Alessio Celi

Non-Abelian gauge fields and topological insulators in shaken optical lattices

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.

Synthetic gauge fields in synthetic dimensions.

We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the dimension provided by the internal atomic degrees of freedom, yielding a synthetic two-dimensional lattice. Suitable laser coupling between these internal states leads to a uniform magnetic flux within the two-dimensional lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter-butterfly spectrum and the chiral edge states of the associated Chern insulating phases.

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 nontrivial realization of a fourth dimension corresponds to the creation of a bi-volume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.

Dirac equation for cold atoms in artificial curved spacetimes

We argue that the Fermi–Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an artificial gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi–Hubbard model subjected to an artificial SU(2) field, corresponding to position-dependent hopping matrices. As an example, we discuss in more detail the physics of the 2+1D Rindler metric and its possible experimental realization and detection.

Tensor Networks for Lattice Gauge Theories with continuous groups

We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we nobtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensornetwork nvariational ansatz for gauge-invariant states that can be used in actual numerical computations. Our nconstruction is also applied to the simplest realization of the quantum link models or gauge magnets and nprovides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge ntheories. We also introduce a new set of gauge-invariant operators that modify continuously RokhsarKivelson nwave functions and can be used to extend the phase diagrams of known models. As an example, nwe characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the RokhsarKivelson npoint of the Uð1Þ gauge magnet in 2D in terms of entanglement entropy. The topological entropy nserves as an order parameter for the transition but not the Schmidt gap.

Quantum simulation of non-trivial topology

We propose several designs to simulate quantum many-body systems in manifolds with a non-trivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of freedom via a suitable use of induced hoppings. The simplest example is the conversion of an open spin-ladder into a closed spin-chain with arbitrary boundary conditions. Further exploitation of the idea leads to the conversion of open chains with internal degrees of freedom into artificial tori and Mobius strips of different kinds. We show that in synthetic lattices the Hubbard model on sharp and scalable manifolds with non-Euclidean topologies may be realized. We provide a few examples of the effect that a change of topology can have on quantum systems amenable to simulation, both at the single-particle and at the many-body level.

Synthetic magnetic fluxes and topological order in one-dimensional spin systems

Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely, trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with nonvanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in wave guides are given.

Synthetic Unruh effect in cold atoms

We propose to simulate a Dirac field near an event horizon using ultracold atoms in an optical lattice. Such a quantum simulator allows for the observation of the celebrated Unruh effect. Our proposal involves three stages: (1) preparation of the ground state of a massless two-dimensional Dirac field in Minkowski space-time; (2) quench of the optical lattice setup to simulate how an accelerated observer would view that state; (3) measurement of the local quantum fluctuation spectra by one-particle excitation spectroscopy in order to simulate a De Witt detector. According to Unruhs prediction, fluctuations measured in such a way must be thermal. Moreover, following Takagis inversion theorem, they will obey the Bose-Einstein distribution, which will smoothly transform into the Fermi-Dirac as one of the dimensions of the lattice is reduced.

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, the planar model with fourth-order anisotropy, and the structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent η has the constant value 1/4, while the exponent v runs in a continuous and monotonic way from I to [from Ising to O(2)]. In the four-loop approximation, for N≥3 we find a cubic fixed point in the region u,v≥0.

Probing the edge with cold atoms

Trapped atoms can mimic the nature of edge currents in quantum Hall systems [Also see Reports by Mancini et al. and Stuhl et al.] The quantum Hall effect is a hallmark of topological physics. It is the first example in which the topology of the system determines a macroscopic phenomenon, the quantization of Hall conductance. In a seminal paper, Halperin related it to the existence of skipping orbits for the electrons at the edge of the sample (1). Although the Hall conductivity is nowadays routinely measured with high precision and used to define the SI unit of electrical resistance, observation of the underlying skipping orbits has been elusive. On pages 1514 and 1510 of this issue, Stuhl et al. (2) and Mancini et al. (3) report a striking visualization of these trajectories using ultracold atoms trapped in a synthetic lattice.