Quantum simulation of an extra dimension

We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest non-trivial realization of a fourth dimension corresponds to the creation of a bivolume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.Comment: 5 pages, 3 figures, revtex style;v2 minor changes, references adde

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

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 (QED) 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 of 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.Comment: 21 pages, 10 figure