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

arXiv:1306.2204

First experimental realization of the Dirac-Moshinsky oscillator

J. A. Franco-Villafañe, Emerson Sadurní, Sonja Barkhofen, Ulrich Kuhl, Fabrice Mortessagne, T. H. Seligman

Published Jun 10, 2013• 0 citations
arXivHTMLPDF

Abstract

We present the first experimental microwave realization of the one-dimensional Dirac-Moshinsky oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac-Moshinsky oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yields the spectrum of the one-dimensional Dirac-Moshinsky oscillator with and without mass term. The flexibility of the experimental set-up allows the implementation of other one-dimensional Dirac type equations.

Related papers

One dimensional Dirac-Moshinsky oscillator-like system and isospectral partners

Alonso Contreras-Astorga

Two different exactly solvable systems are constructed using the supersymmetric quantum mechanics formalism and a pseudoscalar one-dimensional version of the Dirac- Moshinsky oscillator as a departing system. One system is built using a first-order SUSY transformation. The second is obtained through the confluent supersymmetry algorithm. The two of them are explicitly designed to have the same spectrum as the departing system and pseudoscalar potentials.

Journal of Physics Conference Series•Jun 26, 2015•2 citations

Graphical Proposal for a Quantum Simulation of the Two-Dimensional Dirac Oscillator: Optical Trapped-Ion and Microwave Implementations

Abdelmalek Boumali

Abstract The two-dimensional Dirac oscillator is one of the most transparent exactly solvable models in relativistic quantum mechanics. Its Hamiltonian is linear in both momentum and posi- tion and therefore has no direct elementary-particle realization in ordinary harmonic traps. This extended proposal develops two complementary laboratory routes. The first is an optical trapped-ion implementation in which the electronic two-level system encodes the Dirac bispinor and two transverse motional modes encode the two spatial degrees of freedom. Bichromatic red- and blue-sideband laser fields synthesize the Jaynes-Cummings and anti-Jaynes-Cummings cou- plings required by the oscillator. The second route is a microwave-based proposal. Two meanings of “microwave implementation” are distinguished: a microwave-driven trapped-ion implementa- tion using magnetic-gradient-induced spin-motion coupling, and a microwave-resonator/tight- binding analogue based on coupled dielectric resonators. The former remains a genuine single- ion quantum simulator and can, in principle, implement the same effective Hamiltonian with improved phase stability and reduced optical spontaneous-emission errors. The latter is experi- mentally simpler for spectral measurements and can serve as a second proposal, but it is a wave analogue rather than a single-particle trapped-ion quantum simulation. We do not claim the first mapping of the 2 + 1 Dirac oscillator onto trapped-ion dynamics, which is already established in the literature; rather, the contribution is a consolidated, experimentally oriented roadmap that compares the optical trapped-ion, microwave-driven trapped-ion, and microwave-resonator routes, with explicit feasibility conditions, an observable strategy, a corrected graphical map- ping, an explicit separation of the ideal Hamiltonian from its leading correction terms, a worked order-of-magnitude estimate for a 171 Yb+ ion, and an explicit quantitative cross-walk to the trapped-ion and microwave experiments on which the scheme builds. We identify the advan- tages and limitations of each route and propose a staged experimental program for measuring Zitterbewegung, the relativistic square-root spectrum, and chirality-dependent dynamics.

•Jun 23, 2026•0 citations

The Dirac-Moshinsky oscillator: theory and applications

Emerson Sadurní, R. Bijker, Octavio Castaños +2 more

This work summarizes the most important developments in the construction and application of the Dirac‐Moshinsky oscillator (DMO). The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here we make an effort to present the subject in chronological order and also in increasing degree of complexity. We start our discussion with the seminal paper by Moshinsky and Szczepaniak and the immediate implications stemming from it. Then we analyze the extensions of this model to many particles. The one‐particle DMO is revisited in the light of the Jaynes‐Cummings model in quantum optics and exactly solvable extensions are presented. Applications and implementations in hexagonal lattices are given, with a particular emphasis in the emulation of graphene in electromagnetic billiards.

arXiv:1101.3011•AIP conference proceedings•Jan 1, 2011•1 citation

The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

Juan Mauricio Torres, Emerson Sadurní, T. H. Seligman +4 more

The Dirac‐Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes‐Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.

arXiv:1010.5229•AIP conference proceedings•Jan 1, 2010•8 citations

Coherent States for the Two-Dimensional Dirac–Moshinsky Oscillator Coupled to an External Magnetic Field*

D. Ojeda-Guillén, R. D. Mota, V. D. Granados

Abstract We show that the (2+1)-dimensional Dirac–Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the SU(1,1) group theory and its group basis. We use the su(1,1) irreducible representation theory to find the energy spectrum and the eigenfunctions. Also, with the su(1,1) group basis we construct the relativistic coherent states in a closed form for this problem.

arXiv:1411.1968•Communications in Theoretical Physics•Mar 1, 2015•9 citations

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

Keye Zhang, Lu Zhou, Pierre Meystre +1 more

An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.

arXiv:1807.02950•Physical Review Letters•Sep 11, 2018•5 citations
We present the first experimental microwave realization of the one-dimensional Dirac-Moshinsky oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac-Moshinsky oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yields the spectrum of the one-dimensional Dirac-Moshinsky oscillator with and without mass term. The flexibility of the experimental set-up allows the implementation of other one-dimensional Dirac type equations.
Abstract The two-dimensional Dirac oscillator is one of the most transparent exactly solvable models in relativistic quantum mechanics. Its Hamiltonian is linear in both momentum and posi- tion and therefore has no direct elementary-particle realization in ordinary harmonic traps. This extended proposal develops two complementary laboratory routes. The first is an optical trapped-ion implementation in which the electronic two-level system encodes the Dirac bispinor and two transverse motional modes encode the two spatial degrees of freedom. Bichromatic red- and blue-sideband laser fields synthesize the Jaynes-Cummings and anti-Jaynes-Cummings cou- plings required by the oscillator. The second route is a microwave-based proposal. Two meanings of “microwave implementation” are distinguished: a microwave-driven trapped-ion implementa- tion using magnetic-gradient-induced spin-motion coupling, and a microwave-resonator/tight- binding analogue based on coupled dielectric resonators. The former remains a genuine single- ion quantum simulator and can, in principle, implement the same effective Hamiltonian with improved phase stability and reduced optical spontaneous-emission errors. The latter is experi- mentally simpler for spectral measurements and can serve as a second proposal, but it is a wave analogue rather than a single-particle trapped-ion quantum simulation. We do not claim the first mapping of the 2 + 1 Dirac oscillator onto trapped-ion dynamics, which is already established in the literature; rather, the contribution is a consolidated, experimentally oriented roadmap that compares the optical trapped-ion, microwave-driven trapped-ion, and microwave-resonator routes, with explicit feasibility conditions, an observable strategy, a corrected graphical map- ping, an explicit separation of the ideal Hamiltonian from its leading correction terms, a worked order-of-magnitude estimate for a 171 Yb+ ion, and an explicit quantitative cross-walk to the trapped-ion and microwave experiments on which the scheme builds. We identify the advan- tages and limitations of each route and propose a staged experimental program for measuring Zitterbewegung, the relativistic square-root spectrum, and chirality-dependent dynamics.
This work summarizes the most important developments in the construction and application of the Dirac‐Moshinsky oscillator (DMO). The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here we make an effort to present the subject in chronological order and also in increasing degree of complexity. We start our discussion with the seminal paper by Moshinsky and Szczepaniak and the immediate implications stemming from it. Then we analyze the extensions of this model to many particles. The one‐particle DMO is revisited in the light of the Jaynes‐Cummings model in quantum optics and exactly solvable extensions are presented. Applications and implementations in hexagonal lattices are given, with a particular emphasis in the emulation of graphene in electromagnetic billiards.
The Dirac‐Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes‐Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.
An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.