Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2210.15693 · Physical Review Research

Dynamical phase transitions in periodically driven Bardeen-Cooper-Schrieffer systems

H. P. Ojeda Collado, Gonzalo Usaj, C. A. Balseiro, Damián H. Zanette, J. Lorenzana

Published Apr 7, 2023• 18 citations
arXivHTMLPDF

Abstract

We present a systematic study of the dynamical phase diagram of a periodically driven BCS system as a function of drive strength and frequency. Three different driving mechanisms are considered and compared: oscillating density of states, oscillating pairing interaction, and oscillating external paring field. We identify the locus in parameter space of parametric resonances and four dynamical phases: Rabi-Higgs, gapless, synchronized Higgs, and time-crystal phases. We demonstrate that the main features of the phase diagram are quite robust to different driving protocols and discuss the order of the transitions. By mapping the BCS problem to a collection of nonlinear and interacting classical oscillators, we shed light on the origin of time-crystal phases and parametric resonances appearing for subgap excitations.

DOI
10.1103/physrevresearch.5.023014

Related papers

Emergent parametric resonances and time-crystal phases in driven Bardeen-Cooper-Schrieffer systems

H. P. Ojeda Collado, Gonzalo Usaj, C. A. Balseiro +2 more

We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer condensate subject to a periodic drive.We demonstrate that the combined effect of drive and interactions results in emerging parametric resonances, analogous to a vertically driving pendulum.In particular, Arnold tongues appear when the driving frequency matches 2 0 /n, with n being a natural number and 0 being the equilibrium gap parameter.Inside the Arnold tongues we find a commensurate time-crystal condensate which retains the U(1) symmetry breaking of the parent superfluid/superconducting phase and shows an additional time-translational symmetry breaking.Outside these tongues, the synchronized collective Higgs mode found in quench protocols is stabilized without the need of a strong perturbation.Our results are directly relevant to cold-atom and condensed-matter systems and do not require very long energy relaxation times to be observed.

arXiv:2107.09683•Physical Review Research•Nov 10, 2021•38 citations

Population inversion and dynamical phase transitions in a driven superconductor

H. P. Ojeda Collado, J. Lorenzana, Gonzalo Usaj +1 more

We consider a superconductor in which the density of states at the Fermi level or the pairing interaction is driven periodically with a frequency larger than the superconducting gap in the collisionless regime. We show by numerical and analytical computations that a subset of quasiparticle excitations enter into resonance and perform synchronous Rabi oscillations leading to cyclic population inversion with a frequency that depends on the amplitude of the drive. As a consequence a different ``Rabi-Higgs'' mode emerges. Turning off the drive at different times and modulating the strength allows access to all known dynamical phases of the order parameter: persistent oscillations, oscillations with damping and overdamped dynamics. We discuss physical realizations of the drive and methods to detect the dynamics.

arXiv:1808.01287•Physical review. B./Physical review. B•Dec 27, 2018•22 citations

Nonlinear dynamics of driven superconductors with dissipation

H. P. Ojeda Collado, Gonzalo Usaj, J. Lorenzana +1 more

In the absence of dissipation a periodically driven BCS superconductor can enter a coherent nonlinear regime of collective Rabi oscillations which last for arbitrary long times [Ojeda Collado et al., Phys. Rev. B 98, 214519 (2018)]. Here we show that dissipation effects introduce dramatic changes: (i) The collective Rabi mode becomes a transient. (ii) At long times a steady state is reached showing strong nonlinear effects for large enough drive strength. We identify the physical parameters governing the various crossovers and present a detailed computation of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and time-resolved tunneling spectra aiming at detecting the collective Rabi oscillations and the steady-state nonlinearities. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant.

arXiv:1909.12310•Physical review. B./Physical review. B•Feb 6, 2020•15 citations

Robustness anylysis of periodic oscillations in continuous-time crystals

Hongxia Li, LI Tingmei, WANG Zengpu +2 more

Continuous time crystals represent a novel state in many-body systems that can self-organize into timeperiodic oscillations without external periodic driving. Recent experiments have achieved such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A decisive characteristic of time crystals is their robustness, meaning that despite various disturbances, including fluctuations in internal parameters and external noise, they can still maintain rhythmic behavior, which has scientific value and echnological application potential. Although previous studies have shown that specific experimental parameters have robustness, thare is a lack of a systematic framework for quantifying and predicting their resilience to disturbances, and the underlying physics of this robustnessis still not fully understood. The key unresolved problems include how nonlinear interactions and feedback mechanisms contribute to stability, and what the critical thresholds are for parameter variations beyond which temporal order collapses. This work addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are determined by dipole-dipole interactions and atomic transition strengths, which define the temporal symmetry breaking that occurs in the system. Externally, the response of the system is controlled by the strength of the optical driving field and the energy dissipation rate. A key finding is the determination of an intrinsic feedback mechanism for a dynamically stabile time crystal. This mechanism plays a role in restoring force, correcting deviations caused by minor disturbances, and maintaining the coherence of oscillatory phase. Moreover, the system displays nonlinear dynamical behavior, characterized by two different states: one is stable oscillation continuing under moderate disturbance, and the other is stronger disturbance causing dynamical phase transition, resulting in switching between disordered or dynamically unstable state and stable state. These results provide a comprehensive understanding of the various behaviors observed in continuous time crystals and lay an important theoretical foundation for utilizing their unique properties in advanced applications such as quantum information processing and precision metrology.

Acta Physica Sinica•Jan 1, 2025•0 citations

Engineering Higgs dynamics by spectral singularities

H. P. Ojeda Collado, Nicolò Defenu, J. Lorenzana

We generalize the dynamical phase diagram of a Bardeen-Cooper-Schrieffer condensate, considering attractive to repulsive, i.e., critical quenches (CQs) and a nonconstant density of states (DOS). We show that different synchronized Higgs dynamical phases can be stabilized, associated with singularities in the DOS and different quench protocols. In particular, the CQ can stabilize an overlooked high-frequency Higgs dynamical phase related to the upper edge of the fermionic band. For a compensated Dirac system we find a Dirac-Higgs mode associated with the cusp singularity at the Fermi level, and we show that synchronized phases become more pervasive across the phase diagram. The relevance of these remarkable phenomena and their realization in ensembles of fermionic cold atoms confined in optical lattices is also discussed.

arXiv:2205.06826•Physical Review Research•Apr 6, 2023•10 citations

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Marin Bukov, Michael Kolodrubetz, Anatoli Polkovnikov

We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.

arXiv:1510.02744•Physical Review Letters•Mar 21, 2016•187 citations
We present a systematic study of the dynamical phase diagram of a periodically driven BCS system as a function of drive strength and frequency. Three different driving mechanisms are considered and compared: oscillating density of states, oscillating pairing interaction, and oscillating external paring field. We identify the locus in parameter space of parametric resonances and four dynamical phases: Rabi-Higgs, gapless, synchronized Higgs, and time-crystal phases. We demonstrate that the main features of the phase diagram are quite robust to different driving protocols and discuss the order of the transitions. By mapping the BCS problem to a collection of nonlinear and interacting classical oscillators, we shed light on the origin of time-crystal phases and parametric resonances appearing for subgap excitations.
We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer condensate subject to a periodic drive.We demonstrate that the combined effect of drive and interactions results in emerging parametric resonances, analogous to a vertically driving pendulum.In particular, Arnold tongues appear when the driving frequency matches 2 0 /n, with n being a natural number and 0 being the equilibrium gap parameter.Inside the Arnold tongues we find a commensurate time-crystal condensate which retains the U(1) symmetry breaking of the parent superfluid/superconducting phase and shows an additional time-translational symmetry breaking.Outside these tongues, the synchronized collective Higgs mode found in quench protocols is stabilized without the need of a strong perturbation.Our results are directly relevant to cold-atom and condensed-matter systems and do not require very long energy relaxation times to be observed.
We consider a superconductor in which the density of states at the Fermi level or the pairing interaction is driven periodically with a frequency larger than the superconducting gap in the collisionless regime. We show by numerical and analytical computations that a subset of quasiparticle excitations enter into resonance and perform synchronous Rabi oscillations leading to cyclic population inversion with a frequency that depends on the amplitude of the drive. As a consequence a different ``Rabi-Higgs'' mode emerges. Turning off the drive at different times and modulating the strength allows access to all known dynamical phases of the order parameter: persistent oscillations, oscillations with damping and overdamped dynamics. We discuss physical realizations of the drive and methods to detect the dynamics.
In the absence of dissipation a periodically driven BCS superconductor can enter a coherent nonlinear regime of collective Rabi oscillations which last for arbitrary long times [Ojeda Collado et al., Phys. Rev. B 98, 214519 (2018)]. Here we show that dissipation effects introduce dramatic changes: (i) The collective Rabi mode becomes a transient. (ii) At long times a steady state is reached showing strong nonlinear effects for large enough drive strength. We identify the physical parameters governing the various crossovers and present a detailed computation of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and time-resolved tunneling spectra aiming at detecting the collective Rabi oscillations and the steady-state nonlinearities. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant.
Continuous time crystals represent a novel state in many-body systems that can self-organize into timeperiodic oscillations without external periodic driving. Recent experiments have achieved such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A decisive characteristic of time crystals is their robustness, meaning that despite various disturbances, including fluctuations in internal parameters and external noise, they can still maintain rhythmic behavior, which has scientific value and echnological application potential. Although previous studies have shown that specific experimental parameters have robustness, thare is a lack of a systematic framework for quantifying and predicting their resilience to disturbances, and the underlying physics of this robustnessis still not fully understood. The key unresolved problems include how nonlinear interactions and feedback mechanisms contribute to stability, and what the critical thresholds are for parameter variations beyond which temporal order collapses. This work addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are determined by dipole-dipole interactions and atomic transition strengths, which define the temporal symmetry breaking that occurs in the system. Externally, the response of the system is controlled by the strength of the optical driving field and the energy dissipation rate. A key finding is the determination of an intrinsic feedback mechanism for a dynamically stabile time crystal. This mechanism plays a role in restoring force, correcting deviations caused by minor disturbances, and maintaining the coherence of oscillatory phase. Moreover, the system displays nonlinear dynamical behavior, characterized by two different states: one is stable oscillation continuing under moderate disturbance, and the other is stronger disturbance causing dynamical phase transition, resulting in switching between disordered or dynamically unstable state and stable state. These results provide a comprehensive understanding of the various behaviors observed in continuous time crystals and lay an important theoretical foundation for utilizing their unique properties in advanced applications such as quantum information processing and precision metrology.
We generalize the dynamical phase diagram of a Bardeen-Cooper-Schrieffer condensate, considering attractive to repulsive, i.e., critical quenches (CQs) and a nonconstant density of states (DOS). We show that different synchronized Higgs dynamical phases can be stabilized, associated with singularities in the DOS and different quench protocols. In particular, the CQ can stabilize an overlooked high-frequency Higgs dynamical phase related to the upper edge of the fermionic band. For a compensated Dirac system we find a Dirac-Higgs mode associated with the cusp singularity at the Fermi level, and we show that synchronized phases become more pervasive across the phase diagram. The relevance of these remarkable phenomena and their realization in ensembles of fermionic cold atoms confined in optical lattices is also discussed.
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.