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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 Apr 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1002/pssb.202170017

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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.
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.
Signal and idler waves produced by a nondegenerate parametric amplifier feature strong positive correlation between their photon numbers, or in-phase amplitudes. They feature equally strong negative correlation between their phases, or quadrature-phase amplitudes. These photon twins can produce arbitrarily squeezed states via state reduction by appropriate measurements of an idler wave. When the quadrature amplitude of an idler wave is measured, the signal wave is collapsed to a quadrature-amplitude squeezed state. When the two-quadrature amplitudes of an idler wave are measured simultaneously, the signal wave becomes a coherent state.
It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.
It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.
It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.