Abstract Relativistic quantum mechanics has been developed for nearly a century to characterize the high-energy physics in quantum domain, and various intriguing phenomena without low-energy counterparts have been revealed. Recently, with the discovery of Dirac cone in graphene, quantum materials and their classical analogies provide the second approach to exhibit the relativistic wave equation, making large amounts of theoretical predications become reality in the lab. Here, we experimentally demonstrate a third way to get into the relativistic physics. Based on the extended one-dimensional Bose-Hubbard model, we show that two strongly correlated bosons can exhibit Dirac-like phenomena, including the Zitterbewegung and Klein tunneling, in the presence of giant on-site and nearest-neighbor interactions. By mapping eigenstates of two correlated bosons to modes of designed circuit lattices, the interaction-induced Zitterbewegung and Klein tunneling are verified by measuring the voltage dynamics. Our finding not only demonstrates a way to exhibit the relativistic physics, but also provides a flexible platform to further investigate many interesting phenomena related to the particle interaction in experiments.
Abstract Relativistic quantum mechanics has been developed for nearly a century to characterize the high-energy physics in quantum domain, and various intriguing phenomena without low-energy counterparts have been revealed. Recently, with the discovery of Dirac cone in graphene, quantum materials and their classical analogies provide the second approach to exhibit the relativistic wave equation, making large amounts of theoretical predications become reality in the lab. Here, we experimentally demonstrate a third way to get into the relativistic physics. Based on the extended one-dimensional Bose-Hubbard model, we show that two strongly correlated bosons can exhibit Dirac-like phenomena, including the Zitterbewegung and Klein tunneling, in the presence of giant on-site and nearest-neighbor interactions. By mapping eigenstates of two correlated bosons to modes of designed circuit lattices, the interaction-induced Zitterbewegung and Klein tunneling are verified by measuring the voltage dynamics. Our finding not only demonstrates a way to exhibit the relativistic physics, but also provides a flexible platform to further investigate many interesting phenomena related to the particle interaction in experiments.
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.
The Dirac equation elucidates fundamental physical principles and predicts significant physical phenomena. Its simulation further offers explanations for subsequent physics observations. We map the 3+1-dimensional Dirac equation onto the first excited manifold of four qubits to simulate the internal four-component spinor dynamics. Additionally, we simulate two intriguing and challenging-to-implement physical phenomena: the Zitterbewegung effect and the Sauter-Schwinger effect. Compared to previous simulations, our system provides a larger parameter space, allowing for a more comprehensive exploration of physical properties. This work enhances our understanding of spinor dynamics. The Dirac equation, one of the most fundamental equations in relativistic quantum mechanics, has influenced diverse research fields. The authors demonstrate an analogue simulation of the 3+1-dimensional Dirac equation by applying parametric modulations in superconducting circuits.
Two-dimensional massive Dirac systems feature a gapped Dirac-cone dispersion central to a broad range of phenomena in condensed-matter and topological physics. While quantum simulations have demonstrated one-dimensional Dirac dynamics and two-dimensional massless Weyl dynamics, programmable simulation of massive two-dimensional Dirac dynamics remains experimentally unexplored. Here, we realize a programmable two-dimensional free Dirac Hamiltonian in circuit QED, with independently tunable spin-momentum couplings and mass, using a single Rabi-driven qubit coupled to two modes of a multimode cavity. Using this Hamiltonian, we observe rotational Zitterbewegung of a two-dimensional massive Dirac particle and its dependence on the effective mass. Time-dependent master-equation simulations incorporating measured decoherence, corrections beyond the rotating-wave approximation (RWA), and anharmonicity of the transmon reproduce the observed dynamics. Our results establish multimode circuit QED as a compact, programmable platform for higher-dimensional relativistic quantum dynamics and provide a foundation for exploring dynamical and topological phenomena in gapped Dirac systems.
As the characteristic dimensions of a physical system shrink to the nanometer scale, its behavior is governed primarily by quantum mechanics rather than by classical laws. In this regime, effects such as barrier tunnelling, energy quantization, and quantum coherence play a central role in how nanoscale devices function. These phenomena are particularly prominent in platforms such as graphene and semiconductor quantum dots, where they have a pronounced impact on transport properties, optical behavior, and overall device performance. In parallel, lattice-based many-body models offer a concise theoretical framework for describing collective quantum states in engineered structures. The present work provides a conceptually oriented survey that links quantum phenomena at the nanoscale to two benchmark lattice Hamiltonians, namely the Jaynes-Cummings-Hubbard (JCH) and Bose-Hubbard (BH) models. The approach is qualitative and literature-based: results from quantum optics, cold-atom physics, and condensed-matter research are combined to interpret how the parameters of these models relate to experimentally tunable quantities, such as coupling strengths, confinement scales, and interaction energies. The main outcome of the review is threefold. First, tunnelling, graphene, and quantum dots can be viewed as natural settings where effective Hubbard-type descriptions arise. Second, despite describing different degrees of freedom-hybrid light-matter polaritons in the JCH case and interacting bosons in the BH case, both models display analogous phase structures with insulating and superfluid-like regimes. Third, reliable implementation of these phases in nanotechnological devices requires a careful mapping between abstract Hamiltonian parameters and specific design variables. The discussion indicates that JCHand BH-type models should be regarded not only as abstract theoretical constructs but also as practical tools for guiding the design of future quantum technologies. Extensions to driven-dissipative dynamics and topological band structures are identified as promising directions for next-generation quantum simulators and nanoscale sensors. Keywords: quantum tunnelling, graphene, quantum dots, Jaynes-Cummings-Hubbard model, Bose-Hubbard model, quantum simulators
Relativistic wave equations, such as Dirac, Weyl or Maxwell equations, are fundamental equations which we use to describe the dynamics of the microscopic particles. On the other hand, recent experimental and theoretical studies have shown that almost all parameters in cold atomic systems are precisely tunable, so the cold atom systems are considered as an ideal platform to perform quantum simulations. It can be used to study some topics in high energy and condensed matter physics. In this article, we will first introduce the ideas and methods for engineering the Hamiltonian of atoms, mainly related to the theories of laser-assisted tunneling. Based on these methods, one can simulate the equations of motion of relativistic particles and observe some interesting behaviors which are hard to be observed in other systems. The article reviews these recent advances.
We have calculated normalized wave function solutions to the time-dependent Dirac equation on a space-time lattice grid. Using these solutions we systematically explore phenomena that are consistent with the classical relativistic Liouville phase space approach and those that do not have a direct classical counterpart. The examples reviewed are the paradoxical Zitterbewegung, the time-resolved Klein-paradox, the dynamics of spin in an inhomogeneous magnetic field, the suppression of the spatial spreading rate and new dynamical features that occur close to relativistic resonances.