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.
Highlights
Relativistic quantum mechanics has been developed for nearly a century to characterize the high-energy physics in quantum domain, and various intriguing phenomena without lowenergy counterparts have been revealed
With the advantage of diversity and flexibility for circuit elements, except for the above designed LC circuit with matched stationary eigen-equations to the 1D two-boson system, we can design another kind of electric circuit, which is based on resistances and capacitances, to precisely match the time-dependent Schrödinger equation of two correlated bosons
We have experimentally demonstrated that electric circuits can be used as a flexible simulator to investigate the interaction-induced relativistic effects of doublons, whose dispersion contains two minibands being analogous to the positive- and negative-energy branches of the 1D Dirac equation
Summary
Relativistic quantum mechanics has been developed for nearly a century to characterize the high-energy physics in quantum domain, and various intriguing phenomena without lowenergy counterparts have been revealed. The two most famous phenomena are Zitterbewegung, referring to the rapid trembling motion of a free Dirac electron, and Klein tunneling, where a below-barrier Dirac electron can pass through the large potential step without the exponential damping These intriguing phenomena were already proposed for high-energy electrons, the experimental observation of relativistic effects is still an intractable challenge for particle physics. Except for the quantum platform, many classical systems have been proposed to mimic the conical singularity of energy bands in graphene, and the classical wave analogs of relativistic phenomena have been fulfilled latterly20–28 These direct observations of relativistic effects in low-energy systems prove the predicted relativistic effects in high-energy physics, and promote many applications in the field of signal processing, supercollimated beams, and communications. Our proposal provides a useful laboratory tool to investigate and visualize many interesting effects related to the particle interaction, and possesses a great potential in the field of intergraded circuit design and electronic signal control
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