Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Reconstruction of the Time-Dependent Wave Function Exclusively from Position Data

Timothy M. Coffey, Róbert E. Wyatt, Wm. C. Schieve

Published Dec 2, 2011• 14 citations
Publisher

Abstract

A method is presented that reconstructs the amplitude and phase of an unknown time-dependent pure-state wave function entirely from experimental position data. No assumptions about the wave function are needed. At a series of times, a large collection of position data is taken, but no measurements of momentum or energy are necessary. The momenta, however, are required for the reconstruction of the wave function and are supplied by analysis of the position data via quantum particle trajectories. Simulations of the method are provided for helium atoms in single and double slit experiments.

DOI
10.1103/physrevlett.107.230403

Related papers

Monitoring the wave function by time continuous position measurement

Thomas Konrad, Andreas Rothe, Francesco Petruccione +1 more

Motivated by the technical requirements of quantum information processing and nanotechnology, the control of individual quantum systems such as single atoms, ions or even photons has become a highly desirable aim.The monitoring of quantum systems-a direct test and in many cases a prerequisite of their control-has been investigated so far only for certain observables such as the position or momentum of quantum particles.Here, we describe a method to monitor in real time the complete state of a quantum particle with unknown initial state moving in a known potential.The method is based on successively updating an estimate by the results of a continuous position measurement.We demonstrate by numerical simulations that even in a chaotic potential tracking the wave function of a particle is possible, and we show with an example that the monitoring scheme appears to be robust against sudden random perturbations.

arXiv:0902.2249•New Journal of Physics•Apr 21, 2010•17 citations

Reconstruction of Bohm trajectories and wave functions from interferometric measurements

Wolfgang P. Schleich, Matthias Freyberger, Muhammad Suhail Zubairy

We propose a generalization of the technique of quantum state reconstruction to obtain the space derivative of the phase of a wave function, which is central to the hydrodynamic formulation of quantum mechanics in the manner of Madelung and Bohm. In this way we can construct Bohm trajectories and make contact with a recent experiment [Kocsis et al., Science 332, 1170 (2011)] extracting these trajectories after a double slit.

Physical Review A•Jan 16, 2013•29 citations

Complex wave-field reconstruction using phase-space tomography

Michael G. Raymer, M. Beck, D. F. McAlister

A method is proposed for the experimental determination of the amplitude and phase structure of a quasimonochromatic wave field in a plane normal to its propagation direction. The wave field may represent either a scalar electromagnetic (EM) field or the quantum mechanical (QM) wave function of a matter wave. For coherent EM fields or pure QM states, the method uniquely reconstructs the complex wave fields. For partially coherent EM fields or mixed QM states, it reconstructs the two-point correlation function or density matrix. The experiment uses only intensity measurements and refractive optics (lenses), and the data analysis algorithm is noniterative and requires no deconvolution.

Physical Review Letters•Feb 21, 1994•349 citations

Reconstruction of a wave function from theQfunction using a phase-retrieval method in quantum-state measurements of light

Nobuharu Nakajima

A method of reconstructing a wave function from part of the Q function in a pure state of light is proposed. This method involves the use of a noniterative phase-retrieval method based on Gaussian filtering, which allows one to determine a convolution of the wave function with a known Gaussian function for the vacuum state from measured data of the Q function along only two parallel lines in phase space. By using a deconvolution process, the wave function is reconstructed from the convolution, provided that the resolution of the reconstructed wave function is limited by the extent of the Fourier transform of the Gaussian function. Numerical simulations demonstrate the applicability of this method to the reconstruction of the wave function from the Q function obtained from the photoelectric counting statistics in unbalanced homodyne detection.

Physical Review A•Jun 1, 1999•9 citations

The Whittaker-Shannon sampling theorem for experimental reconstruction of free-space wave packets

Michael G. Raymer

A data analysis scheme is proposed for determining the quantum state of a one-dimensional wave packet describing atomic translational motion in free space. The Whittaker-Shannon sampling theorem is applied to reconstruct exactly a certain portion of the momentum-basis density matrix from Fourier transforms of measured position-probability densities. The sampling theorem is valid if the spatial wave correlation function equals zero ouside some finite range. It is most useful in cases where the range of available data is insufficient to allow a complete reconstruction of the state by phase-space tomography, as in recent experimental studies of atomic-beam state reconstruction by Pfau and Kurtsiefer.

Journal of Modern Optics•Nov 1, 1997•19 citations

Quantum State Tomography of Dissociating Molecules

Esben Skovsen, Henrik Stapelfeldt, Søren Juhl +1 more

Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating I2 molecule based on femtosecond time resolved position and momentum distributions of the atomic fragments. The experimental data are recorded by timed ionization of the photofragments with an intense 20 fs laser pulse. Our reconstruction method, which relies on Jaynes's maximum entropy principle, will also be applicable to time resolved position or momentum data obtained with other experimental techniques.

arXiv:quant-ph/0301135•Physical Review Letters•Aug 28, 2003•43 citations
A method is presented that reconstructs the amplitude and phase of an unknown time-dependent pure-state wave function entirely from experimental position data. No assumptions about the wave function are needed. At a series of times, a large collection of position data is taken, but no measurements of momentum or energy are necessary. The momenta, however, are required for the reconstruction of the wave function and are supplied by analysis of the position data via quantum particle trajectories. Simulations of the method are provided for helium atoms in single and double slit experiments.
Motivated by the technical requirements of quantum information processing and nanotechnology, the control of individual quantum systems such as single atoms, ions or even photons has become a highly desirable aim.The monitoring of quantum systems-a direct test and in many cases a prerequisite of their control-has been investigated so far only for certain observables such as the position or momentum of quantum particles.Here, we describe a method to monitor in real time the complete state of a quantum particle with unknown initial state moving in a known potential.The method is based on successively updating an estimate by the results of a continuous position measurement.We demonstrate by numerical simulations that even in a chaotic potential tracking the wave function of a particle is possible, and we show with an example that the monitoring scheme appears to be robust against sudden random perturbations.
A method is proposed for the experimental determination of the amplitude and phase structure of a quasimonochromatic wave field in a plane normal to its propagation direction. The wave field may represent either a scalar electromagnetic (EM) field or the quantum mechanical (QM) wave function of a matter wave. For coherent EM fields or pure QM states, the method uniquely reconstructs the complex wave fields. For partially coherent EM fields or mixed QM states, it reconstructs the two-point correlation function or density matrix. The experiment uses only intensity measurements and refractive optics (lenses), and the data analysis algorithm is noniterative and requires no deconvolution.
A method of reconstructing a wave function from part of the Q function in a pure state of light is proposed. This method involves the use of a noniterative phase-retrieval method based on Gaussian filtering, which allows one to determine a convolution of the wave function with a known Gaussian function for the vacuum state from measured data of the Q function along only two parallel lines in phase space. By using a deconvolution process, the wave function is reconstructed from the convolution, provided that the resolution of the reconstructed wave function is limited by the extent of the Fourier transform of the Gaussian function. Numerical simulations demonstrate the applicability of this method to the reconstruction of the wave function from the Q function obtained from the photoelectric counting statistics in unbalanced homodyne detection.
A data analysis scheme is proposed for determining the quantum state of a one-dimensional wave packet describing atomic translational motion in free space. The Whittaker-Shannon sampling theorem is applied to reconstruct exactly a certain portion of the momentum-basis density matrix from Fourier transforms of measured position-probability densities. The sampling theorem is valid if the spatial wave correlation function equals zero ouside some finite range. It is most useful in cases where the range of available data is insufficient to allow a complete reconstruction of the state by phase-space tomography, as in recent experimental studies of atomic-beam state reconstruction by Pfau and Kurtsiefer.
Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating I2 molecule based on femtosecond time resolved position and momentum distributions of the atomic fragments. The experimental data are recorded by timed ionization of the photofragments with an intense 20 fs laser pulse. Our reconstruction method, which relies on Jaynes's maximum entropy principle, will also be applicable to time resolved position or momentum data obtained with other experimental techniques.