Quantum Hall effect in ideal superconducting arrays at zero temperature

Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems

“…We are led to predict the above startling properties for bosonic Quantum Hall systems, such as someday might be obtained from superconductor-insulator transitions in thin films, or from Josephson-junction arrays [50][51][52][53][54]. Unfortunately, these predictions cannot yet be tested with ordinary superconductors, because charge carrier densities and mobilities in these systems do not put them into the quantum Hall regime [55].…”

“…In fact the form (53) is rather more general than that -it will be argued below that this is the most general possible form in a momentum expansion, independently of any power counting arguments, provided one allows the polarizations to depend on the magnitudes of the external fields, E 2 and B 2 . The mathematical manipulations involving equation (53) can be simplified by writing it in relativistic form using the following trick. We introduce a "metric" on 3-dimensional space-time defined by…”

An analogue of the quantum Hall conductivity for a magnetic quadrupole moment

“…At present days, the quantum Hall effect has been investigated in non-inertial systems [8][9][10][11], in the presence of topological defects [12,13], in Aharonov-Casher systems [14][15][16], anyons [17], graphene [18,19], superconducting arrays [20], noncommutative quantum mechanics [21][22][23][24] and in a background of the violation of the Lorentz symmetry [25]. In studies of the quantum Hall effect, the Landau quantization [26,27] is the simplest system that we can work with, then, with the purpose of extending to neutral particle systems, analogues of the Landau quantization have been proposed in recent years to neutral particles that possess permanent magnetic dipole moment [14], permanent electric dipole moment [28,29] and electric quadrupole moment [30].…”

Quantum simulation architecture for lattice bosons in arbitrary, tunable, external gauge fields

“…The technical challenges are, however, quite daunting: New cooling methods need to be designed to offset heating from the Raman lasers, and the most natural probes are indirect. Another scheme is to use lattices of tiny superconducting grains (charge qubits, [16][17][18][19][20][21]) connected through Josephson junctions. Suitably low temperatures can be reached in a dilution refrigerator, and the system is readily studied using transport measurements.…”