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arXiv:1503.06802 · Physical Review A

Tachyon physics with trapped ions

Tony E. Lee, Unai Alvarez-Rodriguez, Xiao-Hang Cheng, Lucas Lamata, E. Solano

Published Sep 25, 2015• 34 citations
arXivHTMLPDF

Abstract

It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate Dirac tachyons with trapped ions. Quantum measurement on a Dirac particle simulated by a trapped ion causes it to have an imaginary mass so that it may travel faster than the effective speed of light. We show that a Dirac tachyon must have spinor-motion correlation in order to be superluminal. We also show that it exhibits significantly more Klein tunneling than a normal Dirac particle. We provide numerical simulations of realistic ion systems and show that our scheme is feasible with current technology.

DOI
10.1103/physreva.92.032129

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It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate Dirac tachyons with trapped ions. Quantum measurement on a Dirac particle simulated by a trapped ion causes it to have an imaginary mass so that it may travel faster than the effective speed of light. We show that a Dirac tachyon must have spinor-motion correlation in order to be superluminal. We also show that it exhibits significantly more Klein tunneling than a normal Dirac particle. We provide numerical simulations of realistic ion systems and show that our scheme is feasible with current technology.
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.
Simulating quantum phenomena in extreme spacetimes in the laboratory represents a powerful approach to explore fundamental physics in the interplay of quantum mechanics, quantum field theory, and general relativity. Here we propose to simulate the movement of a Dirac particle propagating with a superluminal velocity caused by the emergent Alcubierre warp drive spacetime using trapped ions. We demonstrate that the platform allows for observing the tilted light cone that manifests as a superluminal velocity, which is in agreement with the prediction of general relativity. Furthermore, the Zitterbewegung effect arising from relativistic quantum mechanics persists with the superluminal propagation and is experimentally measurable. The present scheme can be extended to simulate the Dirac equation in other exotic curved spacetimes, thus providing a versatile tool to gain insights into the fundamental limit of these extreme spacetimes.
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scattering and Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the 1+11+11+1 Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states of one ion, while its position and momentum are described by those of a collective motional mode. The second ion is used to build the desired potentials with high spatial resolution.
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.
Tachyons are Scalar Bosons that reside in our fourth dimensional spatial Universe. They are point particles with zero mass, zero charge, and zero spin. Based on the Lorentz Transformation for v > c, tachyons can travel backwards in time to enter our third dimensional spatial Universe and can travel faster than light speed, to transmit information instantaneously between two entangled particles, to change their spin values from a superposition state to a definitive up and down state. We will show that the laws of Quantum Mechanics can be retro-causal while the laws of Classical Mechanics must be causal.
This work presents a speculative theoretical model for a novel quantum gate inspired by the properties of tachyons, hypothetical particles associated with speeds greater than that of light. The research proposes the Tachyonic Phase Gate (TPG), a quantum gate based on non-Hermitian dynamics and PT symmetry, exploring how a tachyonic field could modify quantum states in ways inaccessible to conventional quantum gates. The article develops a description of the mathematical and conceptual architecture of the TPG, including its dynamic behavior, transitions between different physical phases, and effects on the states of individual qubits and entangled systems. A tachyonic entanglement gate for two qubits is also introduced, and potential connections with phenomena such as closed time-curves, relativistic causality, and advanced computational complexity are analyzed. Furthermore, the work compares TPG with standard quantum computing gates, showing that this approach could formally extend traditional models of quantum operations to non-unitary regimes inspired by imaginary mass physics and PT-symmetric systems. The study emphasizes that tachyons lack experimental evidence and that the proposed framework is explicitly speculative. However, some mathematical elements related to non-Hermitian dynamics and PT symmetry do have experimental support in modern optical systems, making the work a conceptual exploration of possible future extensions of quantum computing and theoretical physics.