Quantum asymptotic phase reveals signatures of quantum synchronization

• URL: http://arxiv.org/abs/2006.00760v2
• Date: Sat, 11 Feb 2023 03:41:01 GMT
• Title: Quantum asymptotic phase reveals signatures of quantum synchronization
• Authors: Yuzuru Kato and Hiroya Nakao
• Abstract summary: We propose a fully quantum-mechanical definition of the phase, which is a key quantity in the synchronization analysis of classical nonlinear oscillators. We show that phase locking of the system with a harmonic drive at several different frequencies can be interpreted as synchronization on a torus rather than a simple limit cycle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Synchronization of quantum nonlinear oscillators has attracted much attention recently. To characterize the quantum oscillatory dynamics, we recently proposed a fully quantum-mechanical definition of the asymptotic phase, which is a key quantity in the synchronization analysis of classical nonlinear oscillators (Kato and Nakao 2022 Chaos 32 063133). In this work, we further extend this theory and introduce multiple asymptotic phases using the eigenoperators of the adjoint Liouville superoperator of the quantum nonlinear oscillator associated with different fundamental frequencies. We analyze a quantum van der Pol oscillator with Kerr effect in the strong quantum regime and show that the system has several different fundamental frequencies. By introducing order parameters and power spectra in terms of the associated quantum asymptotic phases, we reveal that phase locking of the system with a harmonic drive at several different frequencies, an explicit quantum signature observed only in the strong quantum regime, can be interpreted as synchronization on a torus rather than a simple limit cycle.

Related papers

• Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
  We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
  arXiv  Detail & Related papers  (2024-08-23T10:45:19Z)
• Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint [0.0]
  We propose a definition of the quantum amplitude for quantum oscillatory systems. We show that the proposed quantum amplitude appropriately yields isostable amplitude values that decay exponentially with a constant rate.
  arXiv  Detail & Related papers  (2024-03-28T10:33:29Z)
• Amplification of quantum transfer and quantum ratchet [56.47577824219207]
  We study a model of amplification of quantum transfer and making it directed which we call the quantum ratchet model. The ratchet effect is achieved in the quantum control model with dissipation and sink, where the Hamiltonian depends on vibrations in the energy difference synchronized with transitions between energy levels. Amplitude and frequency of the oscillating vibron together with the dephasing rate are the parameters of the quantum ratchet which determine its efficiency.
  arXiv  Detail & Related papers  (2023-12-31T14:04:43Z)
• 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)
• A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint [0.0]
  The proposed phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes. We show that the proposed phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.
  arXiv  Detail & Related papers  (2023-02-11T03:08:47Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators [0.0]
  Self-oscillating systems are emerging as canonical models for driven dissipative nonequilibrium open quantum systems. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature.
  arXiv  Detail & Related papers  (2020-11-05T08:51:51Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• 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)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)
• Detecting dynamical quantum phase transition via out-of-time-order correlations in a solid-state quantum simulator [12.059058714600607]
  We develop and experimentally demonstrate that out-of-time-order correlators can be used to detect nonoequilibrium phase transitions in the transverse field Ising model. Further applications of this protocol could enable studies other of exotic phenomena such as many body localization, and tests of the holographic duality between quantum and gravitational systems.
  arXiv  Detail & Related papers  (2020-01-17T14:28:42Z)

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.