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

Journal of Physics Conference Series

Mielnik's evolution loop hexagon in new light

Kurt Bernardo Wolf

Published Jun 26, 2015• 1 citation
Publisher

Abstract

The problem of controlling quantum wavefunctions by means of potential jolts and periods of free evolution was broached by Bogdan Mielnik in 1977. This quantum control became a subject of great interest for the preparation of atomic and particle systems. We point out here that these manipulations are also realized in paraxial geometric and wave optics, with lenses and free spaces, and even more transparently than with matter.

DOI
10.1088/1742-6596/624/1/012010

Related papers

Nonlinear manipulation and control of matter waves

Elena V. Goldstein, M. G. Moore, Pierre Meystre

This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now within experimental reach, has the potential to impact a number of fields of physics, including the manipulation and applications of atomic coherence, and the preparation of quantum entanglement between microscopic and macroscopic systems. Possible applications include quantum information processing, matter-wave holography, and nanofabrication.

arXiv:quant-ph/9906088•Laser Physics•Jun 23, 1999•3 citations

Paraxial-wave optics and relativistic front description. I. The scalar theory

E. C. G. Sudarshan, R. Simon, Narasimhaiengar Mukunda

The scalar wave equation is analyzed in the relativistic front form, appropriate for paraxial-wave optics. The group-theoretical basis for this treatment is uncovered. The formal similarity of the propagation of paraxial beams through optical systems to the quantum mechanics of particles in two dimensions subject to harmonic impulses, and the role of the metaplectic group of Bacry and Cadilhac, are both traced back to the structure of the Poincar\'e group. Light rays are defined in this context as in statistical-wave optics, and the laws for their free propagation as well as transmission through lenses are derived.

Physical Review A•Nov 1, 1983•66 citations

Control of quantum dynamics: The dream is alive

HERSCHEL A. RABITZ

In atomic and molecular physics, a long sought‐after dream has been the use of optical fields to steer wavepackets into desired states. The inherent mechanism of such control consists of manipulating quantum mechanical constructive and destructive interferences. Finding the proper control fields is a problem of design, best expressed in terms of control theory. An overview of the latest developments in this field will be given, along with an indication of where the subject is heading.

AIP conference proceedings•Jan 1, 1995•0 citations

Quantum Control: discovered, repeated and reformulated ideas mark the progress

Bogdan Mielnik

The dynamical manipulation of physical systems is necessary to explain the structure of physical theories. However, the manipulation techniques in quantum theories progress slowly, giving still no certainty that all theoretically described states and all unitary transformations can be indeed achieved. Below, we report some elements of idealized control of the evolution processes in time dependent quadratic potentials, with attention focused on the abstract δ-pulses of the elastic forces. Some of them, if empirically approximated, could become essential for a sequence of difficult interpretation problems.

Journal of Physics Conference Series•May 12, 2014•4 citations

3D strong localization of matter waves by scattering off atoms in a lattice with a confinement-induced resonance

Pietro Massignan, Yvan Castin

The possibility of using ultracold atoms to observe strong localization of matter waves is now the subject of a great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep 3D optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free space inter-species scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.

•Apr 8, 2006•0 citations

Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance

Pietro Massignan, Yvan Castin

The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static-disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep three-dimensional (3D) optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free-space interspecies scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.

arXiv:cond-mat/0604232•Physical Review A•Jul 18, 2006•81 citations
The problem of controlling quantum wavefunctions by means of potential jolts and periods of free evolution was broached by Bogdan Mielnik in 1977. This quantum control became a subject of great interest for the preparation of atomic and particle systems. We point out here that these manipulations are also realized in paraxial geometric and wave optics, with lenses and free spaces, and even more transparently than with matter.
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now within experimental reach, has the potential to impact a number of fields of physics, including the manipulation and applications of atomic coherence, and the preparation of quantum entanglement between microscopic and macroscopic systems. Possible applications include quantum information processing, matter-wave holography, and nanofabrication.
The scalar wave equation is analyzed in the relativistic front form, appropriate for paraxial-wave optics. The group-theoretical basis for this treatment is uncovered. The formal similarity of the propagation of paraxial beams through optical systems to the quantum mechanics of particles in two dimensions subject to harmonic impulses, and the role of the metaplectic group of Bacry and Cadilhac, are both traced back to the structure of the Poincar\'e group. Light rays are defined in this context as in statistical-wave optics, and the laws for their free propagation as well as transmission through lenses are derived.
The dynamical manipulation of physical systems is necessary to explain the structure of physical theories. However, the manipulation techniques in quantum theories progress slowly, giving still no certainty that all theoretically described states and all unitary transformations can be indeed achieved. Below, we report some elements of idealized control of the evolution processes in time dependent quadratic potentials, with attention focused on the abstract δ-pulses of the elastic forces. Some of them, if empirically approximated, could become essential for a sequence of difficult interpretation problems.
The possibility of using ultracold atoms to observe strong localization of matter waves is now the subject of a great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep 3D optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free space inter-species scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.
The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static-disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep three-dimensional (3D) optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free-space interspecies scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.