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arXiv:2104.13136 · Entropy

Multi-Particle Interference in an Electronic Mach–Zehnder Interferometer

Janne Kotilahti, Pablo Burset, Michael Moskalets, Christian Flindt

Published Jun 10, 2021• 13 citations
arXivHTMLPDF

Abstract

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.

DOI
10.3390/e23060736

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The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.
We investigate a Mach-Zehnder interferometer fed by two time-dependently driven single-particle sources, one of them placed in front of the interferometer, the other in the center of one of the arms. As long as the two sources are operated independently, the signal at the output of the interferometer shows an interference pattern, which we analyze in the spectral current, in the charge and energy currents, as well as in the charge current noise. The synchronization of the two sources in this specifically designed setup allows for collisions and absorptions of particles at different points of the interferometer, which have a strong impact on the detected signals. It introduces further relevant time scales and can even lead to a full suppression of the interference in some of the discussed quantities. The complementary interpretations of this phenomenon in terms of spectral properties and tunable two-particle effects (absorptions and quantum exchange effects) are put forward in this paper.
We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.
We propose a modified single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable x, for each passage of a particle through the interferometer. Quantum theory predicts an interference pattern that is independent of the sequence of the values of x. On the other hand, corpuscular models that reproduce the results of quantum optics experiments carried out up to this date show a reduced visibility and a shift of the interference pattern depending on the details of the sequence of the values of x. The key question to be answered in a real laboratory experiment is: Which interference pattern is observed? Despite the general believe that quantum theory might be used to describe all single particle experiments, this is an interesting question to be answered since in the proposed experiment the experimental conditions not only continuously change but they might also have causal effects on the passage of the photons through the interferometer. The proposed experiment can be used to determine to what extent quantum theory provides a description of observed events beyond the usual statistical level.
The phenomenon of interference lies at the heart of quantum physics, and is responsible for many of the unusual aspects of quantum behaviour that deviate from our everyday expectations. Though classical physics allows for waves (e.g. of sound) to interfere, quantum theory allows for interference effects also to affect single particles. One device that demonstrates this experimentally is the Mach-Zehnder interferometer: here a single particle (e.g. a photon) travels down one of two possible paths, and quantum interference between the two paths affects the final position where the particle arrives. In this article, I propose a mechanism to musically demonstrate quantum single-particle interference: the musical Mach-Zehnder interferometer. This new quantum musical instrument makes use of two independently operated electronic keyboards, whose outputs are interfered according to the rules of the Mach-Zehnder interferometer. I discuss the musical possibilities this instrument enables, and outline a method to construct it via software simulation.
We propose a solid-state quantum eraser in which electrons are injected into a mesoscopic conductor in the quantum Hall regime. The conductor is composed of a two-path interferometer, an electronic analog of the optical Mach-Zehnder interferometer, and a quantum point-contact detector capacitively coupled to the interferometer. While the interference of the output current at the interferometer is suppressed by the which-path information, we show that the which-path information is erased and the interference reappears in the cross-correlation measurement between the interferometer and the detector output leads. We also investigate a modified setup in which the detector is replaced by a two-path interferometer. We show that the distinguishability of the path and the visibility of joint detection can be controlled in a continuous manner and satisfy a complementarity relation for the entangled electrons.
Electronic interferometers have been identified as possible candidates for building electronic flying qubits. Such a regime requires ultrafast voltage pulses whose duration is shorter than the time of flight through the device. Understanding the corresponding physics in the presence of such short excitations requires a proper treatment of electron-electron interactions. In this article, we take a step in this direction by performing time-resolved simulations of a Mach-Zehnder interferometer treating the interactions at the time-dependent mean-field level. We find that the main effect of the interaction is the renormalization of the pulse velocity. Very importantly, the interference effects appear to be robust to the presence of interactions.