A Coherent Bi-Directional Virtual Detector for the 1-D Schr\"odinger Equation

• URL: http://arxiv.org/abs/2205.10461v1
• Date: Fri, 20 May 2022 23:36:27 GMT
• Title: A Coherent Bi-Directional Virtual Detector for the 1-D Schr\"odinger Equation
• Authors: Joshua Mann, James Rosenzweig
• Abstract summary: The virtual detector is a commonly utilized technique to measure the properties of a wavefunction in simulation. One type of virtual detector measures the probability density and current at a set position over time, permitting an instantaneous measurement of momentum at a boundary. We show that, in the limit, this bi-directional virtual detector can reproduce an equivalent wavefunction assuming a globally constant potential.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The virtual detector is a commonly utilized technique to measure the properties of a wavefunction in simulation. One type of virtual detector measures the probability density and current at a set position over time, permitting an instantaneous measurement of momentum at a boundary. This may be used as the boundary condition between a quantum and a classical simulation. However, as a tool for measuring spectra, it possesses several problems stemming from its incoherent nature. Another form of virtual detector measures the wavefunction's complex value at a set position in real space over time and Fourier analyzes it to produce an energy spectrum. The spectra it produces are exact provided that the wavefunction propagated through the detector in one direction. Otherwise it will produce a spectrum that includes interference between forward and backward propagating wavepackets. Here we propose a virtual detector which maintains all the benefits of this coherent virtual detector while also being able to resolve the direction of propagation and mitigate nonphysical interference by use of a second measurement point. We show that, in the continuum limit, this bi-directional virtual detector can reproduce an equivalent wavefunction assuming a globally constant potential. It is therefore equivalent to the exact spectrum.

Related papers

• Derivative coupling in horizon brightened acceleration radiation: a quantum optics approach [0.09986418756990156]
  Horizon Brightened Acceleration Radiation (HBAR) signifies a unique radiation process and provides a promising framework in exploring acceleration radiation in flat/ curved spacetime.<n>Our results suggest that the transition probability for the point-like detector is independent of its frequency.<n>This can be interpreted as the influence of the local gravitational field which modifies the sensitivity of the detector to its frequency and broadens its effective frequency range.
  arXiv  Detail & Related papers  (2025-05-22T16:58:22Z)
• Waveguides in a quantum perspective [49.1574468325115]
  Solid state quantum devices, operated at dilution cryostat temperatures, are relying on microwave signals to drive and read-out their quantum states.<n>Here we report on the quantum theory that describes the simplest Cartesian-type geometries: parallel plates, and rectangular tubes.
  arXiv  Detail & Related papers  (2025-05-20T12:42:07Z)
• An Improved Bound on Nonlinear Quantum Mechanics using a Cryogenic Radio Frequency Experiment [41.48817643709061]
  We set a new limit on the electromagnetic nonlinearity parameter $|epsilon| lessapprox 1.15 times 10-12$, at a 90.0% confidence level. This is the most stringent limit on nonlinear quantum mechanics thus far and an improvement by nearly a factor of 50 over the previous experimental limit.
  arXiv  Detail & Related papers  (2024-11-14T17:31:33Z)
• CANISIUS The Austrian Neutron Spin Echo Interferometer [0.0]
  CANISIUS is built in a versatile way, such that it can be operated in both a continuous broad band beam or a pulsed Time of Flight beam. The instrument may also be used as an interferometer, to probe fundamental questions in quantum mechanics.
  arXiv  Detail & Related papers  (2024-08-12T15:12:14Z)
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory [0.6617341769966992]
  Edge burst is a phenomenon in non-Hermitian quantum dynamics. We investigate the evolution of real-space wave functions for this lattice system.
  arXiv  Detail & Related papers  (2023-03-30T08:27:20Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Variational waveguide QED simulators [58.720142291102135]
  Waveguide QED simulators are made by quantum emitters interacting with one-dimensional photonic band-gap materials. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-02-03T18:55:08Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Pointers for Quantum Measurement Theory [0.0]
  We recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors. We show that the unitary dynamics of the premeasurement process restricts the detector outputs to the subspace of single outcomes. We propose a physical extension of this apparatus which replaces each detector with an ancillabit coupled to a readout device.
  arXiv  Detail & Related papers  (2022-03-21T17:23:46Z)
• Enhancing interferometer sensitivity without sacrificing bandwidth and stability: beyond single-mode and resolved-sideband approximation [9.253130051773992]
  Quantum noise limits the sensitivity of precision measurement devices, such as laser interferometer gravitational-wave observatories and axion detectors. One approach to circumvent this limitation in gravitational-wave detectors is to embed an anomalous-dispersion optomechanical filter to broaden the bandwidth. The original filter cavity design, however, makes the entire system unstable. Recently, we proposed the coherent feedback between the arm cavity and the optomechanical filter to eliminate the instability via PT-symmetry. We show that the main conclusion concerning stability remains intact, with both Nyquist analysis and a detailed time-domain simulation.
  arXiv  Detail & Related papers  (2021-04-06T16:33:08Z)
• Quantum optomechanical system in a Mach-Zehnder interferometer [0.0]
  We show that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current.
  arXiv  Detail & Related papers  (2021-01-22T09:17:34Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.