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These direct observations of relativistic effects in low-energy systems not only prove the predicted relativistic effects in high-energy physics, but also promote many applications in the field of signal processing, supercollimated beams, and communications. Except for the quantum platform, many classical systems have also been proposed to mimic the conical singularity of energy bands in graphene, and the classical wave analogs of relativistic phenomena have been fulfilled latterly 20, 21, 22, 23, 24, 25, 26, 27, 28.
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Recently, the non-relativistic electrons in graphene monolayer were found to obey the massless relativistic dispersion known as the Dirac cone, leading to the realization of analogies to Zitterbewegung and Klein tunneling in low-energy condensed-matter physics and atom optics 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Meanwhile, the extremely high fields are required to accelerate the particle and a steep potential step should be constructed to observe the Klein tunneling.
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Because the trembling motion of a free relativistic electron has an extremely small amplitude (in the order of the Compton wavelength ~10 −12 m) and a high frequency (~10 21 Hz). Although these intriguing phenomena were already proposed for high-energy electrons, the experimental observation of relativistic effects is still an intractable challenge for particle physics. The two most famous phenomena are Zitterbewegung 2, referring to the rapid trembling motion of a free Dirac electron, and Klein tunneling 3, where a below-barrier Dirac electron can pass through the large potential step without the exponential damping. In 1928, the Dirac equation was proposed to describe the motion of fermionic particles in the relativistic region, and various interesting effects without low-energy counterparts were predicted afterwards 1. 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. 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. 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. Here, we experimentally demonstrate a third way to get into the relativistic physics. 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. 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.