Nikodem Szpak

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

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.

Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation

We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation utt − uxx + u − |u|2αu = 0 on the line. Using mixed numerical and analytical methods we find that solutions starting from even initial data, fine-tuned to the threshold, are trapped by the static solution S for intermediate times. The details of trapping are shown to depend on the power α, namely, we observe fast convergence to S for α > 1, slow convergence for α = 1, and very slow (if any) convergence for 0 2) by Krieger, Nakanishi, and Schlag [“Global dynamics above from the ground state energy for the one-dimensional NLKG equation,” preprint arXiv:1011.1776 [math.AP]].We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation utt − uxx + u − |u|2αu = 0 on the line. Using mixed numerical and analytical methods we find that solutions starting from even initial data, fine-tuned to the threshold, are trapped by the static solution S for intermediate times. The details of trapping are shown to depend on the power α, namely, we observe fast convergence to S for α > 1, slow convergence for α = 1, and very slow (if any) convergence for 0 2) by Krieger, Nakanishi, and Schlag [“Global dynamics above from the ground state energy for the one-dimensional NLKG equation,” preprint arXiv:1011.1776 [math.AP]].

Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect

While the Sauter-Schwinger effect describes nonperturbative electron-positron pair creation from vacuum by a strong and slowly varying electric field

Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space

E_{\mathrm{strong}}

Linear and nonlinear tails II: exact decay rates in spherical symmetry

via tunneling, the dynamically assisted Sauter-Schwinger effect corresponds to a strong (exponential) enhancement of the pair-creation probability by an additional weak and fast electric or electromagnetic pulse

Linear and nonlinear tails I: general results and perturbation theory

E_{\mathrm{weak}}

Spontaneous emission of light from atoms: the model

. Using the WKB and worldline instanton method, we find that this enhancement mechanism strongly depends on the shape of the fast pulse. For the Sauter profile

Spontaneous particle creation in time-dependent overcritical fields

1/\cosh^2(\omega t)

Late-time attractor for the cubic nonlinear wave equation

considered previously, the threshold frequency

Asymptotics from scaling for nonlinear wave equations

\omega_{\mathrm{crit}}