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arXiv:2011.08496

Demonstration of imaginary-mass particles by optical simulation in non-Hermitian systems

Wange Song, Shenglun Gao, Hanmeng Li, Chen Chen, Shengjie Wu, Shining N. Zhu, Tao Li

Published Nov 17, 2020• 2 citations

Abstract

Unifying quantum mechanics and special relativity, the Dirac equation describes the behaviour of relativistic quantum particles, including imaginary-mass particles with faster-than-light speeds (e.g., tachyon). However, experimental searches for such particles remain negative so far. Fortunately, there are possibilities to investigate the relativistic quantum effects by quantum simulations using a controllable system. However, these simulations are mostly explored in closed physical systems that hinders the demonstration of imaginary-mass particles, whereas the general open framework would promise more possibilities in quantum simulations. Here, we reveal that the dynamic behaviors of imaginary-mass particles can be mapped to the transfer of wave packet in a non-Hermitian silicon optical lattice. We experimentally demonstrate a super-divergent dynamics of tachyon that travels faster than massless particles (e.g., photon). Besides, our simulation suggests another kind of imaginary-mass particles that have rarely been explored, which show non-divergent behaviors with imaginary energy. It is the first experimental quantum simulation being able to observe the imaginary-mass particles that have never been experimentally verified. Our work provides a fully controllable and extensible platform to investigate relativistic quantum phenomena at a chip-scale level, which would inspire more insightful explorations in quantum effects with non-Hermiticity.

DOI: 10.48550/arxiv.2011.08496

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The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in

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dimensions onto a multilevel superconducting Josephson circuit. Resonant drives determine the particle mass and momentum, and the quantum state represents the internal spinor dynamics which are cast in the language of multilevel quantum optics. Zitterbewegung and wave-packet dynamics are reproduced. The degeneracy of the Dirac spectrum corresponds to a degeneracy of bright and dark states within the system, and particle spin and helicity are employed to interpret the multilevel dynamics. We also simulate the Schwinger mechanism of electron-positron pair production by introducing an analogous electric field as a doubly degenerate Landau-Zener problem. All proposed measurements can be performed well within typical decoherence times. This work opens an avenue for experimental study of the Dirac equation and provides a tool for control of complex dynamics in multilevel systems.

Hermiticity has long been a cornerstone of quantum theory, ensuring the conservation of probability and real energy spectra. Recent advances in non-Hermitian physics have revealed that this requirement can be relaxed, giving rise to richer dynamics where the Hilbert space is endowed with a time-dependent inner product defined by a metric operator ρ ( t ) . This dynamical metric fundamentally reshapes quantum predictions, yet direct access to it on physical devices has remained elusive. Here, we bridge this gap by presenting general, platform-agnostic operator-dilation schemes that embed the metric formalism into closed Hermitian systems. Our proposed framework converts any time-dependent non-Hermitian Hamiltonian into a larger unitary evolution, bringing the theory from a purely mathematical curiosity into the experimentally testable realm. This permits the first controlled study of PT -symmetric and symmetry-broken regimes at arbitrarily long timescales. We demonstrate the power of this approach on a digital quantum simulator, showing that cutting-edge questions about non-Hermiticity are already within reach of today's noisy intermediate-scale quantum processors. Our results provide the first direct evidence of a dynamically evolving metric in a single qubit, establishing a new paradigm for simulating non-Hermitian quantum mechanics and opening the door to its realization in the laboratory.