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arXiv:1811.01698 · physica status solidi (b)

An Experimental Proposal to Study Collapse of the Wave Function in Traveling‐Wave Parametric Amplifiers

Thomas H. A. van der Reep, Louk Rademaker, Xavier G. A. Le Large, Ruben H. Guis, Tjerk H. Oosterkamp

Published Dec 17, 2020• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/pssb.202000567

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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.
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.
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.
Two four-wave mixing processes have been employed to experimentally construct a nonlinear interferometer [Jing et al., Appl. Phys. Lett. 99, 011110 (2011)], which has a better phase sensitivity than the traditional linear interferometer. For its applications in quantum measurement, interference fringe visibility can significantly affect the quantum detection efficiency. In this letter, we study how various parameters, such as the pump power, the one-photon detuning, and the two-photon detuning, influence the visibility of nonlinear interferometer. We find that the visibility greater than 0.9 can be achieved for large range of system parameters.
Quantum-limited microwave parametric amplifiers are genuine key pillars for rising quantum technologies and, in general, for applications that rely on the successful readout of weak microwave signals by adding only the minimum amount of noise allowed by quantum mechanics. In this Perspective, after providing a brief overview on the different families of parametric microwave amplifiers, we focus on traveling wave parametric amplifiers, underlining the key achievements of the last few years and the present open challenges. We also discuss possible new research directions beyond amplification such as exploring these devices as a platform for multi-mode entanglement generation and for the development of single photon detectors.
By utilizing amplifiers in a modified interferometer, both particlelike and wavelike characteristics of single input photons are analyzed theoretically. Quantum theory predicts that proposed measurements on the amplified field will indicate that the single input photon exhibits extremes of both wavelike and particlelike characteristics. The evidence for wavelike behavior is fringe visibility at the output of the interferometer. Anticorrelation between the outputs of the two legs of the interferometer provides the evidence for particlelike behavior. Although quantum noise degrades both the particle-sensitive and the wave-sensitive measurement, no trade-off between the wavelike and the particlelike characteristics takes place. Complementarity, however, is maintained by the quantum noise added during amplification.
Abstract Measurement in quantum mechanics is a long-standing issue, and the measurement problem (as it is known) consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we propose an additional solution to the measurement problem, in the hope that alternate perspectives on this problem could eventually lead to its final resolution. We assume that for every eigenvector of an operator there is a set of discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference between a measurement mapping-operator, exhibiting all of the potential eigenvector phases, and the particular phase of a single realization of the quantum object.