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

Russian Microelectronics

Information aspects of “which-path” interference experiments with microparticles

Yu. I. Bogdanov, K. A. Valiev, S. A. Nuyanzin, A. K. Gavrichenko

Published Jul 1, 2010• 4 citations
Publisher

Abstract

The Schmidt expansion method is used to consider the informational aspects of the problem concerned with monitoring the process of interference of quantum particles. The far-field diffraction pattern specified by the probability density of the distribution of the particle momentum is represented as a mixture of densities of the corresponding Schmidt modes, whose number coincides with the number of slits in the screen. The optical coherence is described on the basis of the procedure of complementation of the mixture to a pure state. Information characteristics are introduced to describe the quality of the interference pattern. The relationship between the visibility of the interference pattern and the Schmidt number is found and examined. Different “which-path” experiments are analyzed. The results of numerical simulation of interference at two and three slits for Rydberg atoms, whose path passes through resonators capable of providing data on the trajectory of the atom, are described.

DOI
10.1134/s1063739710040013

Related papers

On the Informational Aspects of Interfering Quantum States

Yu. I. Bogdanov, A. Yu. Bogdanov, S. A. Nuyanzin +1 more

In present work we study informational measures for the problem of interference of quantum particles. We demonstrate that diffraction picture in the far field, which is given by probability density of particle momentum distribution, represents a mixture of probability densities of corresponding Schmidt modes, while the number of modes is equal to the number of slits at the screen. Also, for the first time we introduce informational measures to study the quality of interference picture and analyze the relation between visibility of interference picture and Schmidt number. Furthermore, we consider interference aspects of the problem of a quantum particle tunneling between two potential wells. This framework is applied to describing various isotopic modifications of ammonia molecule. Finally, we calculate limits on the maximum possible degree of entanglement between quantum system and its environment, which is imposed by measurements

arXiv:0812.4808•Dec 29, 2008•1 citation

Schmidt Decomposition and Coherence of Interfering Alternatives

Dmitriy V. Fastovets, Yu. I. Bogdanov, Nadezhda A. Bogdanova +1 more

Abstract The Schmidt decomposition and the correlational analysis based on it make it possible to identify statistical dependences between various subsystems of a single physical system. The systems under consideration can be both quantum states and classical probability distributions. In this study, two different physical systems are considered: quantum Schrödinger cat states and double-slit interference of microparticles. It is shown that the considered systems have a single internal structure and can be described in general terms of interfering alternatives. An effective approach is developed that allows us to calculate optical characteristics of interference such as visibility and coherence. It is shown that the scalar product of the states of the environment of interfering alternatives acts as a natural generalization of the classical complex parameter of the coherence of light oscillations, which determines the visibility of the interference pattern. A simple quantitative relationship is obtained between the visibility of the interference pattern and the Schmidt number, which determines the level of connection between a quantum system and its environment. The developed approaches are generalized to the case of multidimensional Schrödinger cat states.

Russian Microelectronics•Sep 1, 2021•5 citations

Quantum interference with slits

Thomas V Marcella

In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a position-measuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics.

arXiv:quant-ph/0703126•Mar 15, 2007•1 citation

Control of interference and diffraction of a three-level atom in a double-slit scheme with cavity fields

Mario Miranda, Miguel Orszag

A double-cavity with a quantum mechanical and a classical field is placed immediately behind a double-slit in order to analyze the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path information can be recorded on the phase of the quantum field. On the other hand, if the atom crosses a common node, the interaction is null and no path information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude $\ensuremath{\alpha}$ and the classical amplitude $\ensuremath{\varepsilon}$. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.

Physical Review A•Sep 28, 2020•7 citations

On the control of interference and diffraction of a 3-level atom in a double-slit scheme with cavity fields

Mario Miranda Rojas, Miguel Orszag

A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude $α$ and the classical amplitude $\varepsilon$. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.

arXiv:2009.10895•Sep 23, 2020•0 citations

N-slit interference: Path integrals, Bohmian trajectories

Valeriy I. Sbitnev

Path integrals give a possibility to compute in details routes of particles from particle sources through slit gratings and further to detectors. The path integral for a particle passing through the Gaussian slit results in the Gaussian wavepacket. The wavepackets prepared on N slits and superposed together give rise to interference pattern in the near-field zone. It transforms to diffraction in the far-field zone represented by divergent principal rays, at that all rays are partitioned from each other by (N-2) subsidiary rays. The Bohmian trajectories in the near-field zone of N-slit gratings show wavy behavior. And they become straight in the far-field zone. The trajectories show zigzag behavior on the interference Talbot carpet (ratio of particle wavelength to a distance between slits are much smaller than 1 and N>>1). Interference from the the N-slit gratings is simulated by scattering monochromatic neutrons (wavelength=0.5 nm). Also we have considered simulation of interference fringes arising at scattering on an N-slit grating of fullerene molecules (according to the real experiment stated in e-print 1001.0468).

arXiv:1001.0661•Jan 5, 2010•2 citations
The Schmidt expansion method is used to consider the informational aspects of the problem concerned with monitoring the process of interference of quantum particles. The far-field diffraction pattern specified by the probability density of the distribution of the particle momentum is represented as a mixture of densities of the corresponding Schmidt modes, whose number coincides with the number of slits in the screen. The optical coherence is described on the basis of the procedure of complementation of the mixture to a pure state. Information characteristics are introduced to describe the quality of the interference pattern. The relationship between the visibility of the interference pattern and the Schmidt number is found and examined. Different “which-path” experiments are analyzed. The results of numerical simulation of interference at two and three slits for Rydberg atoms, whose path passes through resonators capable of providing data on the trajectory of the atom, are described.
In present work we study informational measures for the problem of interference of quantum particles. We demonstrate that diffraction picture in the far field, which is given by probability density of particle momentum distribution, represents a mixture of probability densities of corresponding Schmidt modes, while the number of modes is equal to the number of slits at the screen. Also, for the first time we introduce informational measures to study the quality of interference picture and analyze the relation between visibility of interference picture and Schmidt number. Furthermore, we consider interference aspects of the problem of a quantum particle tunneling between two potential wells. This framework is applied to describing various isotopic modifications of ammonia molecule. Finally, we calculate limits on the maximum possible degree of entanglement between quantum system and its environment, which is imposed by measurements
Abstract The Schmidt decomposition and the correlational analysis based on it make it possible to identify statistical dependences between various subsystems of a single physical system. The systems under consideration can be both quantum states and classical probability distributions. In this study, two different physical systems are considered: quantum Schrödinger cat states and double-slit interference of microparticles. It is shown that the considered systems have a single internal structure and can be described in general terms of interfering alternatives. An effective approach is developed that allows us to calculate optical characteristics of interference such as visibility and coherence. It is shown that the scalar product of the states of the environment of interfering alternatives acts as a natural generalization of the classical complex parameter of the coherence of light oscillations, which determines the visibility of the interference pattern. A simple quantitative relationship is obtained between the visibility of the interference pattern and the Schmidt number, which determines the level of connection between a quantum system and its environment. The developed approaches are generalized to the case of multidimensional Schrödinger cat states.
In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a position-measuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics.
A double-cavity with a quantum mechanical and a classical field is placed immediately behind a double-slit in order to analyze the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path information can be recorded on the phase of the quantum field. On the other hand, if the atom crosses a common node, the interaction is null and no path information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude $\ensuremath{\alpha}$ and the classical amplitude $\ensuremath{\varepsilon}$. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.
A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude ααα and the classical amplitude ε\varepsilonε. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.
Path integrals give a possibility to compute in details routes of particles from particle sources through slit gratings and further to detectors. The path integral for a particle passing through the Gaussian slit results in the Gaussian wavepacket. The wavepackets prepared on N slits and superposed together give rise to interference pattern in the near-field zone. It transforms to diffraction in the far-field zone represented by divergent principal rays, at that all rays are partitioned from each other by (N-2) subsidiary rays. The Bohmian trajectories in the near-field zone of N-slit gratings show wavy behavior. And they become straight in the far-field zone. The trajectories show zigzag behavior on the interference Talbot carpet (ratio of particle wavelength to a distance between slits are much smaller than 1 and N>>1). Interference from the the N-slit gratings is simulated by scattering monochromatic neutrons (wavelength=0.5 nm). Also we have considered simulation of interference fringes arising at scattering on an N-slit grating of fullerene molecules (according to the real experiment stated in e-print 1001.0468).