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Register a new userFloquet approach to $mathbb{Z}_{2}$ lattice gauge theories with ultracold atoms in optical lattices
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Added by
Christian Schweizer
Publication date
2019
fields
Physics
and research's language is
English
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Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying $mathbb{Z}_2$ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits $mathbb{Z}_2$ symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.
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Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields.
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential we engineer spatially dependent complex tunneling amplitudes. Thereby atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal symmetric Hamiltonian underlying the quantum spin Hall effect, i.e., two different spin components experience opposite directions of the magnetic field.
Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $delta N^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $delta N^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$ and density $n$. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analog to critical opalescence, accompanied by a surprising reduction of the absolute value of their nonlocal contributions. This is a precursory sign of an underlying phase transition between a pseudogap phase and a metallic phase in doped Mott insulators, which should play an important role in the cuprate high-temperature superconductors. Predictions for ultracold atom experiments are made.
Motivated by recent realizations of spin-1 NaRb mixtures in the experiments, here we investigate heteronuclear magnetism in the Mott-insulating regime. Different from the identical mixtures where the boson (fermion) statistics only admits even (odd) parity states from angular momentum composition, for heteronuclear atoms in principle all angular momentum states are allowed, which can give rise to new magnetic phases. Various magnetic phases can be developed over these degenerate spaces, however, the concrete symmetry breaking phases depend not only on the degree of degeneracy, but also the competitions from many-body interactions. We unveil these rich phases using the bosonic dynamical mean-field theory approach. These phases are characterized by various orders, including spontaneous magnetization order, spin magnitude order, singlet pairing order and nematic order, which may coexist, especially in the regime with odd parity. Finally we address the possible parameter regimes for observing these spin-ordered Mott phases.
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