The Copenhagen interpretation of quantum mechanics states
that a measurement collapses a wavefunction onto an eigenstate of the corresponding
measurement operator. This causes a quantum mechanical wavefunction to break
its unitary evolution described by the Schrodinger equation and is the source
of the quantum measurement problem.
In this thesis we take the first steps to an experiment that might shed light
on this century-old problem. We envision a single-microwave-photon
interferometer that has a travelling-wave parametric amplifier (TWPA) added
to each of its arms. We wonder if the process of amplification of the quantum
state causes the wavefunction to collapse, as it might turn into a detector
while smoothly increasing the amplifier's gain. To this end we introduce
necessary concepts from the field of microwave engineering. Then, we develop
a quantum theory to describe TWPAs. This is followed by preliminary
calculations on the expected interference visibility of the envisioned
interferometer as a function of amplifier gain and losses. Furthermore, we
describe how wavefunction collapse might reveal itself in the experimental
results. Finally, the thesis describes our efforts to develop a low-loss TWPA
based on Josephson junctions.
The Copenhagen interpretation of quantum mechanics states
that a measurement collapses a wavefunction onto an eigenstate of the corresponding
measurement operator. This causes a quantum mechanical wavefunction to break
its unitary evolution described by the Schrodinger equation and is the source
of the quantum measurement problem.
In this thesis we take the first steps to an experiment that might shed light
on this century-old problem. We envision a single-microwave-photon
interferometer that has a travelling-wave parametric amplifier (TWPA) added
to each of its arms. We wonder if the process of amplification of the quantum
state causes the wavefunction to collapse, as it might turn into a detector
while smoothly increasing the amplifier's gain. To this end we introduce
necessary concepts from the field of microwave engineering. Then, we develop
a quantum theory to describe TWPAs. This is followed by preliminary
calculations on the expected interference visibility of the envisioned
interferometer as a function of amplifier gain and losses. Furthermore, we
describe how wavefunction collapse might reveal itself in the experimental
results. Finally, the thesis describes our efforts to develop a low-loss TWPA
based on Josephson junctions.
The readout of a microwave qubit state occurs using an amplification chain that enlarges the quantum state to a signal detectable with a classical measurement apparatus. However, at what point in this process is the quantum state really “measured”? To investigate whether the “measurement” takes place in the amplification chain, in which a parametric amplifier is often chosen as the first amplifier, it is proposed to construct a microwave interferometer that has such an amplifier added to each of its arms. Feeding the interferometer with single photons, the interference visibility depends on the gain of the amplifiers and whether a measurement collapse has taken place during the amplification process. The visibility as given by standard quantum mechanics is calculated as a function of gain, insertion loss, and temperature. A visibility of is found in the limit of large gain without considering losses, which is reduced to in case the insertion loss of the amplifiers is at a temperature of . It is shown that if the wave function collapses within the interferometer, the measured visibility is reduced compared with its magnitude predicted by standard quantum mechanics once this collapse process sets in.
During the process of measurement, quantum signals are amplified to human proportions. The question arises whether this amplification stage is responsible for the reduction of the state vector (also known as collapse of the wave function) during measurement. The cover image shows an artist’s impression of the experiment proposed by Tjerk H. Oosterkamp and co-workers (article number 2000567) to test this hypothesis. A single photon, indicated with sinusoids with a well-determined amplitude, but unknown phase, is amplified within an interferometer. At some gain of the amplifiers the state might collapse unto a state with a well-defined phase. The authors study how they can observe whether a collapse took place within the interferometer, or not.
Bringing signals from quantum to classical, from few-photon to many-photon levels for further processing, is a common challenge in rising quantum technologies. These include quantum computing, quantum communication, quantum sensing, radio astronomy, and dark matter searches, typically operating at microwave frequencies and millikelvin temperatures. Superconducting parametric amplifiers, as the first piece in the readout chain, have become a cornerstone of these technologies, since they offer unrivaled noise performance near the quantum-mechanical limit and high gain to surpass the noise of subsequent amplifiers. A notable implementation is the Josephson traveling-wave parametric amplifier (TWPA), which stands out due to its bandwidth of several Gigahertz and high saturation power, often larger than -100 dBm. These key properties come at the cost of complexity in design and fabrication: TWPA metamaterials often contain several thousands of Josephson junctions. Designing high-gain TWPAs involves three major challenges: ensuring impedance-matching, phase-matching of parametric amplification, and suppressing unwanted processes, all achievable through sub-wavelength dispersion engineering. This thesis covers the circuit design and analysis, implementation, and experimental characterization of a dispersion-engineered TWPA based on radio-frequency superconducting interference devices (rf-SQUIDs). It focuses on a detailed investigation of dispersion-engineering techniques and their effects on amplifier performance, particularly through the use of time-domain circuit simulations to analyze the multimode dynamics of the circuit. The experimentally realized device features 18 dB of gain, an instantaneous bandwidth spanning from 2.2 to 6.7 GHz, a system noise of 2.5 quanta, and a saturation power of (−86.5 ± 4.0) dBm. With these characteristics, it is suitable for frequency-multiplexed readout of detector arrays or qubits. Its high saturation power, about 10 dB higher than other reported Josephson-junction-based TWPAs, allows increasing the number of qubits per readout line, or decreasing the intermodulation between frequency-multiplexed qubits, both crucial for scaling up quantum computation.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
Collapse models are posited as a resolution to the measurement problem. On one level, they offer a clear, simple and testable resolution to an age-old problem. Yet at the same time, they raise many new questions of their own - what is the origin of the putative noise field? What are its properties, and why ought it couple to wavefunctions in this particular way, inducing collapse in some analogue of the position basis? How might these models be extended to the realm of relativity without incurring catastrophe? What sort of image of the world do they deliver? In this thesis we begin with a philosophical exploration of collapse theories. We examine, in detail, the relationship between stochastic noise fields and the evolution of the wavefunction - shedding light both on the solutions offered by collapse models and the new issues which they raise. We discuss the possibilities for constructing an ontology based on these theories, and look at possible implications for the arrow of time and the meaning of causation. This in turn motivates the development of protocols for experiments which might be capable of probing these models; to new degrees in some senses, and in new forms in others. We develop a comprehensive theoretical model of a levitated nanosphere held in an electric quadrupole trap, and find the limits to which this can probe the characteristic collapse rate λ and correlation length r of collapse models. Further, we develop a novel treatment of this scenario in the style of open quantum systems, and show that such an apparatus can constitute a general quantum spectrometer, capable of characterising arbitrary correlation functions for a noise source coupled to the oscillator - whether that noise be invoked by collapse models or other, more mundane sources. Finally, we utilise numerical simulations of trap dynamics to demonstrate the capabilities of electronic feedback cooling - showing that quantum states ought to be achievable without the use of optics. This work is motivated by a desire to understand the world, and specifically to address some of the paradoxes which arise when we try to use quantum mechanics to do so. We have aimed to follow what we see as best practice in physics - from a motivation within philosophy, to the development of theory capable of meeting that philosophy, to the design of experiments which would be able to speak to the relationship between that theory and the world.