# Séminaires du Thursday 29 March

## Séminaire du LPTMS: Michele Filippone *** séminaire exceptionnel ***

#### 11:00:00

**Controlled Parity Switch of Persistent Currents and Topological charge-pumping effects induced by bulk magnetic fluxes****
**

### Michele Filippone (Université de Genève, Suisse)

We investigate persistent currents for a fixed number of fermions in periodic quantum ladders threaded by Aharonov-Bohm and transverse magnetic fluxes*Φ*and

*χ*. We show that the coupling between ladder legs provides a way to effectively change the ground-state fermion-number parity, by varying

*χ*. We demonstrate that varying

*χ*by

*2π*(one flux quantum) leads to an apparent fermion-number parity switch. We find that persistent currents exhibit a robust

*4π*periodicity as a function of

*χ*, despite the fact that

*χ→χ+2π*leads to modifications of order

*1/N*of the energy spectrum, where

*N*is the number of sites in each ladder leg. We connect the parity switching effect to the quantum Hall regime in two-dimensional systems. We show that the parity switching effect is related to the parity of the number of filled Landau levels and that it inherits strong robustness against disorder in the Harper-Hofstadter quantum Hall regime. Indeed, we show that the

*4π*periodicity is a mesoscopic manifestation of a novel type of fermionic pumping in topological systems, complementary to Thouless' pump. Focusing on the low-energy edge physics in the general framework of Chern-Simons theory, we discuss this alternative type of pumping in the context of integer and fractional quantum Hall systems. Our construction provides an intuitive setting to understand known effects and explore new ones. In particular, we show that adding superconductivity to the picture allows us to recover the 4π Josephson effect of Majorana fermions and its generalizations to parafermions. The parity-switching and the

*4π*periodicity effects are robust with respect to temperature and disorder and we outline potential physical realizations using Corbino disk geometries in solid state systems, quantum ladders with cold atomic gases and, for bosonic analogs of the effects, photonic lattices. Ref:

- Michele Filippone, Charles-Edouard Bardyn, Thierry Giamarchi,
*Controlled parity switch of persistent currents in quantum ladders*, preprint cond-mat.mes-hall arXiv:1710.02152

## Séminaire du LPTMS: Alexandru Petrescu *** séminaire exceptionnel ***

#### 11:30:00

## Fluxon-based quantum simulation in circuit QED

### Alexandru Petrescu (Department of electrical engineering, Princeton University, USA)

Long-lived fluxon excitations can be trapped inside a superinductor ring, which can be realized with a long array of Josephson junctions, one of which offers the input/output path for the magnetic flux [1]. The superinductor ring can be separated into smaller loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring loops [2]. This model is dual to that of two-leg ladder bosons, which have a rich phase diagram depending on flux and density [3–6]. By tuning the Josephson coupling, and implicitly the tunneling probability amplitude of fluxons, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. In this context, fluxons are lattice bosons with repulsive interactions. We illustrate this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry-protected topological phase with fractionally charged bound states at the edges [7,8]. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.

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**91**, 140406 (2015).

- [6] A. Petrescu, M. Piraud, G. Roux, I. P. McCulloch, and K. Le Hur, Phys. Rev. B
**96**, 014524(2017). - [7] R. Jackiw and C. Rebbi, Phys. Rev. D
**13**, 3398 (1976). - [8] W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett.
**42**, 1698 (1979).