Quantum dynamics of a driven parametric oscillator in a Kerr medium

• URL: http://arxiv.org/abs/2306.02249v1
• Date: Sun, 4 Jun 2023 03:44:37 GMT
• Title: Quantum dynamics of a driven parametric oscillator in a Kerr medium
• Authors: E. Bolandhemmat and F. Kheirandish
• Abstract summary: We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and time-dependent frequency. In the following, to investigate the characteristics and statistical properties of the generated states, we calculate the autocorrelation function, the Mandel $Q$ parameter, and the Husimi $Q$-function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we first analyze a parametric oscillator with both mass and frequency time-dependent. We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and time-dependent frequency followed by a time transformation $t\rightarrow\int_0^t dt'\,1/m(t')$. Then we proceed by investigating the quantum dynamics of a parametric oscillator with unit mass and time-dependent frequency in a Kerr medium under the influence of a time-dependent force along the motion of the oscillator. The quantum dynamics of the time-dependent oscillator is analyzed from both analytical and numerical points of view in two main regimes: (i) small Kerr parameter $\chi$, and (ii) small confinement parameter $k$. In the following, to investigate the characteristics and statistical properties of the generated states, we calculate the autocorrelation function, the Mandel $Q$ parameter, and the Husimi $Q$-function.

Related papers

• Time-dependent Dunkl-Pauli Oscillator [0.0]
  We construct the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and frequency. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems.
  arXiv  Detail & Related papers  (2024-10-24T07:38:02Z)
• 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)
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them [0.0]
  We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system. We show that an equivalence exists between the total costs of obtaining an operator through time evolution.
  arXiv  Detail & Related papers  (2024-05-23T10:32:29Z)
• 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)
• Powering an autonomous clock with quantum electromechanics [42.87502453001109]
  We theoretically analyse an autonomous clock comprising a nanoelectromechanical system, which undergoes self-oscillations driven by electron tunnelling. We simulate the dynamics of the system in the quasi-adiabatic limit of slow mechanical motion, allowing us to infer statistical properties of the clock's ticks from the current auto-correlation function.
  arXiv  Detail & Related papers  (2023-07-18T10:08:37Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator [0.0]
  We study the time-dependent behaviour of quantum correlations of a system governed by out-of-equilibrium dynamics. Next, we study a specific case, where the system exhibits chaotic behaviour by computing the quantum Lyapunov from the time-dependent behaviour of OTOC.
  arXiv  Detail & Related papers  (2022-10-03T18:00:02Z)
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits [0.0]
  We develop the linear response theory formulation suitable for application to various pHH systems. We apply our results to two textitPT-symmetric non-Hermitian quantum systems.
  arXiv  Detail & Related papers  (2022-06-18T10:05:30Z)
• Effects of quenching protocols based on parametric oscillators [2.363392878776903]
  We focus on the case where $omega(t)2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,omega2)$ plane. We provide an insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.
  arXiv  Detail & Related papers  (2020-07-04T17:37:36Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)

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.