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New Journal of Physics

Efficient protocol for exploring the quantum interference and entanglement of Dirac particles

Yuan Qiu, Ke-Xiong Yan, Junhao Lin, Jie Song, Ye‐Hong Chen, Yan Xia

Published Aug 1, 2025• 8 citations
Publisher

Abstract

Abstract We propose a protocol to effectively study the interference of Dirac particles in phase space. The negativity of the quasiprobability distribution in phase space and the entanglement between the internal and external degrees of freedom constitute the non-classical manifestations of this interference. The protocol makes use of a synthetic quantum Rabi model, which is obtained by applying a parametric drive to the Jaynes–Cummings model. When the parametric drive is almost resonant with the cavity frequency, the effective system Hamiltonian takes the same form as the one-dimensional Dirac particle Hamiltonian. We explore the quantum interference using this equivalent model and find that the interference pattern can occur even in the absence of the Zitterbewegung effect. In addition, we simulate the quantum behavior of Dirac particles encountering potential barriers through the simulation of Klein tunneling. These non-classical effects offer potential application in fields such as quantum computing.

DOI
10.1088/1367-2630/adf76f

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Abstract We propose a protocol to effectively study the interference of Dirac particles in phase space. The negativity of the quasiprobability distribution in phase space and the entanglement between the internal and external degrees of freedom constitute the non-classical manifestations of this interference. The protocol makes use of a synthetic quantum Rabi model, which is obtained by applying a parametric drive to the Jaynes–Cummings model. When the parametric drive is almost resonant with the cavity frequency, the effective system Hamiltonian takes the same form as the one-dimensional Dirac particle Hamiltonian. We explore the quantum interference using this equivalent model and find that the interference pattern can occur even in the absence of the Zitterbewegung effect. In addition, we simulate the quantum behavior of Dirac particles encountering potential barriers through the simulation of Klein tunneling. These non-classical effects offer potential application in fields such as quantum computing.
Abstract Although originally predicted in relativistic quantum mechanics, Zitterbewegung can also appear in some classical systems, which leads to the important question of whether Zitterbewegung of Dirac particles is underlain by a more fundamental and universal interference behavior without classical analogs. We here reveal such an interference pattern in phase space, which underlies but goes beyond Zitterbewegung , and whose nonclassicality is manifested by the negativity of the phase space quasiprobability distribution, and the associated pseudospin-momentum entanglement. We confirm this discovery by numerical simulation and an on-chip experiment, where a superconducting qubit and a quantized microwave field respectively emulate the internal and external degrees of freedom of a Dirac particle. The measured quasiprobability negativities agree well with the numerical simulation. Besides being of fundamental importance, the demonstrated nonclassical effects are useful in quantum technology.
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.
We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom, which offers unique opportunities for quantum information and quantum simulation. Here we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics are equivalent to that of a Dirac particle in 1+11+11+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.
We study the relations between massless Dirac fermions in an electromagnetic field and atoms in quantum optics. After getting the solutions for the energy spectrum, we show that it is possible to reproduce the 2D Dirac Hamiltonian, with all its quantum relativistic effects, in a controllable system such as a single trapped ion, through the Jaynes–Cummings and anti-Jaynes–Cummings models. Also we show that under certain conditions, the evolution of the Dirac Hamiltonian provides us with Rashba spin–orbit and linear Dresselhaus couplings. Considering the multimode multiphoton Jaynes–Cummings model interacting with N modes of an electromagnetic field prepared in general pure quantum states, we analyze the Rabi oscillation. Evaluating the time evolution of the Dirac position operator, we determine the Zitterbewegung frequency and the corresponding oscillating term as a function of the electromagnetic field.
Double-slit interference is one of the most fundamental quantum phenomena among photons and other particles. We propose a novel and realist quantum framework in which interference patterns in double-slit experiments arise not from wavefunction self-interference or collapse, but from causal non-local, quantized cavity-induced momentum exchange between the electron and the double-slit field potential. Unlike Copenhagen or Bohmian interpretations, our theory treats the electron as a deterministic, soliton-like entity governed by classical-like trajectories. The quantized potential of the slits—described via creation and annihilation operators—is responsible for discrete momentum transfer through coupling with cavity or barrier modes, modeled via octonionic algebra that differentiates internal particle structure from external field dynamics. The resulting interference pattern emerges from non-local, quantized interactions between the electron and field modes without invoking the probabilistic wavefunction. Our model aligns with experimental violations of Bell’s inequality and avoids conceptual paradoxes such as wavefunction collapse and self-interference. The framework makes several testable predictions, offering a promising new direction for understanding quantum interference with clearer physical realism.
A system evolving under the driven Jaynes–Cummings (JC) model will undergo a phase transition at a critical driving field amplitude. This transition is foreshadowed by a collapse of the quasienergy level spectra of the system and remains present as the model is extended to include a counter-rotating interaction. We study this critical response and obtain the eigenvalues and eigenstates of the extended model by presenting a correspondence between the JC model and a charged Dirac particle subject to an external electromagnetic field. Under this correspondence, the field and two-level system that compose the JC model map to the external and internal degrees of freedom describing the Dirac particle, respectively. The phases of the system below (above) the critical drive are then characterized by discrete (continuous) solutions, with the manipulations required to obtain these solutions appearing naturally as Lorentz transformations.