantum computing), secure information transfer (quantum communication), and high-precision measurements (quantum sensing and metrology). These capabilities often rely on the precise generation, control, and conversion of microwave photons. However, many aspects of their manipulation remain unexplored and require further study to uncover new possibilities. This thesis focuses on one class of devices known as the Josephson parametric converter (JPC). In its conventional implementation, the JPC leverages three-wave mixing to realize quantum-limited amplification and noiseless frequency conversion. Since these applications have been extensively studied, this work considers a modified variant with one junction removed, thereby enabling four-wave mixing. The aim is to analyze this variant to determine whether photon doubling can be achieved with such a relatively simple circuit. Using the normal-mode formalism, the analysis shows that the photon-doubling coefficients are maximized when the junction is biased at half a flux quantum. Numerical simulations relied on a Floquet approach and Suzuki-Trotter decomposition to model the time evolution of the circuit and verify the occurrence of photon doubling. The simulations indicate that the minimal three-junction JPC can theoretically achieve unity conversion for photon doubling, as verified for initial photon populations n=1 and n=2. However, achieving full conversion requires accounting for Stark shifts, conversion speed, and drive frequency precision. Since this device now employs four-wave mixing, its potential should be further explored. With these new capabilities, it is worth investigating whether it can support operations beyond photon doubling, such as the generation of multiphoton states and squeezed states.
Three-wave mixing devices, i.e. non-linear circuits converting power among three microwave signals, are key elements of analog information processing in the microwave domain. However, they are based on dissipative components such as semiconductor diodes, or SIS tunnel junctions biased near the superconducting gap. The loss of signal limits their operation and also introduces noise above the minimum required by quantum mechanics. By using Josephson junctions and superconducting resonators, we've been able to build such a quantum device. In its amplification mode, this device can be used as a preamplifier in many experiments where a few photon wide microwave signals must be measured by commercial instruments, which are sensitive to powers several orders of magnitude larger. The price to pay for this amplification is the necessary degradation of information. Indeed, an extension of the no-cloning theorem imposes that a linear phase preserving amplifier adds at least half a quantum of noise to the signal. By amplifying the finite frequency noise emitted by an NIN tunnel junction, we demonstrated that the total measurement chain adds less than 2.3 quanta to this limit thanks to our device. The operating principle of this device is based on Josephson parametric amplification. I will explain this mechanism and present results which illustrate that it can generate quantum correlated pairs of spatially separated photons with different wavelengths known as two-mode squeezed states. This experiment exploits the tunability of our device and the ease-of-use inherent to micro-wave circuits to perform a quantum optics experiment demonstrating this entanglement.
The flexible engineering of superconducting circuits, together with the nonlinearity available from Josephson junctions, have made microwave quantum optics a blooming research field in the past decade. Key experiments originally performed in the optical domain have become very accessible on this microwave-frequency, such that strong atom-field interactions and optical parametric interactions in microwave. From the latter, one example is the implementation of spontaneous parametric downconversion (SPDC). This process is particularly interesting as it can act as a nonclassical radiation source which give a number of potential applications in quantum information processing. We will focus on studying SPDC in microwave throughout this thesis. \n \nIn the first half of this thesis, from designs to measurements, we will explore the well-known two-photon parametric processes, SPDC and coherent coupling, which are generated by quadratic Hamiltonians. Using three resonant modes of a SQUID-terminated parametric cavity, we proceeded to combine different two-photon processes in an effort to demonstrate a multipartite nonclassical radiation source. With detailed system gain and noise calibration of our cryogenic microwave network, we confirmed our implementation by experimentally verifying that the generated states contain genuine tripartite entanglement. This multimode entangled radiation source can be an important resource for future experiments on quantum networking. \n \nWhile two-photon parametric processes have found numerous important applications, they have also been the limit of experiments for over three decades, with higher-order parametric processes seemingly out of reach. In the second half of this thesis, we explore the potential of parametric resonators for achieving such higher-order processes. To do this, we first studied the necessary conditions for accessing cubic Hamiltonians through our SQUID-based interactions. We then fabricated a device dedicated to performing three-photon processes through these cubic Hamiltonians. For the first time, we observed a direct generation of photon triplets by a single SPDC process in microwave . The generation rate can exceed a photon flux density of 60 photon per second per Hertz at the device output, far surpassing any record to date for photon triplets. We studied various pump configurations corresponding to different three-photon SPDC processes starting from a cold vacuum state. Pumping at triple the frequency of a single mode, we observed a phase-space distribution with a non-Gaussian profile which shows strong skewness (third moment) in the quadrature amplitude distribution. We reconstruct the Wigner function of the propagating states from the directly measured moment matrix, demonstrating Wigner negativity. Pumping at the sum frequency of three modes, we observed non-zero coskewness between the quadrature amplitudes of the modes. By analysing the output signals and comparing their characteristics to the predicted theoretical signatures, we confirm our implementation of three-photon SPDC processes generated by specific cubic Hamiltonians. These types of non-Gaussian states have been suggested as a resource enabling universal quantum computation with continuous variables. Our results thus open up the realm of three-photon quantum optics, enabling a wealth of novel experimental and theoretical studies.
Three-wave mixing devices, i.e. non-linear circuits converting power among three microwave signals, are key elements of analog information processing in the microwave domain. However, they are based on dissipative components such as semiconductor diodes, or SIS tunnel junctions biased near the superconducting gap. The loss of signal limits their operation and also introduces noise above the minimum required by quantum mechanics. By using Josephson junctions and superconducting resonators, we've been able to build such a quantum device. In its amplification mode, this device can be used as a preamplifier in many experiments where a few photon wide microwave signals must be measured by commercial instruments, which are sensitive to powers several orders of magnitude larger. The price to pay for this amplification is the necessary degradation of information. Indeed, an extension of the no-cloning theorem imposes that a linear phase preserving amplifier adds at least half a quantum of noise to the signal. By amplifying the finite frequency noise emitted by an NIN tunnel junction, we demonstrated that the total measurement chain adds less than 2.3 quanta to this limit thanks to our device. The operating principle of this device is based on Josephson parametric amplification. I will explain this mechanism and show preliminary results which illustrate that it can generate quantum correlated pairs of spatially separated photons with different wavelengths known as two-mode squeezed states. This experiment exploits the tunability of our device and the ease-of-use inherent to micro-wave circuits to perform a quantum optics experiment demonstrating this entanglement.
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
Quantum computing and quantum information processing are fast developing fields. As more and more qubits are integrated into the quantum computing systems, a deeper understanding and more careful modeling of the dynamics of these quantum systems in presence of driving and/or loss are necessary, not only for optimizing existing quantum devices, but also for designing and achieving novel method for more precise manipulation of these quantum systems. Our work investigating these quantum systems is inspired by quantum optics, a field focused on the quantum description of light and light-matter interactions. In this thesis, we use the theoretical toolboxes provided by quantum optics as well as condensed matter theory to investigate and model realistic quantum systems. Specifically, we focus on the Nitrogen-vacancy centers in diamond crystal, a Josephson parametric amplifier (that uses Josephson junctions as its non-linear elements), and plasmonic nanowire system. With the knowledge of the dynamics of these systems, we proposed single-photon heralded two-NV center quantum gates; designed and optimized the superconducting circuit for a Josephson parametric amplifier to improve the amplifier's saturation power; and designed new methods for robust light manipulation using topologically protected plasmonic modes. All the devices that we study are either ready to be implemented in experiments or have already been built. Further, as discussed in this thesis, our theoretical analysis of NV-centers can be extended to similar device types like solid-state defect centers, while our analysis of Josephson parametric amplifiers can be extended to other types of superconducting circuit systems.
Quantum computing is a relatively new computing paradigm that leverages entanglement to implement algorithms beyond the reach of classical hardware. Superconducting quantum circuits have emerged as a platform to build quantum processors, with demonstrations of quantum supremacy over classical supercomputers and quantum error correction beyond fault tolerance. However, current noisy devices require significant improvements to unlock the full potential of quantum algorithms.This thesis investigates intrinsic noise channels in superconducting circuits and the design of noise-resilient qubits. By characterizing high-quality superconducting resonators, we identify lossy dielectric materials at the interfaces as the dominant loss mechanism, which we mitigate via targeted surface treatments. Subsequently, we leverage Josephson junction nonlinearity to engineer noise-biased qubits utilizing the Kerr parametric oscillator (KPO). By analyzing the efficiency of strong, far-off-resonance driving to facilitate three- and four-wave mixing processes, we demonstrate high-fidelity operations on Fock, Kerr-cat, and dual-rail qubits. For the Kerr-cat qubit, we introduce a novel 2D architecture that enables strong light-matter coupling with suppressed Purcell decay, yielding millisecond-scale bit-flip lifetimes. Within this same architecture, we demonstrate a longitudinal qubit readout with a 99.6% quantum nondemolition score, alongside a high-fidelity universal single-qubit gate set, all while maintaining bit-flip error suppression. Finally, we exploit the efficient wave-mixing of strongly coupled, far-detuned KPOs to realize a dynamically protected dual-rail qubit exhibiting both erasure bias and high-fidelity single-qubit gates.