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Register a new userRealization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
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Added by
Monika Aidelsburger
Publication date
2013
fields
Physics
and research's language is
English
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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.
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Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect, where the plateaus depicted by the Hall conductivity were attributed to a topological invariant characterizing Bloch bands: the Chern number. Until now, topological transport associated with non-zero Chern numbers has only been revealed in electronic systems. Here we use studies of an atomic clouds transverse deflection in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band $ u_{mathrm{exp}} =0.99(5)$. This result, which constitutes the first Chern-number measurement in a non-electronic system, is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.
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.
We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadters butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.
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.
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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