We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron–positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations . Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose–Einstein condensates interacting with fermionic atoms. Numerical calculations based on functional integral techniques give a unique access to the physical parameters required to realize QED phenomena in a cold atom experiment. In particular, we use our approach to consider quantum link models in a yet unexplored parameter regime and give bounds for their ability to capture essential features of the physics . The results suggest a paradigmatic change towards realizations using coherent many-body states for quantum simulations of high-energy particle physics phenomena.
We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron–positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations . Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose–Einstein condensates interacting with fermionic atoms. Numerical calculations based on functional integral techniques give a unique access to the physical parameters required to realize QED phenomena in a cold atom experiment. In particular, we use our approach to consider quantum link models in a yet unexplored parameter regime and give bounds for their ability to capture essential features of the physics . The results suggest a paradigmatic change towards realizations using coherent many-body states for quantum simulations of high-energy particle physics phenomena.
We discuss the experimental engineering of model systems for the description of quantum electrodynamics (QED) in one spatial dimension via a mixture of bosonic 23 Na and fermionic 6 Li atoms. The local gauge symmetry is realized in an optical superlattice, using heteronuclear boson–fermion spin-changing interactions which preserve the total spin in every local collision. We consider a large number of bosons residing in the coherent state of a Bose–Einstein condensate on each link between the fermion lattice sites, such that the behavior of lattice QED in the continuum limit can be recovered. The discussion about the range of possible experimental parameters builds, in particular, upon experiences with related setups of fermions interacting with coherent samples of bosonic atoms. We determine the atomic system’s parameters required for the description of fundamental QED processes, such as Schwinger pair production and string breaking. This is achieved by benchmark calculations of the atomic system and of QED itself using functional integral techniques. Our results demonstrate that the dynamics of one-dimensional QED may be realized with ultracold atoms using state-of-the-art experimental resources. The experimental setup proposed may provide a unique access to longstanding open questions for which classical computational methods are no longer applicable.
Predicting the quantum dynamics of charged matter interacting with dynamical gauge fields poses an outstanding challenge in theoretical physics. Lacking a generally applicable computational method, quantum simulators offer a promising alternative. \n \nIn this thesis, we contribute to the quantum simulation of high-energy physics, focusing on the platform of ultracold atoms. Using Wilson fermions, we propose to improve implementations of lattice gauge theories based on mixtures of cold atoms in optical lattices. Numerical benchmarks indicate that this makes the realization of Schwinger pair production feasible with current technology. Our proposal is modular and an elementary building is demonstrated experimentally. We further identify dynamical topological transitions, which we discovered in the massive Schwinger model, as a suitable target for quantum simulators. Defining a gauge-invariant order parameter, these transitions are shown to persist beyond weak coupling. \n \nIn the second part of this thesis, we develop a framework for analyzing quantum simulators in terms of experimentally accessible irreducible correlation functions at equal times. We verify this approach numerically for the sine-Gordon model in thermal equilibrium, quantum simulated by two tunnel-coupled superfluids. Finally, we apply our analysis to the non-equilibrium dynamics of a spinor Bose gas, revealing suppressed effective interactions in a strongly-correlated infrared regime.
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.
In the context of quantum electrodynamics, a strong electric field can trigger the production of particle-antiparticle pairs, a phenomenon known as the Schwinger effect. In practical experimental scenarios, producing a pair requires quantum tunneling of particles over a long distance, thus suppressing the production rate and making this process very challenging to observe. Here we report an experimental investigation, in a cold-atom quantum simulator, of the effect of the external background field on pair production from the infinite-mass vacuum in a 1+1D U(1) lattice gauge theory in its quantum link model formulation, which we address through a genuine out-of-equilibrium protocol. The ability to tune the background field allows us to study pair production in a favorable regime of a large production rate. Furthermore, we probe the time evolution of the model in the zero fermion mass limit. We find that the energy spectrum of the time-evolved observables displays excitation peaks analogous to the (massive) bosonic modes of the Schwinger model and whose phenomenology can be interpreted as a string inversion mechanism. Our Letter opens the door to quantum-simulation experiments that can controllably tune the production of pairs and manipulate their far-from-equilibrium dynamics.
One of the fundamental predictions of Quantum Electrodynamics (QED) is the spontaneous creation of particle--antiparticle pairs from vacuum in presence of a very strong electric field. Under these extreme conditions a strongly bound state can fetch an otherwise unobservable electron from the Dirac sea, leaving behind a hole representing a positron. Although generally known for many decades, the effect has not yet been demonstrated experimentally. We propose an analogue model of the quantum Dirac field, realized by ultra--cold fermionic atoms in an optical lattice, aiming at an experimental simulation of this intriguing non--perturbative phenomenon. Numerical simulations demonstrate the effect of spontaneous pair creation in the optical analogue system, in qualitative agreement with QED: in the adiabatic regime the vacuum can be destabilized only by supercritical fields exceeding a critical threshold.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems.
In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.