arXiv subjects

Miguel A. Bastarrachea-Magnani

Publications and source records attributed to Miguel A. Bastarrachea-Magnani.

17 recordsLinked to original sources

arXiv2026

Classical and Quantum Properties of the Spin-Boson Dicke Model: Chaos, Localization, and Scarring

This review article describes major developments associated with the Dicke model, from its introduction in the 1950s to explain the transition from a normal to a superradiant phase to its modern applications in quantum many-body physics. Over the decades, this interacting spin-boson model has played a central role in the study of collective light-matter interactions, chaos, and quantum phase transitions. We focus on properties and phenomena that are best understood when seen from both the classical and quantum perspectives, with particular emphasis on the emergence of chaos, localization, and scarring. While our primary emphasis is on the isolated model, we also discuss recent advances in the open Dicke model, where environmental couplings are needed for describing realistic experimental platforms and exploring new regimes of quantum dynamics.

quant-ph↗

arXiv2025

Effective Mass in Dissipative Coupled Polaritons

Dissipative coupling refers to the effect where two systems interact with each other mediated by dissipation channels. Recent advances in controlling light-matter systems have opened new avenues to explore non-Hermitian effects arising from dissipative coupling, such as level attraction and anomalous dispersions. In this work, we perform a parametric study of these effects in a polariton system, i.e., a light-matter superposition, under both dissipative and coherent coupling. We characterize the effects of different sources of non-Hermitian behavior and analytically identify the conditions for the emergence of negative effective mass, exceptional points, and bound states in the continuum as a function of the light-matter detuning, the coherent-to-dissipative coupling ratio, and the relative decay rate of the non-interacting subsystems. We also analyze the classical limit of the polariton system within a non-Hermitian framework, employing coherent states.

cond-mat.mes-hall↗

arXiv2025

Quantum multifractality as a probe of phase space in the Dicke model

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.

quant-ph↗

arXiv2025

Phase space geometry of collective spin systems: Scaling and Fractality

We examine the scaling of the inverse participation ratio of spin coherent states in the energy basis of three collective spin systems: a bounded harmonic oscillator, the Lipkin-Meshkov-Glick model, and the Quantum Kicked Top. The finite-size quantum probing provides detailed insights into the structure of the phase space, particularly the relationship between critical points in classical dynamics and their quantum counterparts in collective spin systems. We introduce a finite-size scaling mass exponent that makes it possible to identify conditions under which a power-law behavior emerges, allowing to assign a fractal dimension to a coherent state. For the Quantum Kicked Top, the fractal dimension of coherent states -- when well-defined -- exhibits three general behaviors: one related to the presence of critical points and two associated with regular and chaotic dynamics. The finite-size scaling analysis paves the way toward exploring collective spin systems relevant to quantum technologies within the quantum-classical framework.

quant-ph↗

arXiv2023

Mediated interactions between Fermi polarons and the role of impurity quantum statistics

The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle, a polaron, is an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. As an inherent and important property such quasi-particles interact with each other via modulation of the medium. While quantum simulation experiments with ultracold atoms have significantly improved our understanding of individual polarons, the detection of their interactions has remained elusive in these systems. Here, we report the unambiguous observation of mediated interactions between Fermi polarons consisting of K impurities embedded in a Fermi sea of Li atoms. Our results confirm two landmark predictions of Landau's Fermi-liquid theory: the shift of the polaron energy due to mediated interactions, linear in the concentration of impurities, and its sign inversion with impurity quantum statistics. For weak to moderate interactions between the impurities and the medium, we find excellent agreement with the static (zero-momentum and energy) predictions of Fermi-liquid theory. For stronger impurity-medium interactions, we show that the observed behaviour at negative energies can be explained by a more refined many-body treatment including retardation and molecule formation

cond-mat.quant-gas↗

arXiv2023

Chaos and Thermalization in the Spin-Boson Dicke Model

We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.

quant-ph↗

arXiv2022

Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite dimensional systems, such as localization and scarring.

quant-ph↗

arXiv2022

Identification of quantum scars via phase-space localization measures

There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the $α$-moments of the Husimi function and is known as the Rényi occupation of order $α$. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with $α>1$ are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments ($α>1$) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.

quant-ph↗

arXiv2021

Quantum scarring in a spin-boson system: fundamental families of periodic orbits

As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom-photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

cond-mat.stat-mech↗

arXiv2021

Ubiquitous quantum scarring does not prevent ergodicity

In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite of that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.

cond-mat.stat-mech↗

arXiv2020

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behaviour of the particles launched either at the single particle ground state or saddle point energy, in a time-independent potential. We complement these results by a characterisation of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time-evolution of a single particle's von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (\textsc{Mctdh-x}) -- which also allows us to extrapolate our results for increasing particle numbers.

quant-ph↗

arXiv2020

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.

cond-mat.stat-mech↗

arXiv2019

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.

cond-mat.stat-mech↗

arXiv2019

Analytical description of the survival probability of coherent states in regular regimes

Using coherent states as initial states, we investigate the quantum dynamics of the Lipkin-Meshkov-Glick (LMG) and Dicke models in the semi-classical limit. They are representative models of bounded systems with one- and two-degrees of freedom, respectively. The first model is integrable, while the second one has both regular and chaotic regimes. Our analysis is based on the survival probability. Within the regular regime, the energy distribution of the initial coherent states consists of quasi-harmonic sub-sequences of energies with Gaussian weights. This allows for the derivation of analytical expressions that accurately describe the entire evolution of the survival probability, from $t=0$ to the saturation of the dynamics. The evolution shows decaying oscillations with a rate that depends on the anharmonicity of the spectrum and, in the case of the Dicke model, on interference terms coming from the simultaneous excitation of its two-degrees of freedom. As we move away from the regular regime, the complexity of the survival probability is shown to be closely connected with the properties of the corresponding classical phase space. Our approach has broad applicability, since its central assumptions are not particular of the studied models.

quant-ph↗

arXiv2016

Thermal and Quantum Phase Transitions in Atom-Field Systems: a Microcanonical Analysis

The thermodynamical properties of a generalized Dicke model are calculated and related with the critical properties of its energy spectrum, namely the quantum phase transitions (QPT) and excited state quantum phase transitions (ESQPT). The thermal properties are calculated both in the canonical and the microcanonical ensembles. The latter deduction allows for an explicit description of the relation between thermal and energy spectrum properties. While in an isolated system the subspaces with different pseudo spin are disconnected, and the whole energy spectrum is accesible, in the thermal ensamble the situation is radically different. The multiplicity of the lowest energy states for each pseudo spin completely dominates the thermal behavior, making the set of degenerate states with the smallest pseudo spin at a given energy the only ones playing a role in the thermal properties, making the positive energy states thermally inaccesible. Their quantum phase transitions, from a normal to a superradiant phase, are closely associated with the thermal transition. The other critical phenomena, the ESQPTs occurring at excited energies, have no manifestation in the thermodynamics, although their effects could be seen in finite sizes corrections. A new superradiant phase is found, which only exists in the generalized model, and can be relevant in finite size systems.

quant-ph↗

arXiv2013

Efficient basis for the Dicke Model II: wave function convergence and excited states

An extended bosonic coherent basis has been shown by Chen et al to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space and many excited states by analyzing the convergence in the wave functions.

quant-ph↗

arXiv2011

Numerical solutions of the Dicke Hamiltonian

We study the numerical solutions of the Dicke Hamiltonian, which describes a system of many two level atoms interacting with a monochromatic radiation field into a cavity. The Dicke model is an example of a quantum collective behavior which shows superradiant quantum phase transitions in the thermodynamic limit. Results obtained employing two different bases are compared. Both of them use the pseudospin basis to describe the atomic states. For the photon states we use in one case Fock states, while in the other case we use a basis built over a particular coherent state, associated to each atomic state. It is shown that, when the number of atoms increases, the description of the ground state of the system in the superradiant phase requires an equivalent number of photons to be included. This imposes a strong limit to the states that can be calculated using Fock states, while the dimensionality needed to obtain convergent results in the other basis decreases when the atomic number increases, allowing calculations that are very difficult in the Fock basis. Naturally, it reduces also the computing time, economizing computing resources. We show results for the energy, the photon number and the number of excited atoms, for the ground and the first excited state.

quant-ph↗