## Fast quantum transfer mediated by topological domain walls

Juan Zurita, Charles Creffield and Gloria Platero

**Abstract**

The duration of bidirectional transfer protocols in 1D topological models usually scales exponentially with distance. In this work, we propose transfer protocols in multidomain SSH chains and Creutz ladders that lose the exponential dependence, greatly speeding up the process with respect to their single-domain counterparts, reducing the accumulation of errors and drastically increasing their performance, even in the presence of symmetry-breaking disorder. We also investigate how to harness the localization properties of the Creutz ladder-with two localized modes per domain wall-to choose the two states along the ladder that will be swapped during the transfer protocol, without disturbing the states located in the intermediate walls between them. This provides a 1D network with all-to-all connectivity that can be helpful for quantum information purposes.

## Thesis Defense: Topological Systems Interacting with Classical and Quantum Light, by Beatriz Pérez González

On March 17th, one of our Ph.D. students, **Beatriz Pérez González**, will defend her thesis entitled: **Topological Systems Interacting with Classical and Quantum Light.**

##### Abstract

In the field of quantum materials, there is an ubiquitous quest for different strategies to control and manipulate their properties. Along this direction, driving materials out of equilibrium with a time-periodic modulation has proven to be an efficient tool for realizing unconventional configurations as transient states, or even novel out-of-equilibrium phases. In these systems, known as Floquet materials, the electronic degrees of freedom are dressed by the interaction with the electric field, which can be exploited to engineer the electronic, dynamical and topological properties of materials. In solid-state platforms, such fields can be implemented by shining classical light, i.e., a high-intensity laser, on the sample.

In recent years, the idea of using quantum light for the same task has gathered considerable attention. In these set-ups, the high-intensity laser can be replaced by individual photons trapped inside a quantum cavity that are made to interact coherently with a quantum material. Although there are crucial differences between both approaches, the strategies of driven systems can guide this new research route, and the resulting hybrid systems have been denominated cavity quantum materials.

The present dissertation explores the interaction of both classical and quantum light with a particular class of quantum materials: topological insulators. The non-trivial topological properties of the bulk, which can be characterized by the value of a topological invariant, are related with the physics at the boundary, and lead to the appearance of topologically protected edge states. From a theoretical point of view, we investigate how the interaction with light can alter the topological features of a system, in two different aspects: first, by modifying the existing phase or by inducing non-trivial features in an otherwise trivial sample, and second, by hindering them. For this, different issues have to be addressed: are there any broken symmetries in the interacting system? What is the fate of the edge states in a finite system? Are they topologically protected? Is the topological invariant well-defined? From these questions it becomes clear that complete characterization of topological phases requires studying both the boundary and the bulk physics.

## New Editors’ Suggestion: Proposal for Detection of the 0′ and π′ Phases in Quantum-Dot Josephson Junctions

##### We are pleased to announce our latest article and thank the APS for considering it an Editors’ Suggestion on PRL. Congrats, everyone!

##### Minchul Lee, Rosa López, H. Q. Xu, and Gloria Platero

##### Phys. Rev. Lett. **129**, 207701

##### The competition between the Kondo correlation and superconductivity in quantum-dot Josephson junctions (QDJJs) has been known to drive a quantum phase transition between 0 and π junctions. Theoretical studies so far have predicted that under strong Coulomb correlations the 0−π transition should go through intermediate states, 0′ and π′ phases. By combining a nonperturbative numerical method and the resistively shunted

##### junction model, we investigated the magnetic-field-driven phase transition of the QDJJs in the Kondo regime and found that the low-field magnetotransport exhibits a unique feature which can be used to distinguish the intermediate phases. In particular, the magnetic-field driven π′−π transition is found to lead to the enhancement of the supercurrent which is strongly related to the Kondo effect.

## Group Seminar: Controlling Topological Phases of Matter with Quantum Light

**Olesia Dmytruk**, from the CNRS, Collège de France, PSL Research University, Paris

**Date: November 22, 2022, 12:00h**

**Location: **Instituto de Ciencias de Materiales de Madrid (ICMM-CSIC), Salón de Actos

**Abstract:**

Controlling the topological properties of quantum matter is a major goal of condensed matter physics. A major effort in this direction has been devoted to using classical light in the form of Floquet drives to manipulate and induce states with non-trivial topology. A different route can be achieved with cavity photons. In this talk, I will discuss a prototypical model for topological phase transition, the one-dimensional Su-Schrieffer-Heeger (SSH) model, coupled to a single mode cavity [1]. I will demonstrate that quantum light can affect the topological properties of the system, including the finite-length energy spectrum hosting edge modes and the topological phase diagram. In particular, I will show that depending on the lattice geometry and the strength of light-matter coupling one can either turn a trivial phase into a topological one or vice versa using quantum cavity fields. Furthermore, the polariton spectrum of the coupled electron-photon system contains signatures of the topological phase transition in the SSH model.

**References:**

[1] Olesia Dmytruk and Marco Schiró, Controlling topological phases of matter with quantum light, arXiv:2204.05922.

## Group Seminar: Illuminating van der Waals materials: from graphene to twisted MoS2

**Marta Prada, **from the Institute for Theoretical Physics, Universität Hamburg, will give a seminar entitled **«Illuminating van der Waals materials: from graphene to twisted MoS2».**

**Date: October 11th, 2022, 11:00h.**

**Location: **Instituto de Ciencias Materiales de Madrid (ICMM-CSIC)

We address the low-lying energy levels of van-der Waals structures via resistively-detected electron spin resonance (ESR). In graphene, the structure of the topological bands is reflected in transport experiments, where our numerical models allow us to identify the resonance signatures. We resolve the intrinsic spin-orbit gap [1], the g-factor anisotropic corrections [2, 3], the sub-lattice splitting [4], and the hyperfine-induced splitting in 13C-based graphene [5]. Using Floquet formalism, we find theoretical evidence of a topological transition by illuminating an ideal sample of graphene and the connection between angular momentum and sublattice spin. Finally, we study twisted MoS2 samples, where we resolve low-lying Moiré bands near the conduction band.

Keywords: Twisted bilayer MoS2, Moiré, superlattices, Mini-bands, Schottky barrier, Resonant Tunneling,

Transition metal dichalcogenides

[1] J. Sichau, M. Prada, T. Anlauf, T. J. Lyon, B. Bosnjak, L. Tiemann, and R. H. Blick, Phys. Rev. Lett. 122, 046402 (2019).

[2] M. Prada, L. Tiemann, J. Sichau and R. H. Blick. Phys. Rev. B 104, 075401 (2021).

[3] M. Prada, Phys. Rev. B 103, 115425 (2021).

[4] R. Singh, M. Prada, V. Strenzke, B. Bosnjak, T. Schmirander, Lars Tiemann, and Robert H. Blick. Phys. Rev. B 102, 245134 (2020).

[5] V. Strenzke, Phys. Rev. B 105, 144303 (2022).

## Seminar: «Introduction to machine learning and its applications in scientific research

**Lamberto Oltra Nieto,** a member of our group, will give a seminar entitled **«Introduction to machine learning and its applications in scientific research»**.

**Date: March 9th, 2022, 10:00 h. **

**Location**: online

**Abstract**: Nowadays, the importance of new technologies, more specifically artificial intelligence, in science is undeniable and must be taken into account in new scientific research. This seminar aims to be an introduction to the basics of machine learning with the objective of highlighting this importance in research. Applications in various fields such as error correction in different quantum systems or material research will also be discussed.

## Seminar: «Hole spin qubits in elongated quantum dots»

**Mónica Benito****,** from the Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, will give a seminar entitled **«Hole spin qubits in elongated quantum dots»**.

**Date: March 9th, 2022, 11:00 h. **

**Location**: Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)

**Abstract**: Rapid development has positioned quantum wells in planar germanium heterostructures at the head of semiconductor quantum dot platforms for quantum information processing [1,2]. We find nuclear-spin-free isotopes, low charge noise and low disorder. The focus is on hole states, due to the absence of valley states, a technically advantageous low effective mass, and the strong spin-orbit coupling that allows for all-electric operation. These works employ heavy-hole spin qubits, which constitute the ground states in these planar devices. Theory predicts an even more promising future for germanium and/or silicon based quantum dots fabricated in nanowires, based on tunable and even stronger spin-orbit coupling relying on the high degree of heavy-light hole mixtures [3]. I will present recent theoretical efforts to understand and experimentally identify the low-energy physics of hole germanium nanowires, including the effect of orbital effects of the magnetic field [4]. We predict optimal qubit operation at a sweet spot with Rabi frequencies in the GHz regime. We find that they can present strong and tunable spin-orbit coupling if the confinement potential is properly squeezed [5]. This confinement-induced spin-orbit coupling, and therefore the qubit-resonator coupling, could be turned on and off, overcoming present scalability challenges.

[1] Hendrickx et al., Nature 591, 580 (2021)

[2] F. van Riggelen, et al., arXiv:2202.11530

[3] C. Kloeffel, et al., Phys. Rev. B 84, 195314 (2011)

[4] C. Adelsberger, M. Benito, S. Bosco, J. Klinovaja, and D. Loss, PRB 105, 075308 (2022)

[5] S. Bosco, M. Benito, C. Adelsberger, and D. Loss, PRB 104, 115425 (2021)

## Seminar: «Entanglement generation and simulation of relativistic effects with parametric oscillators in cQED»

**David Fernández****,** from Instituto de Física Fundamental (IFF-CSIC), will give a seminar entitled **«Entanglement generation and simulation of relativistic effects with parametric oscillators in cQED»**.

**Date: February 23rd, 2022, 11:00 h. **

**Location**: Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)

**Abstract**: Present day quantum technologies aim at building quantum computers and networks that outperform their classical counterparts. From a physical perspective, these technologies need to be systems whose parameters are modified in real time, so that a programable sequence of operations is performed to deliver different quantum applications. Then, it is only natural to consider parametric oscillators as a primitive for these devices. In this seminar, we will discuss the basics of parametric oscillators in superconducting circuits and their applications to two promising topics: Firstly, the generation of multipartite entanglement thanks to the parametric amplification of vacuum in microwave one-dimensional cavities. Additionally, we will introduce protocols for the detection of said entanglement, which lead to connections in open questions in quantum information theory. Secondly, we will present superconducting circuits designed for the analog simulation of relativistic phenomena such as the Unruh and dynamical Casimir effects.

## Thesis Defense: «AC Dynamics of Quantum Dots and Josephson Junctions for Quantum Technologies», by Jordi Picó Cortés

## Group Seminar: «Hole spin qubits manipulation with shortcuts to adiabaticity protocols», David Fernández

**David Fernández****,** a MSC student in our group, will give a seminar entitled **«Hole spin qubits manipulation with shortcuts to adiabaticity protocols»**, as part of the group seminars.

**Date: June 8th, 2021, 10:30 h. **

**Location**: online

**Abstract**: Hole spins in semiconductor QDs are also attracting significant attention as candidates for fast, highly co-

herent, spin qubits. They have long coherence time due to the weak hyperfine coupling to nuclear spins , and have demonstrated to have rapid operation times due to the inherently strong spin–orbit coupling (SOC), which also allows spin states to be controlled locally with electric fields applied to the gate electrodes.

Recently, Landau Zener Stückelberg Majorana spectroscopy on two-hole GaAs double quantum dot has been experimentally implemented. Motivated by these experiments, we investigate how to control and manipulate a spin qubit consisting on a triplet and a singlet hole state, by alternative driving protocols which reduce the otherwise unavoidable presence of charge noise. Shortcuts to adiabaticity (STA) are a set of techniques to reduce the duration of slow adiabatic processes, minimizing noise effects while keeping or enhancing robustness. Different driving protocols have been developed, which reduce the time of the process below characteristic decoherence times. Here we will consider the fast quasi-adiabatic (FAQUAD) approach and we will analyze its feasibility to manipulate hole spin qubits and compare with other alternative protocols.