Geometric Phase in Quantum Synchronization

• URL: http://arxiv.org/abs/2302.08866v2
• Date: Mon, 10 Jul 2023 14:05:20 GMT
• Title: Geometric Phase in Quantum Synchronization
• Abstract summary: We show that a quantum limit-cycle oscillator attains a geometric phase when the rotation is sufficiently slow. In the presence of an external signal, the geometric phase as a function of the signal strength and the detuning shows a structure that is strikingly similar to the Arnold tongue of synchronization. We derive an analytic expression for the geometric phase of this system, valid in the limit of slow rotation of the quantization axis and weak external signal strength.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a quantum limit-cycle oscillator implemented in a spin system whose quantization axis is slowly rotated. Using a kinematic approach to define geometric phases in nonunitary evolution, we show that the quantum limit-cycle oscillator attains a geometric phase when the rotation is sufficiently slow. In the presence of an external signal, the geometric phase as a function of the signal strength and the detuning between the signal and the natural frequency of oscillation shows a structure that is strikingly similar to the Arnold tongue of synchronization. Surprisingly, this structure vanishes together with the Arnold tongue when the system is in a parameter regime of synchronization blockade. We derive an analytic expression for the geometric phase of this system, valid in the limit of slow rotation of the quantization axis and weak external signal strength, and we provide an intuitive interpretation for this surprising effect.

Related papers

• The Geometric Phase as a Diagnostic for Driven-Dissipative Oscillators [13.38226745175549]
  We show that driven-dissipative quantum oscillators lock their phase, deform their limit cycles, and undergo dissipative phase transitions.<n>This behavior is read from unrelated quantities defined on the same steady-state density matrix.<n>We show that a single geometric quantity organizes them.
  arXiv  Detail & Related papers  (2026-08-26T12:52:36Z)
• Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations [0.48342038441006796]
  We extend the model to include overtone-synthesized sinusoidal coupling with adiabatic temporal modulation.<n>We extend the analysis to the quantum regime, where we find a counterintuitive result: the breakdown of winding-number quantization.
  arXiv  Detail & Related papers  (2026-02-25T00:06:56Z)
• Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising interaction [0.0]
  We present a unified geometric and dynamical framework for a physical system consisting of $n$ spin-$1/2$ particles with all-range Ising interaction.<n>Our analysis reveals that the system evolves over a smooth, compact, two-dimensional manifold with spherical topology.<n>We explore the role of entanglement in shaping the state space geometry, modulating geometric phase, and controlling evolution speed and brachistochrone time.
  arXiv  Detail & Related papers  (2025-12-24T19:37:07Z)
• Symmetry re-breaking in an effective theory of quantum coarsening [0.0]
  We find an apparent speeding up of the coarsening process as the phase transition is approached.<n> persistent oscillations of the order parameter after quenches within the ordered phase.<n>We term this phenomenon symmetry re-breaking, as the resulting late-time magnetization can have a sign opposite to the initial magnetization.
  arXiv  Detail & Related papers  (2025-07-23T10:28:46Z)
• Time-dependent quantum geometric tensor and some applications [0.0]
  We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time- parameter space for a quantum state. This tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states.
  arXiv  Detail & Related papers  (2025-02-03T20:08:02Z)
• Emergent Continuous Time Crystal in Dissipative Quantum Spin System without Driving [1.641189223782504]
  Time crystal, a nonequilibrium phenomenon extending spontaneous symmetry breaking into the temporal dimension, holds fundamental significance in quantum many-body physics. We numerically identify the emergence of novel nonstationary oscillatory states by analyzing the spin dynamics. This study provides many insights into the intricate interplay between the dissipation-induced spin downwards and anisotropic-interaction-induced spin precession or spin fluctuation.
  arXiv  Detail & Related papers  (2024-03-13T12:40:32Z)
• Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response [0.0]
  This work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator. Two non-linear terms break the rotational phase space symmetry, Wigner distribution of quantum mechanical limit cycle state is not rotationally symmetric. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue.
  arXiv  Detail & Related papers  (2024-01-08T11:19:51Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model [0.0]
  We investigate the equilibrium properties and relaxation features of the dissipative quantum Rabi model. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength.
  arXiv  Detail & Related papers  (2022-05-23T18:13:10Z)
• Out-of-time-order correlator in the quantum Rabi model [62.997667081978825]
  We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase. We show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size.
  arXiv  Detail & Related papers  (2022-01-17T10:56:57Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase [0.9176056742068814]
  We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type. Adiabatic evolution over time-period $mathcalT$ is studied in Heisenberg picture to compute the expression of geometric phase-shift.
  arXiv  Detail & Related papers  (2021-10-10T08:05:18Z)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• Metastable quantum entrainment [0.0]
  We show that quantum entrainment is here characterized by fluctuations driving an incoherent process between two metastable phases. We discuss connections with the phenomena of dissipative phase transitions and transient synchronization in open quantum systems.
  arXiv  Detail & Related papers  (2021-09-03T10:58:21Z)
• Synchronisation phase as an indicator of persistent quantum correlations between subsystems [68.8204255655161]
  Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. We show that our analysis applies to a variety of spontaneously synchronising open quantum systems.
  arXiv  Detail & Related papers  (2020-06-29T17:21:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.