Publications

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Localization engineering by resonant driving in dissipative polariton arrays

Gonzalo Usaj

SciPost Phys. Core 7, 052 (2024) · published 9 August 2024 | · pdf

Arrays of microcavity polaritons are very versatile systems that allow for broad possibilities for the engineering of multi-orbital lattice geometries using different state preparation schemes. One of these schemes, spatially modulated resonant driving, can be used, for instance, to selectively localize the polariton field within the particular region of the lattice enclosed by the driving laser. Both the frequency and the spatial amplitude distribution (module and phase) of the driven laser field are important and serve as a knob to control the leakage outside that region and hence the extend of the spatial localization. Here, we analyse both the linear and nonlinear regimes using the lattice Green function formalism that is particularly suitable for the case of polariton arrays described in a tight-binding approximation. We identify the conditions for the laser induced localization to occur on arbitrary lattice's geometries and discuss some experimentally relevant cases. We find that the polariton-polariton interaction leads to a frequency shift of the optimal localization condition that could be used to further control it.
Bloch-Lorentz magnetoresistance oscillations in delafossites

Kostas Vilkelis, Lin Wang, Anton Akhmerov

SciPost Phys. 15, 019 (2023) · published 20 July 2023 | · pdf

Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO$_2$ and PtCoO$_2$) observed oscillations closely resembling the Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are explained by the Bloch-like oscillations of the out-of-plane electron trajectories. We develop a semiclassical theory of these Bloch-Lorentz oscillations and show that they are a consequence of the ballistic motion and quasi-2D dispersion of delafossites. Our model identifies the sample wall scattering to be the most likely factor limiting the visibility of these Bloch-Lorentz oscillations in existing experiments.
Chaos enhancement in large-spin chains

Yael Lebel, Lea F. Santos, Yevgeny Bar Lev

SciPost Phys. 15, 022 (2023) · published 21 July 2023 | · pdf

We study the chaotic properties of a large-spin XXZ chain with onsite disorder and a small number of excitations above the fully polarized state. We show that while the classical limit, which is reached for large spins, is chaotic, enlarging the spin suppresses quantum chaos features. We examine ways to facilitate chaos by introducing additional terms to the Hamiltonian. Interestingly, perturbations that are diagonal in the basis of product states in the $z$-direction do not lead to significant enhancement of chaos, while off-diagonal perturbations restore chaoticity for large spins, so that only three excitations are required to achieve strong level repulsion and ergodic eigenstates.
Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice

Nicolas Crampé

SciPost Phys. 2, 006 (2017) · published 24 February 2017 | · pdf

We show that an inhomogeneous coagulation/decoagulation model can be mapped to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum for this inhomogeneous model is computed exactly and the spectral gap is described for some examples. We construct our inhomogeneous model from two different homogeneous models joined by one special bond (impurity). The homogeneous models we started with are the coagulation/decoagulation models studied previously using the Jordan-Wigner transformation.
Connected correlations in partitioning protocols: A case study and beyond

Saverio Bocini

SciPost Phys. 15, 027 (2023) · published 25 July 2023 | · pdf

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is local enough to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.
Fermionic defects of topological phases and logical gates

Ryohei Kobayashi

SciPost Phys. 15, 028 (2023) · published 25 July 2023 | · pdf

We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic defects called "gauged Gu-Wen SPT defects" that can shift self-statistics of anyons. We derive a canonical form of a general fermionic invertible defect, in terms of the fusion of a gauged Gu-Wen SPT defect and a bosonic invertible defect decoupled from fermions on the defect. We then derive the fusion rule of generic invertible fermionic defects. The gauged Gu-Wen SPT defects give rise to interesting logical gates of stabilizer codes in the presence of additional ancilla fermions. For example, we find a realization of the CZ logical gate on the (2+1)D $\mathbb{Z}_2$ toric code stacked with a (2+1)D ancilla trivial atomic insulator. We also investigate a gapped fermionic interface between (2+1)D bosonic topological phases realized on the boundary of the (3+1)D Walker-Wang model. In that case, the gapped interface can shift the chiral central charge of the (2+1)D phase. Among these fermionic interfaces, we study an interesting example where the (3+1)D phase has a spatial reflection symmetry, and the fermionic interface is supported on a reflection plane that interpolates a (2+1)D surface topological order and its orientation-reversal. We construct a (3+1)D exactly solvable Hamiltonian realizing this setup, and find that the model generates the $\mathbb{Z}_8$ classification of the (3+1)D invertible phase with spatial reflection symmetry and fermion parity on the reflection plane. We make contact with an effective field theory, known in literature as the exotic invertible phase with spacetime higher-group symmetry.
Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field

Archisman Panigrahi, Subroto Mukerjee

SciPost Phys. Core 6, 052 (2023) · published 31 July 2023 | · pdf

We demonstrate that the well-known expression for the charge magnetization of a sample with a non-zero Berry curvature can be obtained by demanding that the Einstein relation holds for the electric transport current. We extend this formalism to the transport energy current and show that the energy magnetization must satisfy a particular condition. We provide a physical interpretation of this condition, and relate the energy magnetization to circulating energy currents in Chern insulators due to chiral edge states. We further recover the expression for the energy magnetization with this alternative formalism. We also solve the Boltzmann Transport Equation for the non-equilibrium distribution function in 2D for systems with a non-zero Berry curvature in a magnetic field. This distribution function can be used to obtain the regular Hall response in time-reversal invariant samples with a non-zero Berry curvature, for which there is no anomalous Hall response.
$\Delta$S$^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C$_{60}$: Origin and the role of symmetry

Nikolaos P. Konstantinidis

SciPost Phys. 15, 037 (2023) · published 31 July 2023 | · pdf

The quantum antiferromagnetic Heisenberg model on the fullerene C$_{60}$ in a magnetic field has $4s$ ground-state magnetization discontinuities with $\Delta S^z=2$ as a function of the spin quantum number $s$ that disappear at the classical limit. The molecule can be seen as the fullerene C$_{20}$ with interpentagon interactions that generate the discontinuities when sufficiently strong. The discontinuities originate from the antiferromagnetic Ising limit for both molecules. The results show how spatial symmetry dictates the magnetic response of the $I_h$ fullerene molecules.
Quenched dynamics and pattern formation in clean and disordered Bogoliubov-de Gennes superconductors

Bo Fan, Antonio Miguel García García

SciPost Phys. 17, 049 (2024) · published 13 August 2024 | · pdf

We study the quench dynamics of a two dimensional superconductor in a square lattice of size up to $200× 200$ employing the self-consistent time dependent Bogoliubov-de Gennes (BdG) formalism. In the clean limit, the dynamics of the order parameter for short times, characterized by a fast exponential growth and an oscillatory pattern, agrees with the Bardeen-Cooper-Schrieffer (BCS) prediction. However, unlike BCS, we observe for longer times a universal exponential decay of these time oscillations. We show explicitly that the origin of this exponential decay is the full emergence of spatial inhomogeneities of the order parameter characterized by the exponential growth of its variance. The addition of a weak disorder does not alter these results qualitatively. In this region, the spatial inhomogeneities rapidly develop into an intricate spatial structure consisting of ordered fragmented stripes in perpendicular directions where the order parameter is heavily suppressed. As the disorder strength increases, the fragmented stripes gradually turn into a square lattice of approximately circular spatial regions where the condensate is heavily suppressed. A further increase of disorder leads to the deformation and ultimate destruction of this lattice. We show these emergent spatial patterns are sensitive to the underlying lattice structure. We explore suitable settings for the experimental confirmation of these findings.
Fermionic quantum computation with Cooper pair splitters

Kostas Vilkelis, Antonio Manesco, Juan Daniel Torres Luna, Sebastian Miles, Michael Wimmer, Anton Akhmerov

SciPost Phys. 16, 135 (2024) · published 27 May 2024 | · pdf

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device consists of quantum dots tunnel-coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions implements the universal set of quantum gates defined by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002)]. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweet spot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.

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