arXiv subjects

Francisco Pérez-Bernal

Publications and source records attributed to Francisco Pérez-Bernal.

At least 19 recordsLinked to original sources

arXiv2026

Instability-enhanced quantum sensing with tunable multibody interactions

Dynamical instabilities can amplify small perturbations into measurable signals, offering a route to quantum-enhanced sensing. This mechanism was experimentally demonstrated in a collective spin system with quadratic interactions, described by a twist-and-turn Hamiltonian, where quantum evolution near an unstable point leads to exponential growth of spin fluctuations, enabling metrological gain beyond the standard quantum limit. Here, we show that a quartic extension of this Hamiltonian substantially increases the amplification. This additional nonlinear term reshapes the phase-space structure, generating new unstable fixed points with larger local Lyapunov exponents and therefore faster signal amplification at shorter evolution times. Remarkably, even for the same instability rate (equal Lyapunov exponent), collective multibody interactions outperform the quadratic case, demonstrating that metrological gain is not determined by the Lyapunov exponent alone. We show analytically that the finite-time growth of the gain is governed also by the local phase-space curvature around the unstable point. Only for a symmetric unstable point, as in the quadratic case, is the finite-time gain described by the Lyapunov exponent alone. Our results identify local phase-space curvature as an additional resource for optimizing the speed and performance of quantum sensors.

quant-ph↗

arXiv2026

Degeneracy beyond the parity-symmetry protection in the Lipkin-Meshkov-Glick model

Degeneracy patterns in quantum mechanics stem from the system symmetries. In particular, the broken-symmetry phase in the well-known Lipkin-Meshkov-Glick (LMG) model is composed of doubly-degenerate states of different parity. In this work, we show that such doublets can exist even if parity is not conserved. For this purpose, our starting point is an anharmonic LMG Hamiltonian with a second-order ground-state quantum phase transition (GSQPT) and a rich spectrum, with two different excited-state quantum phase transitions. The inclusion in the Hamiltonian of a term inducing a first-order GSQPT breaks the parity symmetry but conserving the exponential degeneracy in the energy doublets. We demonstrate that this phenomenon can be traced back to the existence of a $\mathbb{Z}_2$ symmetry (reflection symmetry) in the system's classical limit phase space that leads to an anti-unitary $\mathbb{Z}_2$ symmetry in the quantum system.

quant-ph↗

arXiv2026

Steady-state spectral kissing and dissipative phase transitions

Spectral kissing, recently realized in a Kerr parametric oscillator (KPO), refers to the merging of pairs of energy levels and arises as a manifestation of an excited-state quantum phase transition (ESQPT). Here, we show that this phenomenon has a dissipative counterpart encoded in the spectrum of the steady-state density matrix. Using a dissipative KPO as a representative example, we demonstrate that, in the weak-dissipation regime, the eigenvalues of the steady-state density matrix organize into quasi-degenerate pairs that mirror the spectral kissing of the corresponding closed system. As the dissipation strength increases, this pairing gradually disappears. By analyzing the classical limit of the system, we derive analytical expressions for the critical lines governing both the onset of steady-state spectral kissing and its disappearance at a dissipative phase transition.

quant-ph↗

arXiv2026

Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator

One-dimensional quantum systems that undergo spontaneous symmetry-breaking, having a symmetric (non-degenerate) and a broken-symmetry (doubly-degenerate) phase, have been intensely studied in different branches of physics. In most cases, the spontaneously-broken symmetry is parity. However, it is possible to obtain similar phases in systems without parity symmetry, through an antiunitary symmetry that implies a two-fold symmetry either on momentum or coordinate in the system's classical limit. To illustrate this phenomenon, we use a Kerr parametric oscillator (KPO) with one- and two-photon drives that, despite the breaking of parity symmetry, may have doubly-degenerate levels. Different realizations of squeezed KPOs convey a great deal of attention, as effective Hamiltonians for driven superconducting circuits and the occurrence of degeneracy in such systems could be of practical interest in their application to obtain protected qubits in parity-breaking setups. In addition to this, the reported spectral features strongly indicate the existence of additional symmetries in the system.

quant-ph↗

arXiv2025

Phase transitions, symmetries, and tunneling in Kerr parametric oscillators

Quantum Kerr parametric oscillators (KPOs) are systems out of equilibrium with a wide range of applications in quantum computing, quantum sensing, and fundamental research. They have been realized in superconducting circuits and photonic platforms. In this work, we explore the onset of ground-state and excited-state quantum phase transitions in KPOs, focusing on the role of the phase-space rotational symmetry when the driving frequency is $μ$ times the oscillator's natural frequency, specifically for $μ=1,2,3,4$. These cases are experimentally accessible in superconducting circuits, where the Floquet quasienergy spectrum can also be studied as a function of tunable control parameters. Using the classical Hamiltonian of the system, we identify the critical points associated with quantum phase transitions and analyze the emergence of both real and avoided level crossings, examining their influence on the energy spectrum and tunneling dynamics. Our findings provide insights into the engineering of robust quantum states, quantum dynamics control, and onset of quantum phase transitions with implications for critical quantum sensing.

quant-ph↗

arXiv2025

Characterizing the Lipkin-Meshkov-Glick excited spectrum through the quantum coherence spectrum

Excited-state quantum phase transitions extend the quantum phase transition concept beyond the ground state and offer insights into the complex behavior of quantum systems. In the present work, we assess the use of the multiple quantum coherence spectrum as a valid tool to probe excited state quantum phase transitions within the framework of the Lipkin-Meshkov-Glick model. The time dependence and the long-time average of the multiple quantum coherence spectrum reveal the intricate dynamics that stems from the existence of singularities in the excited spectrum of a quantum many-body system.

quant-ph↗

arXiv2024

Quantum sensing in Kerr parametric oscillators

Quantum metrology and quantum sensing aim to use quantum properties to enhance measurement precision beyond what could be classically achieved. Here, we demonstrate how the analysis of the phase space structure of the classical limit of Kerr parametric oscillators can be used for determining control parameters values that lead to the squeezing of the uncertainty in position and the amplification of the quantum Fisher information. We also explore how quantum sensing can benefit from excited-state quantum phase transitions, even in the absence of a conventional quantum phase transition. The system that we consider models exciton-polariton condensates and superconducting circuits, making our study relevant for potential experimental applications.

quant-ph↗

arXiv2024

Simulating Chemistry on Bosonic Quantum Devices

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

quant-ph↗

arXiv2024

Driving superconducting qubits into chaos

Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages toward the encoding and manipulation of error-protected quantum information. The recent realization of Kerr-cat qubits made use of the nonlinearity of the SNAIL transmon superconducting circuit and a squeezing drive. Increasing nonlinearities can enable faster gate times, but, as shown here, can also induce chaos and melt the qubit away. We determine the region of validity of the Kerr-cat qubit and discuss how its disintegration could be experimentally detected. The danger zone for parametric quantum computation is also a potential playground for investigating quantum chaos with driven superconducting circuits.

quant-ph↗

arXiv2023

Symmetries of the squeeze-driven Kerr oscillator

We study the symmetries of the static effective Hamiltonian of a driven superconducting nonlinear oscillator, the so-called squeeze-driven Kerr Hamiltonian, and discover a remarkable quasi-spin symmetry $su(2)$ at integer values of the ratio $η=Δ/K$ of the detuning parameter $Δ$ to the Kerr coefficient $K$. We investigate the stability of this newly discovered symmetry to high-order perturbations arising from the static effective expansion of the driven Hamiltonian. Our finding may find applications in the generation and stabilization of states useful for quantum computing. Finally, we discuss other Hamiltonians with similar properties and within reach of current technologies.

quant-ph↗

arXiv2023

Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

quant-ph↗

arXiv2023

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Phys. Rev. E 106, 044125 (2022)]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.

quant-ph↗

arXiv2023

Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator

The quasi-energy spectrum recently measured in experiments with a squeeze-driven superconducting Kerr oscillator showed good agreement with the energy spectrum of its corresponding static effective Hamiltonian. The experiments also demonstrated that the dynamics of low-energy states can be explained with the same emergent static effective model. The spectrum exhibits real (avoided) level crossings for specific values of the Hamiltonian parameters, which can then be chosen to suppress (enhance) quantum tunneling. Here, we analyze the spectrum and the dynamics of the effective model up to high energies, which should soon be within experimental reach. We show that the parameters values for the crossings, which can be obtained from a semiclassical approach, can also be identified directly from the dynamics. Our analysis of quantum tunneling is done with the effective flux of the Husimi volume of the evolved states between different regions of the phase space. Both initial coherent states and quench dynamics are considered. We argue that the level crossings and their consequences to the dynamics are typical to any quantum system with one degree of freedom, whose density of states presents a local logarithmic divergence and a local step discontinuity.

quant-ph↗

arXiv2022

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects

The basic Lipkin-Meshkov-Glick model displays a second order ground state quantum phase transition and an excited state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The new ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.

quant-ph↗

arXiv2022

Exceptional Spectral Phase in a Dissipative Collective Spin Model

We study a model of a quantum collective spin weakly coupled to a spin-polarized Markovian environment and find that the spectrum is divided into two regions that we name normal and exceptional Liouvillian spectral phases. In the thermodynamic limit, the exceptional spectral phase displays the unique property of being made up exclusively of second order exceptional points. As a consequence, the evolution of any initial density matrix populating this region is slowed down and cannot be described by a linear combination of exponential decays. This phase is separated from the normal one by a critical line in which the density of Liouvillian eigenvalues diverges, a phenomenon analogous to that of excited-state quantum phase transitions observed in some closed quantum systems. In the limit of no bath polarization, this criticality is transferred onto the steady state, implying a dissipative quantum phase transition and the formation of a boundary time crystal.

quant-ph↗

arXiv2022

Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model

In most cases, excited state quantum phase transitions can be associated with the existence of critical points (local extrema or saddle points) in a system's classical limit energy functional. However, an excited-state quantum phase transition might also stem from the lowering of the asymptotic energy of the corresponding energy functional. One such example occurs in the 2D limit of the vibron model, once an anharmonic term in the form of a quadratic bosonic number operator is added to the Hamiltonian. The study of this case in the broken-symmetry phase was presented in Phys. Rev. A. 81 050101 (2010). In the present work, we delve further into the nature of this excited-state quantum phase transition and we characterize it in the, previously overlooked, symmetric phase of the model making use of quantities such as the effective frequency, the expected value of the quantum number operator, the participation ratio, the density of states, and the quantum fidelity susceptibility. In addition to this, we extend the usage of the quasilinearity parameter, introduced in molecular physics, to characterize the phases in the spectrum of the anharmonic 2D limit of the vibron model and a down-to-earth analysis has been included with the characterization of the critical energies for the linear isomers HCN/HNC.

quant-ph↗

arXiv2021

Equilibration time in many-body quantum systems

Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from perturbation to equilibration, of a paradigmatic disordered many-body quantum system in the chaotic regime. We investigate how the equilibration time depends on the system size and observables. We show that if dynamical manifestations of spectral correlations in the form of the correlation hole ("ramp") are taken into account, the time for equilibration scales exponentially with system size, while if they are neglected, the scaling is better described by a power law with system size, though with an exponent larger than what is expected for diffusive transport.

cond-mat.dis-nn↗

arXiv2021

Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy

Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick (LMG) model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We further consider the diagonal entropy as a random variable over a certain time interval and we find that its associated probability distribution provides a clear distinction between the different phases of ESQPT. We observe that the probability distribution of the diagonal entropy at the ESQPT critical point has an universal form, well described by a beta distribution, and we demonstrate that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.

quant-ph↗