Relativistic wave equations, such as Dirac, Weyl or Maxwell equations, are fundamental equations which we use to describe the dynamics of the microscopic particles. On the other hand, recent experimental and theoretical studies have shown that almost all parameters in cold atomic systems are precisely tunable, so the cold atom systems are considered as an ideal platform to perform quantum simulations. It can be used to study some topics in high energy and condensed matter physics. In this article, we will first introduce the ideas and methods for engineering the Hamiltonian of atoms, mainly related to the theories of laser-assisted tunneling. Based on these methods, one can simulate the equations of motion of relativistic particles and observe some interesting behaviors which are hard to be observed in other systems. The article reviews these recent advances.
Relativistic wave equations, such as Dirac, Weyl or Maxwell equations, are fundamental equations which we use to describe the dynamics of the microscopic particles. On the other hand, recent experimental and theoretical studies have shown that almost all parameters in cold atomic systems are precisely tunable, so the cold atom systems are considered as an ideal platform to perform quantum simulations. It can be used to study some topics in high energy and condensed matter physics. In this article, we will first introduce the ideas and methods for engineering the Hamiltonian of atoms, mainly related to the theories of laser-assisted tunneling. Based on these methods, one can simulate the equations of motion of relativistic particles and observe some interesting behaviors which are hard to be observed in other systems. The article reviews these recent advances.
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.
We offer here a brief introduction to the idea of quantum simulations with cold atomic gases, with focus on the recent efforts towards artificial gauge potentials and fields.This is mainly intended as a sort of "pedestrian guide" for people not yet working in the field, but curious to get a first contact with it; longer and deeper reviews are addressed for deeper details.As a special case, we focus here on reviewing some own previous contributions about a flexible toolbox based on bichromatic optical lattices and Raman assisted tunnelling.Such a scheme would allow good control on the mass and kinetic terms of a lattice Hamiltonian in different effective dimensions.If realized with fermionic atoms, the low-energy sector effectively describes their relativistic dynamics in a variety of situations, among which 3D axion electrodynamics.We conclude with a short discussion of possible future directions. QCD-TNT-III-From quarks and gluons tohadronic matter: A bridge too far?, 2-6 September, 2013 European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Villazzano, Trento (Italy) * Speaker.
Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.
We present our recent results in the rapidly developing field of synthetic magnetic fields for atoms and photons, in optical lattices and photonic structures, respectively. First, we show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three- dimensional optical lattices [1]. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions [1], which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected 'Fermi arc' surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well-within experimental reach with an extension of techniques recently used in ultracold gases [2]. We also present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [2]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two- dimensional dielectric photonic lattices. We propose the implementation of the Harper- Hofstadter Hamiltonian in these photonic lattices [2]. [1] Dubcek et al., Phys. Rev. Lett. 114, 225301 (2015). [2] Dubcek et al., New Journal of Phys., New J. Phys. 17, 125002 (2015).
The dispersion relation of ultracold atoms in variably shaped optical lattices can be tuned to resemble that of a relativistic particle, i.e. be linear instead of the usual nonrelativistic quadratic dispersion relation of a free atom. Cold atoms in such a lattice can be used to carry out quantum simulations of relativistic wave equation predictions. We begin this article by describing a Raman technique that allows to selectively load atoms into a desired Bloch band of the lattice near a band crossing. Subsequently, we review two recent experiments with quasirelativistic rubidium atoms in a bichromatic lattice, demonstrating the analogues of Klein tunnelling and Veselago lensing with ultracold atoms, respectively.
"The many weird properties of quantum mechanics at the very small scale have led to surprising and useful discoveries that manifest at the macroscopic level, like the quantum Hall effect and high temperature superconductivity. Yet trying to understand the origin of correlated behavior from interacting quantum systems via classical simulation requires an infeasible level of computing power. Instead, we can use an easily tunable, clean quantum system as a quantum simulation of a more unwieldy system, building the same model to study the same physics, but in a more controlled environment. Our field of cold neutral atoms in optical lattices has seen success over many years as a platform for quantum simulation of various lattice models from condensed matter physics. The recent (2015) implementation of lattices not in position, but in a synthetic dimension by coupling individual quantum states with lasers has led to a more bottom-up approach to engineering lattice models. In this thesis, we present our ""momentum-space lattice"" technique in which we use individual laser frequencies to couple the momentum states of a rubidium-87 Bose-Einstein condensate, in order to create lattices with site-by-site and link-by-link precision. This technique is simple to implement experimentally, requiring just two additional common optical components (acousto-optic modulators) compared to a real-space lattice, yet is incredibly versatile. Using momentum-space lattices, we have studied the physics of artificial magnetic fields, disorder and pseudodisorder-induced localization, and atomic interactions across eight works described in this thesis. More interesting are the not-so-well-known effects that arise in the interplay among these three components of topology, disorder, and interactions, and we have made headway towards studying physics in this regime. To be more specific, in our studies we have generated an artificial magnetic field for neutral atoms, and directly observed the resulting chiral currents in both a square ladder and zigzag lattice geometry. We have further monitored the quantum walk behavior of atoms under disordered and pseudodisordered lattices, observing a transition to localization under a quasiperiodic potential. We have been able to introduce a tunable energy dependence to this localization transition (single-particle mobility edge) in two ways: with the addition of more tunneling pathways, and by modifying the form of the potential. Finally, we have studied the effects of nonlinear inter-atomic interactions in the momentum-space lattice, observing self-trapping in a double well system as well as on a full lattice, showing a skewed current-phase relationship in an analog to Josephson junction arrays, and investigating an interaction-induced shift in localization behavior under pseudodisorder. In constructing the momentum-space lattice apparatus, Eric, Bryce, and I have created a promising new platform for Hamiltonian engineering. The studies described here not only show off the capabilities of the technique, but also realize new models, reveal new physics, and provide a new perspective complementary to both real-space lattice techniques and real materials. We have observed topological edge states more directly than previous works and engineered precise lattice parameter variations unavailable to other techniques, and yet the best is still to come. With our ongoing experimental upgrades comes access to the regime of strong inter-particle interactions, which promises more challenging yet more rewarding experiments."