Artificial magnetic-field quenches in synthetic dimensions

Physical Review B

We study the robustness of the quantization of the Hall conductivity in the Harper-Hofstadter model towards the details of the protocol with which a longitudinal uniform driving force Fx(t) is turned on. In the vector potential gauge, through Peierls substitution, this involves the switchingon of complex time-dependent hopping amplitudes e − i Ax(t) in thex-direction such that ∂tAx(t) = Fx(t). The switching-on can be sudden, Fx(t) = θ(t)F , where F is the steady driving force, or more generally smooth Fx(t) = f (t/t0)F , where f (t/t0) is such that f (0) = 0 and f (1) = 1. We investigate how the time-averaged (steady-state) particle current density jy in theŷ-direction deviates from the quantized value jy h/F = n due to the finite value of F and the details of the switching-on protocol. Exploiting the time-periodicity of the HamiltonianĤ(t), we use Floquet techniques to study this problem. In this picture the (Kubo) linear response F → 0 regime corresponds to the adiabatic limit forĤ(t). In the case of a sudden quench jy h/F shows F 2 corrections to the perfectly quantized limit. When the switching-on is smooth, the result depends on the switch-on time t0: for a fixed t0 we observe a crossover force F * between a quadratic regime for F < F * and a non-analytic exponential e −γ/|F | for F > F * . The crossover F * decreases as t0 increases, eventually recovering the topological robustness. These effects are in principle amenable to experimental tests in optical lattice cold atomic systems with synthetic gauge fields. arXiv:1809.05562v1 [cond-mat.quant-gas]

Physical Review B, 1997

A self-consistent treatment of exchange and correlation interactions in a quantum wire (QW) subject to a strong perpendicular magnetic field is presented using a modified local-density approximation (MLDA). The influence of many-body interactions on the spin-splitting between the two lowest Landau levels (LLs) is calculated within the screened Hartree-Fock approximation (SHFA), for filling factor ν = 1, and the strong spatial dependence of the screening properties of electrons is taken into account. In comparison with the Hartree-Fock result, the spatial behavior of the occupied LL in a QW is strongly modified when correlations are included. Correlations caused by screening at the edges strongly suppress the exchange splitting and smoothen the energy dispersion at the edges. The theory accounts well for the experimentally observed strong suppression of the spin-splitting pertinent to the ν = 1 quantum Hall effect (QHE) state as well as the destruction of this state in long, quasi-ballistic GaAlAs/GaAs QWs.

Physical Review Letters, 2006

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. Such transitions have been extensively studied for magnetic fields corresponding to Abelian gauges; they occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U (2) gauge fields, which can be realized with atoms with two pairs of degenerate internal states. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum and the minimum energy viewed as a function of momentum exhibits a step structure.

Physical Review A, 2013

We show that the recently developed optical lattices with Peierls substitution-which can be modeled as a lattice with a complex tunneling coefficient-may be used to induce controllable quantum transport of ultra-cold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi steady-state current (QSSC) ensues from the exact dynamics of non-interacting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed non-interacting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite-temperature are present, which suggests that our findings should be observable with available experimental capabilities.

EPL (Europhysics Letters)

Physical Review A

In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The schemes consist of coupled transmons whose flux are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the fixed phase offset of each site on the complex coupling rate between coupled qubits. These configurations can be directly realised in a superconducting circuit and is easily extendable to a scalable lattice. Due to the intrinsic non-linearity of the transmon qubits such lattices would be an ideal platform for simulating Bose-Hubbard Hamiltonians with non-trivial gauge fields.

Pramana, 2002

With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantised conductances and an interesting odd-even effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the odd-even effect. We end with a brief summary and discussion of future projects.

In this paper, bound states energies and corresponding wave functions of H-shaped quantum wires are calculated numerically in the presence of external magnetic and electric fields and within the Landau gauge. With a suitable definition of external confinement potential, we present a numerical algorithm to calculate the profile of probability distribution of charge carriers. Our analysis shows that in the presence of external electric and magnetic fields, bound state properties of carriers are sensitive functions of an asymmetric parameter a = Wx Wy which measures the relative width of the well in two directions. We also study many body effect of bandgap renormalization in this quasi one dimensional system within dynamical random phase approximation.

Physical Review Letters, 2018

Physical Review Letters, 2012

Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arc length of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short-circuit the bulk current paths and inhibit the observation of the quantized twoterminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a small sample size. PACS numbers: 72.80.Vp,73.22.Pr