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

Szpak, Nikodem; Schützhold, Ralf

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

Cited by 45 publications

(58 citation statements)

References 70 publications

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“…In order to write down the time-evolution in Dirac theory, the plane wave solutions of the Dirac equation (7) are to be considered. These are usually obtained by applying the plane waves e kx i at the Hamiltonian and solving the eigenvector and eigenvalue problem of the Hamiltonian matrix.…”

Section: Time Evolution Of the Effective Dirac Equationmentioning

confidence: 99%

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Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

et al. 2015

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Strong field processes which occur in intense laser fields are a test area for relativistic quantum field theory, but difficult to study experimentally and theoretically. Thus, modelling relativistic quantum dynamics and therewith the Dirac equation can help to understand quantum field theory. We develop a dynamic description of an effective Dirac theory in metamaterials in which the wave function is modelled by the corresponding electric and magnetic field in the metamaterial. This electromagnetic field can be probed in the experimental setup, which means that the wave function of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion which establishes the identification of Dirac spinors with single-frequency excitations of the electromagnetic field in the metamaterial. We check the validity of our relativistic quantum dynamics simulation by demonstrating the emergence of Zitterbewegung and verifying it with an analytic solution.OPEN ACCESS RECEIVED waveguide operates in the microwave regime, the simulated wave function can be directly probed in the experiment. But only quasi-stationary field configurations have been investigated and the question arises, whether the time-independent description in terms of frequency-eigensolutions is capable of forming dynamics which correspond to the Dirac equation.Here, we extend the quasi-static theory to a dynamic description of an effective Dirac equation (section 2) and use it for the demonstration of the Zitterbewegung in theory. In the sections 2.1 and 2.2 we repeat the already established description [38] of the Maxwell equations in metamaterials and show how solutions of the Dirac equation can be deduced. Next, we formulate a formal solution of the Maxwell equations by an expansion in plane-wave solutions in section 2.3. This solution can be identified with the unitary time-evolution of the Dirac equation, which is discussed in section 2.4, in which we also give an explicit mapping between the electromagnetic field and the Dirac wave-function in frequency-and momentum space. The effective parameters for the mass and the speed of light of the emulated Dirac equation depend on the metamaterial and are derived in section 2.5. In section 3 we refer back to the Maxwell equations for deriving boundary conditions, with which electromagnetic input pulses can be injected at the metamaterial interfaces in our simulation.After the introduction of the theory foundations, we describe the numerical implementation in section 4, in which we also consider the properties of periodic boundary conditions which are implied by our simulation method.In the results section 5, we present the metamaterial simulations in three kinds of dynamical scenarios, in which we first consider the easiest possible setup for a Zitterbewegung with a Gaussian wave packet excitation 5.1. This setup is modified into a counterpropagating excitation, such that an experimental realization might be more feasible 5.2 and finally we also account for the influence of t...

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Section: Time Evolution Of the Effective Dirac Equationmentioning

confidence: 99%

“…These are usually obtained by applying the plane waves e kx i at the Hamiltonian and solving the eigenvector and eigenvalue problem of the Hamiltonian matrix. The left-hand side of the Dirac equation (7) turns into the matrix…”

Section: Time Evolution Of the Effective Dirac Equationmentioning

confidence: 99%

Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

et al. 2015

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“…This gives, using the scalar products introduced above Eqs. (17) to (19), ||u n+1 || 2 − ||u n || 2 ∆t = − (u n+1 + u n ; v n ) 0,− − (u n+1 + u n ;…”

Section: Appendix B Derivation Of a Functional For The Norm Which Ismentioning

confidence: 99%

“…Layered high-T c systems may be seen as an example in the wider sense [15]. Optical lattices also constitute a rich play ground for the engineering of 2D physics with the possibility of tuning various parameters and therewith controlling atom localization and effective many-body interactions [17][18][19]. Surfaces of solids in general provide a natural environment for the study of (quasi-) 2D phenomena, with a remarkable recent example provided by the topologically protected 2D metallic surface states of TIs.…”

Section: Introductionmentioning

confidence: 99%

Staggered grid leap-frog scheme for the Dirac equation

Hammer

Pötz

2014

Computer Physics Communications

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A numerical scheme utilizing a grid which is staggered in both space and time is proposed for the numerical solution of the (2+1)D Dirac equation in presence of an external electromagnetic potential. It preserves the linear dispersion relation of the free Weyl equation for wave vectors aligned with the grid and facilitates the implementation of open (absorbing) boundary conditions via an imaginary potential term. This explicit scheme has second order accuracy in space and time. A functional for the norm is derived and shown to be conserved. Stability conditions are derived. Several numerical examples, ranging from generic to specific to textured topological insulator surfaces, demonstrate the properties of the scheme which can handle general electromagnetic potential landscapes.

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“…Electric fields on this scale are not experimentally accessible; even the largest laboratory fields produced by ultrashort laser pulses [6] fall short, making direct observation of pair creation out of reach of current experiments. Subsequently, analog experiments have been proposed that simulate high-field effects with laboratory accessible energy scales in cold atoms [7][8][9][10], graphene [11][12][13][14][15][16], and other condensed matter systems [12,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Sauter–Schwinger effect with a quantum gas

Piñeiro

Genkina

et al. 2019

New J. Phys.

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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 ≈10 18 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.

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

Cited by 45 publications

References 70 publications

Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

Staggered grid leap-frog scheme for the Dirac equation

Sauter–Schwinger effect with a quantum gas

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