I. L. Egusquiza

University of the Basque Country

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J. G. Muga

University of the Basque Country

E. Solano

Ikerbasque

Lucas Lamata

Universidad de Sevilla

A. D. Baute

University of the Basque Country

A. Parra-Rodriguez

Université de Sherbrooke

Adolfo del Campo

University of Luxembourg

R. Sala Mayato

Universidad de La Laguna

J. A. Damborenea

University of the Basque Country

Mikel Sanz

University of the Basque Country

J. Casanova

University of the Basque Country

Cooperative Institutions

University of the Basque Country

Ikerbasque

Centre National de la Recherche Scientifique

Universität Ulm

Université Paris Cité

Max Planck Institute of Quantum Optics

Donostia International Physics Center

Universidad de La Laguna

Universidad Autónoma de Madrid

Laboratoire Matériaux et Phénomènes Quantiques

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Faddeev-Jackiw quantisation of nonreciprocal quasi-lumped electrical networks

arXiv (Cornell University) (2024)

A. Parra-Rodriguez I. L. Egusquiza

Following a consistent geometrical description previously introduced in Parra-Rodriguez et al. (2023), we present an exact method for obtaining canonically quantisable Hamiltonian descriptions of nonlinear, nonreciprocal quasi-lumped electrical networks. Utilising the Faddeev-Jackiw method once more, we identify and classify all possible singularities arising in the quest for Hamiltonian descriptions of general quasi-lumped element networks, and we offer systematic solutions to them--a major challenge in the context of canonical circuit quantisation. Accordingly, the solution relies on the correct identification of the reduced classical circuit-state manifold, i.e., a mix of flux and charge fields and functions. Starting from the geometrical description of the transmission line, we provide a complete program including lines coupled to one-port lumped-element networks, as well as multiple lines connected to nonlinear lumped-element networks. On the way, we naturally extend the canonical quantisation of transmission lines coupled through frequency-dependent, nonreciprocal linear systems, such as practical circulators. Additionally, we demonstrate how our method seamlessly facilitates the characterisation of general nonreciprocal, dissipative linear environments. This is achieved by extending the Caldeira-Leggett formalism, utilising continuous limits of series of immittance matrices. We expect this work to become a useful tool in the analysis and design of electrical circuits and of special interest in the context of canonical quantisation of superconducting networks. For instance, this work will provide a solid ground for a precise input-output theory in the presence of nonreciprocal devices, e.g., within waveguide QED platforms.

Hamiltonian (control theory)

Canonical form

10.48550/arxiv.2401.09120

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Advanced-Retarded Differential Equations in Quantum Photonic Systems

Scientific Reports (2017)

Unai Alvarez-Rodriguez Armando Pérez-Leija I. L. Egusquiza Markus Gräfe Mikel Sanz

We propose the realization of photonic circuits whose dynamics is governed by advanced-retarded differential equations. Beyond their mathematical interest, these photonic configurations enable the implementation of quantum feedback and feedforward without requiring any intermediate measurement. We show how this protocol can be applied to implement interesting delay effects in the quantum regime, as well as in the classical limit. Our results elucidate the potential of the protocol as a promising route towards integrated quantum control systems on a chip.

Realization (probability)

Feed forward

10.1038/srep42933

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Consistent histories, the quantum Zeno effect, and time of arrival

Physical Review A (2000)

I. L. Egusquiza J. G. Muga

We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view.

Quantum Zeno effect

Operator (biology)

Arrival time

Zeno's paradoxes

10.1103/physreva.62.032103

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Citations (14)

Digital Quantum Simulation of MinimalAdS/CFT

Physical Review Letters (2017)

Laura García-Álvarez I. L. Egusquiza Lucas Lamata Adolfo del Campo Julian Sonner

We propose the digital quantum simulation of a minimal $\mathrm{AdS}/\mathrm{CFT}$ model in controllable quantum platforms. We consider the Sachdev-Ye-Kitaev model describing interacting Majorana fermions with randomly distributed all-to-all couplings, encoding nonlocal fermionic operators onto qubits to efficiently implement their dynamics via digital techniques. Moreover, we also give a method for probing nonequilibrium dynamics and the scrambling of information. Finally, our approach serves as a protocol for reproducing a simplified low-dimensional model of quantum gravity in advanced quantum platforms as trapped ions and superconducting circuits.

Scrambling

10.1103/physrevlett.119.040501

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Citations (149)

Classical Strings in FRW Spacetimes

I. L. Egusquiza

Friedmann–Lemaître–Robertson–Walker metric

Source

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Canonical quantization of telegrapher's equations coupled by ideal nonreciprocal elements.

arXiv (Cornell University) (2020)

A. Parra-Rodriguez I. L. Egusquiza

We develop a systematic procedure to quantize canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED set-up. This is achieved through a description of the distributed subsystems in terms of both flux and charge fields. We prove that this apparent redundancy is required for the general derivation of the Hamiltonian for a wider class of networks. By making use of the electromagnetic duality symmetry in 1+1 dimensions, we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. This doubled description can also treat the case of other extended lumped interactions in a regular manner that presents no spurious divergences, as we show explicitly in the example of a circulator connected to a Josephson junction through a transmission line. This theory enhances the quantum engineering toolbox to design complex networks with nonreciprocal elements.

Hamiltonian (control theory)

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Sources of quantum waves

Journal of Physics A Mathematical and General (2001)

A. D. Baute I. L. Egusquiza J. G. Muga

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.

10.1088/0305-4470/34/20/303

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Quantum Simulator for Transport Phenomena in Fluid Flows

Scientific Reports (2015)

Antonio Mezzacapo Mikel Sanz Lucas Lamata I. L. Egusquiza Sauro Succi

Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.

Lattice Boltzmann methods

10.1038/srep13153

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Time in Quantum Mechanics

J. G. Muga R. Sala Mayato I. L. Egusquiza

Characteristic Times in One-Dimensional Scattering.- The Time-Energy Uncertainty Relation.- Jump Time and Passage Time: The Duration ofs a Quantum Transition.- Bohm Trajectory Approach to Timing Electrons.- Decoherent Histories for Space-Time Domains.- Quantum Traversal Time, Path Integrals and Superluminal Tunnelling.- Quantum Clocks and Stopwatches.- The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics.- Standard Quantum-Mechanical Approach to Times of Arrival.- Experimental Issues in Quantum-Mechanical Time Measurement.- Microwave Experiments on Tunneling Time.- The Two-State Vector Formalism: An Updated Review.

Superluminal motion

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On atomic time-of-arrival measurements with a laser of finite beam width

Journal of Physics B Atomic Molecular and Optical Physics (2003)

J. A. Damborenea I. L. Egusquiza Gerhard C. Hegerfeldt J. G. Muga

A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.

Atomic beam

10.1088/0953-4075/36/12/320

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Citations (31)