arXiv subjects

Álvaro Gómez-León

Publications and source records attributed to Álvaro Gómez-León.

At least 19 recordsLinked to original sources

arXiv2026

Decoherence-free subspaces in the noisy dynamics of discrete-step quantum walks in a photonic lattice

We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics. We experimentally confirm our findings in a time multiplexed photonic lattice implemented in a double-fiber ring setup subject to laser pulse input states, in which we engineer different types of temporal noise.

quant-ph↗

arXiv2026

Floquet Topological Frequency-Converting Amplifier

We introduce a driven-dissipative Floquet model in which a single harmonic oscillator, with both frequency and decay rate modulated, realizes a non-Hermitian synthetic lattice with an effective electric-field gradient in frequency space. Using the Floquet-Green's function and the doubled Hamiltonian representation of non-Hermitian matrices, we show that the linear response of this system is characterized by a local winding number. Nontrivial values of the winding number induce directional amplification in the synthetic dimension, thereby converting input signals to different frequencies. The underlying mode structure is well described by a Jackiw-Rebbi-like continuum theory with Dirac cones and solitonic topological zero modes in synthetic frequency. Our results establish a simple and experimentally feasible route to non-Hermitian topological amplification, naturally implementable in current quantum technologies such as superconducting circuits.

quant-ph↗

arXiv2025

Photon-mediated interactions by Floquet photonic lattices

We investigate the interactions between two-level emitters mediated by time-dependent, one-dimensional, structured photonic baths, focusing on Floquet topological lattices. Building on the framework of periodically driven photonic lattices, we demonstrate and characterize the emergence of tunable-range emitter's interactions mediated by bound states absent in static photonic lattices. In particular, we show that one can not only obtain different spatial interaction dependencies with respect to the static bath scenarios, but also in qualitatively different regimes due to the time-dependent nature of the bath, for example, when the emitters have different frequencies. This work sheds light on the interplay between non-equilibrium photonics and quantum optics and can serve as the basis for analyzing Floquet photonic lattices in higher dimensions.

quant-ph↗

arXiv2025

Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths

We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling, including symmetry-broken phases. We present and compare two different approaches. First, using a coherent path integral formulation for the partition function to obtain thermal Green functions. This approach relies on a saddle point expansion for the action, that can be truncated in the thermodynamic limit. Second, by formulating the equations of motion for the retarded Green functions and solving them. We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations. Both approaches yield identical results in the calculation of response functions for the cavity and material. These are obtained in terms of the bare cavity and material responses. In combination, the two techniques clarify the validity of a mean-field decoupling in correlated light-matter systems and provide complementary means to compute finite-size corrections to the thermodynamic limit. The theory is formulated for a general model that encompasses most of the systems typically considered in the field of cavity QED materials. Finally, we provide a detailed application of the theory to the Quantum Hall effect and to a collection of spin models.

quant-ph↗

arXiv2025

Bound polariton states in the Dicke-Ising model

We present a study of hybrid light-matter excitations in cavity QED materials using the Dicke-Ising model as a theoretical framework. Leveraging linear response theory, we derive the exact excitations of the system in the thermodynamic limit. Our results demonstrate that the cavity can localize spin excitations, leading to the formation of bound polaritons, where the cavity acts as an impurity of the two-excitation band, localizing spin-wave pairs around single-spin domains. We derive the condition for the existence of these bound states and discuss its satisfiability in different regimes. Finally, we show that these effects persist in finite systems using exact-diagonalization calculations.

quant-ph↗

arXiv2025

Light-matter correlations in Quantum Floquet engineering of cavity quantum materials

Quantum Floquet engineering (QFE) seeks to generalize the control of quantum systems with classical external fields, widely known as Semi-Classical Floquet engineering (SCFE), to quantum fields. However, to faithfully capture the physics at arbitrary coupling, a gauge-invariant description of light-matter interaction in cavity-QED materials is required, which makes the Hamiltonian highly non-linear in photonic operators. We provide a non-perturbative truncation scheme of the Hamiltonian, which is valid or arbitrary coupling strength, and use it to investigate the role of light-matter correlations, which are absent in SCFE. We find that even in the high-frequency regime, light-matter correlations can be crucial, in particular for the topological properties of a system. As an example, we show that for a SSH chain coupled to a cavity, light-matter correlations break the original chiral symmetry of the chain, strongly affecting the robustness of its edge states. In addition, we show how light-matter correlations are imprinted in the photonic spectral function and discuss their relation with the topology of the bands.

cond-mat.mes-hall↗

arXiv2024

Observation of extrinsic topological phases in Floquet photonic lattices

Discrete-step walks describe the dynamics of particles in a lattice subject to hopping or splitting events at discrete times. Despite being of primordial interest to the physics of quantum walks, the topological properties arising from their discrete-step nature have been hardly explored. Here we report the observation of topological phases unique to discrete-step walks. We use light pulses in a double-fibre ring setup whose dynamics maps into a two-dimensional lattice subject to discrete splitting events. We show that the number of edge states is not simply described by the bulk invariants of the lattice (i.e., the Chern number and the Floquet winding number) as would be the case in static lattices and in lattices subject to smooth modulations. The number of edge states is also determined by a topological invariant associated to the discrete-step unitary operators acting at the edges of the lattice. This situation goes beyond the usual bulk-edge correspondence and allows manipulating the number of edge states without the need to go through a gap closing transition. Our work opens new perspectives for the engineering of topological modes for particles subject to quantum walks.

quant-ph↗

arXiv2024

Topological Josephson parametric amplifier array: A proposal for directional, broadband, and low-noise amplification

Low-noise microwave amplifiers are crucial for detecting weak signals in fields such as quantum technology and radio astronomy. However, designing an ideal amplifier is challenging, as it must cover a wide frequency range, add minimal noise, and operate directionally - amplifying signals only in the observer's direction while protecting the source from environmental interference. In this work, we demonstrate that an array of non-linearly coupled Josephson parametric amplifiers (JPAs) can collectively function as a directional, broadband quantum amplifier by harnessing topological effects. By applying a collective four-wave-mixing pump with inhomogeneous amplitudes and linearly increasing phase, we break time-reversal symmetry in the JPA array and stabilize a topological amplification regime where signals are exponentially amplified in one direction and exponentially suppressed in the opposite. We show that compact devices with few sites $N\sim 11-17$ can achieve exceptional performance, with gains exceeding 20 dB over a bandwidth ranging from hundreds of MHz to GHz, and reverse isolation suppressing backward noise by more than 30 dB across all frequencies. The device also operates near the quantum noise limit and provides topological protection against up to 15% fabrication disorder, effectively suppressing gain ripples. The amplifier's intrinsic directionality eliminates the need for external isolators, paving the way for fully on-chip, near-ideal superconducting pre-amplifiers.

quant-ph↗

arXiv2024

Anomalous Floquet Phases. A resonance phenomena

Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a $π$-flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants.

quant-ph↗

arXiv2024

Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete-step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time-dependence or micromotion in discrete-step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete-step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics.

cond-mat.mes-hall↗

arXiv2024

High-quality poor man's Majorana bound states from cavity embedding

Poor man's Majorana Bound States (MBS) arise in minimal Kitaev chains when the parameters are fine-tuned to a sweet spot. We consider an interacting two-site Kitaev chain coupled to a single-mode cavity and show that the sweet spot condition can be controlled with the cavity frequency and the hopping between sites. Furthermore, we demonstrate that photon-mediated effective interactions can be used to screen intrinsic interactions, improving the original quality of the MBS. We describe experimental signatures in the cavity transmission to detect their presence and quality. Our work proposes a new way to tune poor man's MBS in a quantum dot array coupled to a cavity.

cond-mat.mes-hall↗

arXiv2023

Many-body origin of anomalous Floquet phases in cavity-QED materials

Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics of Floquet engineering in its semi-classical limit. However, the mapping between these two widely different scenarios remains mysterious in many aspects. We discuss the emergence of anomalous topological phases in cavity-QED materials, and link topological phase transitions in the many-body spectrum with those in the $0$- and $π$-gaps of Floquet quasienergies. Our results allow to establish the microscopic origin of an emergent discrete time-translation symmetry in the matter sector, and link the physics of isolated many-body systems with that of periodically driven ones. Finally, the relation between many-body and Floquet topological invariants is discussed, as well as the bulk-edge correspondence.

quant-ph↗

arXiv2023

Driven-dissipative topological phases in parametric resonator arrays

We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.

quant-ph↗

arXiv2022

Multi-qudit interactions in molecular spins

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

quant-ph↗

arXiv2022

Dispersive readout of molecular spin qudits

We study the physics of a magnetic molecule described by a "giant" spin with multiple ($d > 2$) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions under which the qudit read-out is a non-demolition measurement and consider possible experimental protocols to perform it. Finally, we illustrate our results with simulations performed for realistic models of existing magnetic molecules.

quant-ph↗

arXiv2022

Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.

quant-ph↗

arXiv2022

Topology detection in cavity QED

We explore the physics of topological lattice models in c-QED architectures for arbitrary coupling strength, and the use of the cavity transmission as a topological marker. For this, we develop an approach combining the input-output formalism with an expansion in quantum fluctuations which allows to go beyond the small-coupling regime. We apply our formalism to a fermionic Su-Schrieffer-Heeger (SSH) chain coupled to a single-mode cavity, and find that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crutial role. Additionally, we discuss the persistence of topological features as the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy.

cond-mat.mes-hall↗

arXiv2021

Bridging the gap between topological non-Hermitian physics and open quantum systems

We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain all the relevant topological information. We arrive at a frequency dependent topological index that is linked to the response of the system to perturbations at a given frequency. We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases

quant-ph↗