What are quantum Simulations?
The concept of quantum simulations was born due to an idea of Richard Feynman, who suggested
to simulate quantum systems using analog quantum computers. It took several years for this idea
to evolve and become a rich, fast growing research area, thanks to the significant progress achieved
in the field of quantum computation: many methods, both theoretical and experimental, have been
developed over the recent decads, leading to the possibility of handling and controlling quantum
information in robust and efficient ways. Experimental systems such as trapped ions, cold atoms,
Josephson junctions and Rydberg atoms are now fully controllable in laboratories. Although the
implementation of a fullfledged quantum computer using such systems still requires both theoretical
and experimental progress, they are sufficient for the purpose of mimicking the dynamics of many
other quantum systems, hence setting the way for quantum simulation.
The advantages of quantum simulation are numerous: first, one can use it to study physical
systems which are not experimentally accessible (systems of large or small scales, for example), or
to observe the physical properties of "unreal" physical systems, which are not known to be found
in nature, but can be mapped to the simulating systems. So far, a lot of quantum simulations were
suggested, and some were even experimentally implemented. The simulated systems come from
almost every area of physics: condensed matter models, gravity and general relativity, relativistic
quantum mechanics and even particle physics and quantum field theory  which is the physics we
simulate, and specifically gauge theories. This is a new direction in quantum simulations: as many
quantum simulations of condensed matter models have been already proposed (and even realized),
quantum simulations of high energy physics and QFT are a newer branch.


The optical lattice structure required for our first proposed method of simulating a pure gauge U(1) theory (see ref. [1]  the figure is taken from there).

Quantum simulations of gauge theories
Gauge theories, manifesting the important and nontrivial gauge symmetry, are in the core of
the standard model of particle physics, where gauge bosons are the force mediators. Our research
focuses on simulating gauge theories with ultracold atoms in optical lattices: design of the atomic
Hamiltoian and interactions; Tailoring the specifically needed interactions and processes, either
"naturally" or effectively in order to obtain gauge invariance; and finally the way to measure and
observe interesting QFT phenomena  altogether forming the construction of a mapping between
the atomic and the QFT Hamiltonians.
Our simulation proposals include simulations of compact QED  a U(1) lattice gauge theory, which is
the most simple nontrivial continuous gauge theory manifesting confinement. We have used two
approaches, using either Bose Einstein condensates or single atoms, to simulate both pure gauge
and gauge field coupled to dynamic fermions. The suggested simulations are in 2+1 dimensions,
and their goal is to observe flux tubes and loops, and also the breaking of a flux tube in the case of
the dynamic matter theory. A newer proposal focuses on simulating a nonabelian gauge theory  SU(2),
which is a "toy model" with qualitative features and phenomena common to the SU(3) gauge theory of QCD.


The optical lattice structure required for our simulation method of a nonabelian gauge theory (SU(2)  see ref. [5]  the figure is taken from there).

Publications (to date)
 Confinement and Lattice QuantumElectrodynamic Electric Flux Tubes Simulated with Ultracold Atoms
Erez Zohar, Benni Reznik Phys. Rev. Lett. 107, 275301 (2011) Preprint: arXiv: 1108.1562v2 [quantph]
 Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
Erez Zohar, J. Ignacio Cirac, Benni Reznik Phys. Rev. Lett. 109, 125302 (2012) Preprint: arXiv: 1204.6574 [quantph]
 Topological Wilsonloop area law manifested using a superposition of loops
Erez Zohar, Benni Reznik
New J. Phys. 15 (2013) 043041
Preprint: arXiv:1208.1012 [quantph]
Accepted to New J. Phys.
 Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
Erez Zohar, J. Ignacio Cirac, Benni Reznik
Phys. Rev. Lett. 110, 055302 (2013) Preprint: arXiv:1208.4299 [quantph]
 A coldatom quantum simulator for SU(2) YangMills lattice gauge theory
Erez Zohar, J. Ignacio Cirac, Benni Reznik
Phys. Rev. Lett. 110, 125304 (2013) Preprint: arXiv:1211.2241 [quantph]
 Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
Erez Zohar, J. Ignacio Cirac, Benni Reznik
Phys. Rev. A 88, 023617 (2013)
Preprint: arXiv:1303.5040 [quantph]
A significant part of this research is performed in collaboration with the Theory division of Max Planck Institute for Quantum Optics, headed by Prof. J. Ignacio Cirac.
Quantum simulations of gravitational effects


A schematic representation of the ions simulating a black hole (see ref. [9]  the figure is taken from there).

Publications
 Origin of the thermal radiation in a solidstate analogue of a black hole
Benni Reznik
Phys. Rev. D 62, 044044 (2000) Preprint: arXiv:grqc/9703076
 Methods for Detecting Acceleration Radiation in a BoseEinstein Condensate
Alex Retzker, J. Ignacio Cirac, Martin B. Plenio and Benni Reznik
Phys. Rev. Lett. 101, 110402 (2008) Preprint: arXiv:0709.2425 [quantph]
 Hawking Radiation from an Acoustic Black Hole on an Ion Ring
Birger Horstmann, Benni Reznik, Serena Fagnocchi and J. Ignacio Cirac Phys. Rev. Lett. 104, 250403 (2010) Preprint: arXiv:0904.4801 [quantph]
 Hawking radiation on an ion ring in the quantum regime
Birger Horstmann, Ralf Schützhold, Benni Reznik, Serena Fagnocchi and J. Ignacio Cirac New J. of Phys. 13 045008 (2011) Preprint: arXiv:1008.3494 [quantph]
A significant part of this research is performed in collaboration with the Theory division of Max Planck Institute for Quantum Optics, headed by Prof. J. Ignacio Cirac.
