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 full-fledged 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 non-abelian 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 non-abelian gauge theory (SU(2) - see ref. [5] - the figure is taken from there).

Publications (to date)

  1. Confinement and Lattice Quantum-Electrodynamic Electric Flux Tubes Simulated with Ultracold Atoms
    Erez Zohar, Benni Reznik
    Phys. Rev. Lett. 107, 275301 (2011)
    Preprint: arXiv: 1108.1562v2 [quant-ph]

  2. 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 [quant-ph]

  3. Topological Wilson-loop area law manifested using a superposition of loops
    Erez Zohar, Benni Reznik
    New J. Phys. 15 (2013) 043041
    Preprint: arXiv:1208.1012 [quant-ph]
    Accepted to New J. Phys.

  4. 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 [quant-ph]

  5. A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
    Erez Zohar, J. Ignacio Cirac, Benni Reznik
    Phys. Rev. Lett. 110, 125304 (2013)
    Preprint: arXiv:1211.2241 [quant-ph]

  6. 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 [quant-ph]

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

  1. Origin of the thermal radiation in a solid-state analogue of a black hole
    Benni Reznik
    Phys. Rev. D 62, 044044 (2000)
    Preprint: arXiv:gr-qc/9703076

  2. Methods for Detecting Acceleration Radiation in a Bose-Einstein Condensate
    Alex Retzker, J. Ignacio Cirac, Martin B. Plenio and Benni Reznik
    Phys. Rev. Lett. 101, 110402 (2008)
    Preprint: arXiv:0709.2425 [quant-ph]

  3. 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 [quant-ph]

  4. Hawking radiation on an ion ring in the quantum regime
    Birger Horstmann, Ralf Sch├╝tzhold, Benni Reznik, Serena Fagnocchi and J. Ignacio Cirac
    New J. of Phys. 13 045008 (2011)
    Preprint: arXiv:1008.3494 [quant-ph]

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.