Publications

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Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field

Jeong Ryeol Choi

SciPost Phys. Core 4, 024 (2021) · published 20 September 2021 | · pdf

We investigate entanglement dynamics for a nanomechanical resonator coupled to an optical cavity field through the analysis of the associated entanglement entropies. The effects of time variation of several parameters, such as the optical frequency and the coupling strength, on the evolution of entanglement entropies are analyzed. We consider three kinds of entanglement entropies as the measures of the entanglement of subsystems, which are the linear entropy, the von Neumann entropy, and the Renyi entropy. The analytic formulae of these entropies are derived in a rigorous way using wave functions of the system. In particular, we focus on time behaviors of entanglement entropies in the case where the optical frequency is modulated by a small oscillating factor. We show that the entanglement entropies emerge and increase as the coupling strength grows from zero. The entanglement entropies fluctuate depending on the adiabatic variation of the parameters and such fluctuations are significant especially in the strong coupling regime. Our research may deepen the understanding of the optomechanical entanglement, which is crucial in realizing hybrid quantum-information protocols in quantum computation, quantum networks, and other domains in quantum science.

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Time rescaling of nonadiabatic transitions

Takuya Hatomura

SciPost Phys. 15, 036 (2023) · published 31 July 2023 | · pdf

Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by applying additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.

1 citation
Traveling discontinuity at the quantum butterfly front

Camille Aron, Éric Brunet, Aditi Mitra

SciPost Phys. 15, 042 (2023) · published 2 August 2023 | · pdf

We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.

1 citation
On the quantum simulation of complex networks

Duarte Magano, João Moutinho, Bruno Coutinho

SciPost Phys. Core 6, 058 (2023) · published 24 August 2023 | · pdf

Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.

1 citation
Twisted-bilayer FeSe and the Fe-based superlattices

Paul M. Eugenio, Oskar Vafek

SciPost Phys. 15, 081 (2023) · published 6 September 2023 | · pdf

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the $\Gamma$ and $M$ high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on $\Gamma$, and show the possibility of moire bands with $C=0$ or ±1 topological quantum numbers without breaking time-reversal symmetry. In the $C=0$ region for $\theta→0$ (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.

1 citation
The inversion of the Lorentz integral transform with controlled resolution

Winfried Leidemann, Victor D. Efros, Veronica Yu. Shalamova

SciPost Phys. Proc. 3, 037 (2020) · published 26 February 2020 | · pdf

The Lorentz integral transform (LIT) method is briefly presented. The ill-posedness of the inversion is discussed and it is pointed out that the LIT is an integral transform with a controlled resolution. As application the dipole response of a three-particle system bound in a hypercentral potential is considered. The inversion is performed in two ways, both employ expansions of the response function and of the LIT on a basis set and a transformed basis set, respectively. A previous study of the process under consideration seemed to point to serious problems in the inversion process. In the present work, however, it is shown that the LIT approach can be carried out in a reliable way.

1 citation
Robust extended states in Anderson model on partially disordered random regular graphs

Daniil Kochergin, Ivan M. Khaymovich, Olga Valba, Alexander Gorsky

SciPost Phys. 16, 106 (2024) · published 19 April 2024 | · pdf

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d,$\beta$) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.

1 citation
How to determine the shape of nuclear molecules with polarized gamma-rays

Lorenzo Fortunato

SciPost Phys. Proc. 3, 035 (2020) · published 26 February 2020 | · pdf

A method has been recently proposed to establish the geometry of the alpha-cluster arrangement in $^{12}$C making use of polarized gamma-rays. The ratio of intensities of scattered radiation at 90 degrees along and perpendicular to the initial direction of the electric field vector, called depolarization ratio, is a key quantity that allows to underpin the nature of totally symmetric modes of vibrations. This allows to connect with the underlying point-group structure and therefore to the geometric shape of the nuclear molecule. This method is reviewed for $^{12}$C and extended to other configurations, such as three unequal clusters and four identical clusters (e.g. $^{16}$O).

1 citation
A time-dependent regularization of the Redfield equation

Antonio D'Abbruzzo, Vasco Cavina, Vittorio Giovannetti

SciPost Phys. 15, 117 (2023) · published 27 September 2023 | · pdf

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial state, we introduce a new quantitative approach based on the Choi-Jamiołkowski isomorphism.

1 citation
Maximum entanglement of mixed symmetric states under unitary transformations

Eduardo Serrano-Ensástiga, John Martin

SciPost Phys. 15, 120 (2023) · published 28 September 2023 | · pdf

We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable (SAS) states, or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.

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