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arXiv:1207.7272 · Physical Review Letters

Mimicking Interacting Relativistic Theories with Stationary Pulses of Light

Dimitris G. Angelakis, Ming-Xia Huo, Darrick E. Chang, L. C. Kwek, V. E. Korepin

Published Mar 5, 2013• 24 citations
arXivHTMLPDF

Abstract

One of the most well known relativistic field theory models is the Thirring model. Its realization can demonstrate the famous prediction for the renormalization of mass due to interactions. However, experimental verification of the latter requires complex accelerator experiments whereas analytical solutions of the model can be extremely cumbersome to obtain. In this work, following Feynman's original proposal, we propose an alternative quantum system as a simulator of the Thirring model dynamics. Here, the relativistic particles are mimicked, counterintuitively, by polarized photons in a quantum nonlinear medium. We show that the entire set of regimes of the Thirring model--bosonic or fermionic, and massless or massive--can be faithfully reproduced using coherent light trapping techniques. The correlation functions of the model can be extracted by simple probing of the coherence functions of the output light using standard optical techniques.

DOI
10.1103/physrevlett.110.100502

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One of the most well known relativistic field theory models is the Thirring model. Its realization can demonstrate the famous prediction for the renormalization of mass due to interactions. However, experimental verification of the latter requires complex accelerator experiments whereas analytical solutions of the model can be extremely cumbersome to obtain. In this work, following Feynman's original proposal, we propose an alternative quantum system as a simulator of the Thirring model dynamics. Here, the relativistic particles are mimicked, counterintuitively, by polarized photons in a quantum nonlinear medium. We show that the entire set of regimes of the Thirring model--bosonic or fermionic, and massless or massive--can be faithfully reproduced using coherent light trapping techniques. The correlation functions of the model can be extracted by simple probing of the coherence functions of the output light using standard optical techniques.
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We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
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Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.