Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings

• URL: http://arxiv.org/abs/2412.11980v1
• Date: Mon, 16 Dec 2024 17:02:57 GMT
• Title: Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings
• Authors: Luis A. Medina-Dozal, Alejandro R. Urzúa, José Récamier-Angelini,
• Abstract summary: We consider the case of a non-driven system and find its exact time evolution operator. We consider the case of a forced system whose time evolution operator is obtained in an approximate form.
• Score: 44.99833362998488
• License:
• Abstract: In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a non-driven system and find its exact time evolution operator, secondly we consider the case of a forced system whose time evolution operator is obtained in an approximate form. We confront our analytical results with a numerical simulation and find a good agreement between them.

Related papers

• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Temporal evolution of a driven optomechanical system in the strong coupling regime [0.0]
  We obtain a time-evolution operator for a forced optomechanical quantum system. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function.
  arXiv  Detail & Related papers  (2023-09-28T00:52:14Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• Finite resolution ancilla-assisted measurements of quantum work distributions [77.34726150561087]
  We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation.
  arXiv  Detail & Related papers  (2021-11-30T15:08:25Z)
• 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)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics [0.0]
  Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function. This approach is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously. We show how the lengthy process of applying the Floquet formalism to the original equations of motion and deriving a Lyapunov equation from their time-
  arXiv  Detail & Related papers  (2020-02-28T16:20:27Z)
• The interplay between local and non-local master equations: exact and approximated dynamics [0.0]
  We derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. We investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time.
  arXiv  Detail & Related papers  (2020-01-31T16:55:01Z)

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.