Alessio Calzona

Time-resolved energy dynamics after single electron injection into an interacting helical liquid

The possibility to inject a single electron into ballistic conductors is at the basis of the new field of electron quantum optics. Here, we consider a single electron injection into the helical edge channels of a topological insulator. Their counterpropagating nature and the unavoidable presence of electron-electron interactions dramatically affect the time evolution of the single wavepacket. Modeling the injection process from a mesoscopic capacitor in presence of non-local tunneling, we focus on the time resolved charge and energy packet dynamics. Both quantities split up into counterpropagating contributions whose profiles are strongly affected by the interactions strength. In addition, stronger signatures are found for the injected energy, which is also affected by the finite width of the tunneling region. Indeed, the energy flow can be controlled by tuning the injection parameters and we demonstrate that, in presence of non-local tunneling, it is possible to achieve situation in which charge and energy flow in opposite directions.

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay in system spectral properties

Nonequilibrium effects on charge and energy partitioning after an interaction quench

\propto t^{-2}

Time-resolved pure spin fractionalization and spin-charge separation in helical Luttinger liquid based devices

, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay

Charge and energy fractionalization mechanism in one-dimensional channels

\propto t^{-2}

Transient dynamics of spin-polarized injection in helical Luttinger liquids

induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.

Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature

Charge and energy fractionalization are among the most intriguing features of interacting onedimensional fermion systems. In this work we determine how these phenomena are modified in the presence of an interaction quench. Charge and energy are injected into the system suddenly after the quench, by means of tunneling processes with a non-interacting one-dimensional probe. Here, we demonstrate that the system settles to a steady state in which the charge fractionalization ratio is unaffected by the pre-quenched parameters. On the contrary, due to the post-quench nonequilibrium spectral function, the energy partitioning ratio is strongly modified, reaching values larger than one. This is a peculiar feature of the non-equilibrium dynamics of the quench process and it is in sharp contrast with the non-quenched case, where the ratio is bounded by one.

Z4 parafermions in one-dimensional fermionic lattices

Helical Luttinger liquids, appearing at the edge of two-dimensional topological insulators, represent a new paradigm of one-dimensional systems, where peculiar quantum phenomena can be investigated. Motivated by recent experiments on charge fractionalization, we propose a setup based on helical Luttinger liquids that allows one to time-resolve, in addition to charge fractionalization, also spin-charge separation and pure spin fractionalization. This is due to the combined presence of spin-momentum locking and interactions. We show that electric time-resolved measurements can reveal both charge and spin properties, avoiding the need of magnetic materials. Although challenging, the proposed setup could be achieved with present-day technologies, promoting helical liquids as interesting playgrounds to explore the effects of interactions in one dimension.

Parafermionic Bound States in 1D Lattices of Spinful Fermions

We study the problem of injecting single electrons into interacting one-dimensional quantum systems, a fundamental building block for electron quantum optics. It is well known that such injection leads to charge and energy fractionalization. We elucidate this concept by calculating the nonequilibrium electron distribution function in the momentum and energy domains after the injection of an energy-resolved electron. Our results shed light on how fractionalization occurs via the creation of particle-hole pairs by the injected electron. In particular, we focus on systems with a pair of counterpropagating channels, and we fully analyze the properties of each chiral fractional excitation which is created by the injection. We suggest possible routes to access their energy and momentum distribution functions in topological quantum Hall or quantum spin-Hall edge states.

The dynamics of charge and energy fractionalization in one-dimensional channels

Abstract We analyze the time evolution of spin-polarized electron wave packets injected into the edge states of a two-dimensional topological insulator. In the presence of electron interactions, the system is described as a helical Luttinger liquid and injected electrons fractionalize. However, because of the presence of metallic detectors, no evidences of fractionalization are encoded in dc measurements, and in this regime the system does not show deviations from its non-interacting behavior. Nevertheless, we show that the helical Luttinger liquid nature emerges in the transient dynamics, where signatures of charge/spin fractionalization can be clearly identified.