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arXiv:1109.2426 · New Journal of Physics

Optical lattice quantum simulator for quantum electrodynamics in strong external fields: spontaneous pair creation and the Sauter–Schwinger effect

N Szpak, R Schützhold

Published Mar 1, 2012• 47 citations

Abstract

The spontaneous creation of electron–positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy–momentum relation for the Dirac fermions. This fundamental prediction of quantum electrodynamics has not yet been confirmed experimentally, as the generation of a sufficiently strong electric field extending over a large enough space–time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low-energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter–Schwinger effect. This motivates our proposal for a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.

DOI: 10.1088/1367-2630/14/3/035001

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The spontaneous creation of electron–positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy–momentum relation for the Dirac fermions. This fundamental prediction of quantum electrodynamics has not yet been confirmed experimentally, as the generation of a sufficiently strong electric field extending over a large enough space–time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low-energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter–Schwinger effect. This motivates our proposal for a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.

One of the fundamental predictions of Quantum Electrodynamics (QED) is the spontaneous creation of particle--antiparticle pairs from vacuum in presence of a very strong electric field. Under these extreme conditions a strongly bound state can fetch an otherwise unobservable electron from the Dirac sea, leaving behind a hole representing a positron. Although generally known for many decades, the effect has not yet been demonstrated experimentally. We propose an analogue model of the quantum Dirac field, realized by ultra--cold fermionic atoms in an optical lattice, aiming at an experimental simulation of this intriguing non--perturbative phenomenon. Numerical simulations demonstrate the effect of spontaneous pair creation in the optical analogue system, in qualitative agreement with QED: in the adiabatic regime the vacuum can be destabilized only by supercritical fields exceeding a critical threshold.

Ultracold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian (whose effective parameters can be tuned in a wide range) describing electrons and positrons in an external electric field. This analogy facilitates the experimental simulation of (so far unobserved) fundamental quantum phenomena such as the Schwinger effect, i.e., spontaneous electron-positron pair creation out of the vacuum by a strong electric field. Such an experiment would also test nonperturbative aspects of these lattice systems.

Abstract The creation of particle–antiparticle pairs from vacuum by a large electric field is at the core of quantum electrodynamics. Despite the wide acceptance that this phenomenon occurs naturally when electric field strengths exceed E c ≈ 1018 V m−1, it has yet to be experimentally observed due to the limitations imposed by producing electric fields at this scale. The high degree of experimental control present in ultracold atomic systems allow experimentalists to create laboratory analogs to high-field phenomena. Here we emulated massive relativistic particles subject to large electric field strengths, thereby quantum-simulated particle–antiparticle pair creation, and experimentally explored particle creation from ‘the Dirac vacuum’. Data collected from our analog system spans the full parameter regime from low applied field (negligible pair creation) below the Sauter–Schwinger limit, to high field (maximum rate of pair creation) far in excess of the Sauter–Schwinger limit. In our experiment, we perform direct measurements on an analog atomic system and show that this high-field phenomenon is well-characterized by Landau–Zener tunneling, well known in the atomic physics context, and we find full quantitative agreement with theory with no adjustable parameters.

We quantum-simulated particle-antiparticle pair production with a bosonic quantum gas in an optical lattice by emulating the requisite 1d Dirac equation and uniform electric field. We emulated field strengths far in excess of Sauter-Schwinger's limit for pair production in quantum electrodynamics, and therefore readily produced particles from "the Dirac vacuum" in quantitative agreement with theory. The observed process is equivalently described by Landau-Zener tunneling familiar in the atomic physics context.

We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron–positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations . Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose–Einstein condensates interacting with fermionic atoms. Numerical calculations based on functional integral techniques give a unique access to the physical parameters required to realize QED phenomena in a cold atom experiment. In particular, we use our approach to consider quantum link models in a yet unexplored parameter regime and give bounds for their ability to capture essential features of the physics . The results suggest a paradigmatic change towards realizations using coherent many-body states for quantum simulations of high-energy particle physics phenomena.