Quantum-jump vs stochastic Schr\"{o}dinger dynamics for Gaussian states with quadratic Hamiltonians and linear Lindbladians

• URL: http://arxiv.org/abs/2203.11530v2
• Date: Thu, 27 Oct 2022 12:24:40 GMT
• Title: Quantum-jump vs stochastic Schr\"{o}dinger dynamics for Gaussian states with quadratic Hamiltonians and linear Lindbladians
• Authors: Robson Christie, Jessica Eastman, Roman Schubert and Eva-Maria Graefe
• Abstract summary: We consider quantum-jump and Schr"odinger dynamics for initially Gaussian states. While both unravellings converge to the same Lindblad dynamics when averaged, the individual dynamics can differ qualitatively.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The dynamics of Gaussian states for open quantum systems described by Lindblad equations can be solved analytically for systems with quadratic Hamiltonians and linear Lindbladians, showing the familiar phenomena of dissipation and decoherence. It is well known that the Lindblad dynamics can be expressed as an ensemble average over stochastic pure-state dynamics, which can be interpreted as individual experimental implementations, where the form of the stochastic dynamics depends on the measurement setup. Here we consider quantum-jump and stochastic Schr\"odinger dynamics for initially Gaussian states. While both unravellings converge to the same Lindblad dynamics when averaged, the individual dynamics can differ qualitatively. For the stochastic Schr\"odinger equation, Gaussian states remain Gaussian during the evolution, with stochastic differential equations governing the evolution of the phase-space centre and a deterministic evolution of the covariance matrix. In contrast to this, individual pure-state dynamics arising from the quantum-jump evolution do not remain Gaussian in general. Applying results developed in the non-Hermitian context for Hagedorn wavepackets, we formulate a method to generate quantum-jump trajectories that is described entirely in terms of the evolution of an underlying Gaussian state. To illustrate the behaviours of the different unravellings in comparison to the Lindblad dynamics, we consider two examples in detail, which can be largely treated analytically, a harmonic oscillator subject to position measurement and a damped harmonic oscillator. In both cases, we highlight the differences as well as the similarities of the stochastic Schr\"odinger and the quantum-jump dynamics.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Lindbladian dynamics with loss of quantum jumps [4.889561507168047]
  We investigate the balance-breaking dynamics by partly eliminating jumps from postselection experiments. To describe this dynamics, a non-linear Lindblad master equation (NLME) is derived from quantum trajectory method. The NLME shows significant advantages in analytical analysis over quantum trajectory method.
  arXiv  Detail & Related papers  (2024-05-20T06:15:25Z)
• Quantum simulation of the Fokker-Planck equation via Schrodingerization [33.76659022113328]
  This paper studies a quantum simulation technique for solving the Fokker-Planck equation. We employ the Schrodingerization method-it converts any linear partial and ordinary differential equation with non-Hermitian dynamics into systems of Schrodinger-type equations.
  arXiv  Detail & Related papers  (2024-04-21T08:53:27Z)
• Quasi-integrability and nonlinear resonances in cold atoms under modulation [11.286969347667473]
  We present an exact analysis of the evolution of a two-level system under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces, one of them binding while the other one scattering type.
  arXiv  Detail & Related papers  (2023-09-08T09:42:25Z)
• From Lindblad master equations to Langevin dynamics and back [0.0]
  A case study of the non-equilibrium dynamics of open quantum systems is presented. The quantum Langevin equations are derived from an identical set of physical criteria. The associated Lindblad equations are derived but only one of them is completely positive.
  arXiv  Detail & Related papers  (2023-05-10T16:59:48Z)
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schr\"odinger equation [8.374675687855248]
  Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics. We show a feasible quantum simulation approach for dissipative quantum dynamics with Schr"odinger equation.
  arXiv  Detail & Related papers  (2022-06-30T08:48:25Z)
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue [0.0]
  The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM) The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales. The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
  arXiv  Detail & Related papers  (2022-06-14T11:23:04Z)
• 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)
• Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian [0.0]
  We study the dynamics of entanglement in the quantum Ising chain with dephasing dissipation in a Lindblad master equation form. We consider two unravelings which preserve the Gaussian form of the state, allowing to address large system sizes.
  arXiv  Detail & Related papers  (2021-11-22T15:53:50Z)
• False signals of chaos from quantum probes [0.0]
  We demonstrate that two-time correlation functions, which are generalizations of out-of-time-ordered correlators, can show 'false-flags' of chaos. We analyze a system of bosons trapped in a double-well potential and probed by a quantum dot.
  arXiv  Detail & Related papers  (2021-08-20T22:36:06Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)

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.