On this PhD thesis we cover the results contained in arXiv:2001.07050, arXiv:2111.10096 and arXiv:2011.02822, while providing further details about their derivations. In the first two papers, we study the generation and detection of entangled non-Gaussian states of microwave radiation. These states are produced in a new parametric oscillator, built recently within the field of cQED, capable of down-converting a microwave tone into three different tones at once. These three photons share among their magnitudes quantum correlations, in particular genuine entanglement. In this text we refer to it as non-Gaussian because of its manifestation on statistical moments higher than covariances, and we propose a simple and practical criterion for the design of witnesses capable of detecting it: they must be built from higher statistical moments that change through time. Additionally, we speculate on the theoretical implications of the criterion and find suggestive connections to other entanglement classes, such as the paradigmatic nonequivalent GHZ and W three qubit states. In the third paper, we explore one of the possible applications of quantum technologies: analog simulation of quantum systems. The literature prior to this thesis showcases multiple examples of superconducting circuits capable of mimicking systems in which one must consider both quantum and relativistic phenomena, such as the dynamical Casimir and Unruh effects. This work explores the information that can be obtained through analog simulation, proposing a circuit capable of featuring the internal dynamics of a mirror experiencing a relativistic trajectory, that is, a mirror producing the dynamical Casimir effect.
On this PhD thesis we cover the results contained in arXiv:2001.07050, arXiv:2111.10096 and arXiv:2011.02822, while providing further details about their derivations. In the first two papers, we study the generation and detection of entangled non-Gaussian states of microwave radiation. These states are produced in a new parametric oscillator, built recently within the field of cQED, capable of down-converting a microwave tone into three different tones at once. These three photons share among their magnitudes quantum correlations, in particular genuine entanglement. In this text we refer to it as non-Gaussian because of its manifestation on statistical moments higher than covariances, and we propose a simple and practical criterion for the design of witnesses capable of detecting it: they must be built from higher statistical moments that change through time. Additionally, we speculate on the theoretical implications of the criterion and find suggestive connections to other entanglement classes, such as the paradigmatic nonequivalent GHZ and W three qubit states. In the third paper, we explore one of the possible applications of quantum technologies: analog simulation of quantum systems. The literature prior to this thesis showcases multiple examples of superconducting circuits capable of mimicking systems in which one must consider both quantum and relativistic phenomena, such as the dynamical Casimir and Unruh effects. This work explores the information that can be obtained through analog simulation, proposing a circuit capable of featuring the internal dynamics of a mirror experiencing a relativistic trajectory, that is, a mirror producing the dynamical Casimir effect.
In this thesis we examine a variety of question regarding several quantum information-theoretic concepts as they manifest in the context of relativistic quantum fields. In particular, we study the qualitative and quantitative structure of entanglement (as well as more generalized quantum correlations) in field theory. Primarily we study the nature of vacuum entanglement, but consider spatial correlations in more general field states as well. We also discuss several novel aspects of particle creation phenomena, which generally go hand in hand with the presence of field entanglement. Such investigations are important from two perspectives. First, we gain enlightening new insight into the nature of quantum fields and, therefore, into the fundamental constituents of the matter contained in our universe. Second, we are able to consider the possibility of utilizing the relativistic nature of quantum fields as a resource for quantum technological tasks such as entanglement distribution, information processing, and metrology. \n \nAs a general guiding principle, here we approach such questions from an operational perspective. That is, we focus less on the mathematical facts derivable from a given theory and instead attempt to answer in what concretely physical ways such facts manifest themselves. For example, in what ways can vacuum entanglement actually be experimentally detected and measured, at least in principle? Such an approach allows us to circumvent otherwise problematic interpretational issues. It also lends itself more naturally to the proposal of real world experiments regarding, and utilizations of, the physics being investigated. In this thesis we utilize two models of detection as applied to field theory. \n \nThe first is one that we will develop from scratch and use to great effect in a number of studies; this is the non-perturbative oscillator detector. In this context, a ``detector" is simply some quantum system that is allowed to interact in some way with a quantum field. The response of this system then gives us information about the field properties. Typically such studies are done perturbatively, which presents several severe limitations on what may be investigated. We develop an alternative model, in which the detector is identified as a quantum harmonic oscillator, that allows non-perturbative solutions. We go on to apply this model to a variety of studies. We start by the examining the Unruh effect in a cavity setting. Not only are we able to examine the thermalization behavior of such a detector (which is stronger than what can be achieved perturbatively), we also demonstrate that the Unruh response is largely independent of the cavity boundary conditions, indicating a surprising amount of generality and universality to the phenomenon. We also consider the spacelike extraction of spatial entanglement by a set of such detectors. This includes the harvesting of genuine tripartite entanglement out of the vacuum, as well as the observation that the extractable quantum discord (a generalized measure of quantum correlations) can be greatly amplified by thermal fluctuations in the field, in opposite behavior to entanglement. This calls into question the nature of quantum discord, but also suggests at the possibility of actually using environmental noise as a quantum computational resource. Next, we use the oscillator detector model to great effect by proposing a method of reliably and sustainably generating and distributing entanglement via a cavity field. This protocol is inherently non-perturbative, and we refer to it as entanglement farming. Lastly, we modify the farming scenario to discover a very sensitive resonance effect that generates a large difference in the protocol output due to a minute change in system parameters, including the length of cavity being used. We put this forth as a potential method of quantum seismic metrology. \n \nThe second model that we will consider simply involves performing projective measurements onto a given set of field modes. We will find, however, that such an approach allows us to solve previously intractable problems. In particular, we apply this procedure to the physically sensible choice of localized, positive frequency field modes. Using this model we perform two different studies. In the first, we consider the response of an observer accelerating not through the vacuum state but rather a thermal state. Such a setting has not been (properly) studied previously, due to the computational challenges involved. By applying the localized projective measurement model we are able determine that such an observer sees both an Unruh response from acceleration and a response from the field thermality and that, critically, these responses are distinguishable. We then go on to examine the degradation of quantum correlations between two observers due to the acceleration of one of the observers. This is a prototypical scenario of interest and, by applying realistic measurement assumptions, we obtain results qualitatively different from many previous works on the issue. \n \nIn addition to these models, we question the nature of vacuum entanglement and particle creation by considering an operationally straightforward procedure that greatly demystifies these phenomena and puts them on to solid, physically concrete grounds. This operation is that of very quickly introducing a boundary condition onto one's field, for example by creating a mirror. The real particles generated in this process will then be quantum entangled with each other, even if they are created at spatially separate locations, and this entanglement derives exactly from the previously present vacuum entanglement. Not only does this realization provide an operationally satisfying interpretation of vacuum entanglement, it also suggests a straightforward procedure for its experimental verification. \n \nIn all of this, the computational framework that we will rely upon is that of Gaussian quantum mechanics. This is a restriction of continuous variable quantum mechanics that, while limited in its applicability, provides extremely powerful computational tools in the cases that it may be used. The scenarios of interest in this thesis fall within this category and lend themselves naturally to a Gaussian approach. With this we are able to perform, near trivially, many otherwise intractable studies.
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.
According to quantum field theory, the vacuum is filled with virtual particles which can be turned into real ones under the influence of external perturbations. Phenomena of this kind are commonly referred to as quantum vacuum phenomena. Several quantum vacuum phenomena related to the peculiar nature of the quantum vacuum have been predicted, some of which, such as the Lamb shift and the Casimir effect, have been experimentally found. Other examples of quantum vacuum phenomena include the Unruh effect, the dynamical Casimir effect and the dynamical Lamb effect. The dynamical Lamb effect was first predicted by considering the situation of an atom passing through a cavity at relativistic speed. In this case, the excitation of the atom and the generation of photons is thought to arise because of the sudden change of Lamb shift of the atom. If multiple atoms concurrently experience the dynamical Lamb effect, they can become entangled. A theoretical framework to investigate the time-evolution of a system of N qubits, modeling atoms, coupled to a harmonic oscillator, modeling a cavity, with time-dependent coupling is developed. For the case of a closed system, three different analytical approaches are presented. First, a perturbative approach in the time-domain. This is the standard approach in the solution of Schrödinger equation. Second, a perturbative approach in the Laplace-domain. This can simplify the solution of Schrödinger equation with time-dependent Hamiltonians. However, both approaches require the interaction part of the Hamiltonian to be small compared to the unperturbed Hamiltonian. Third, the framework of Floquet theory is introduced. This can be used in the case of periodic Hamiltonians regardless of the interaction strength. For the case of an open system, the dynamics is investigated by numerically solving the Lindblad master equation. These approaches are then applied to the study of the time-evolution of the quantum entanglement between two and three qubits coupled to a harmonic oscillator. It is demonstrated that different measures of entanglement show a different level of detail of the latter and that time-dependent Greenberger-Horne-Zeilinger states can be created even in the presence of dissipation.The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched “on” and “off”nonadiabatically. We show that by using a superconducting circuit which allows one to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible to observe the dynamical Lamb effect. The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops. Superconducting circuits of this kind are routinely used as quantum information processors. These devices take advantage of quantum properties for mathematical computations, improving their computational capabilities compared to regular computers. We have implemented Shor’s factoring algorithm, in a simplified form, on one such device made available through the cloud by IBM. We study the results of the algorithm on the ibmqx5 superconducting chip, for the particular case of factoring N= 15, 21, and 35. Positive results are obtained for factoring15 and 21, although the device fails to compute the factors of 35 due to the errors introduced by the presence of noise.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrödinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).