Dirac Oscillator with Microwaves

C. Quesne

D. Dutta, Orlando Panella, P. Roy

Toshihiro Iwai, Boris I Zhilinskií

J. A. Franco-Villafañe, Emerson Sadurní, Sonja Barkhofen +3 more

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.

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.

Emerson Sadurní