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Quantum simulator for the Schwinger effect with atoms in an optical lattice

Nikodem Szpak, Ralf Schützhold

Published Mar 2, 2011• 0 citations
OpenAlex

Abstract

Ultra-cold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian describing electrons and positrons in an external electric field. This 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.

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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.

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Ultra-cold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian describing electrons and positrons in an external electric field. This 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.
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.
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.
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.
The goal of this article is to review developments regarding the use of ultra-cold atoms as quantum simulators. Special emphasis is placed on relativistic quantum phenomena, which are presumably most interesting for the audience of this journal. After a brief introduction into the main idea of quantum simulators and the basic physics of ultra-cold atoms, relativistic quantum phenomena of linear fields are discussed, including Hawking radiation, the Unruh effect, cosmological particle creation, the Gibbons–Hawking and Ginzburg effects, super-radiance, Sauter–Schwinger and Breit–Wheeler pair creation, as well as the dynamical Casimir effect. After that, the focus is shifted to phenomena of non-linear fields, such as the sine–Gordon model, the Kibble–Zurek mechanism, false-vacuum decay, and quantum back-reaction. In order to place everything into proper context, the basic underlying mechanisms of these phenomena are briefly recapitulated before their simulators are discussed. Even though effort is made to provide a review as fair as possible, there can be no claim of completeness and the selection as well as the relative weights of the topics may well reflect the personal view and taste of the author.
The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.