Abstract
We study the evolution in time of the quantum Mathieu oscillator (QMO), according to the motion of a charged particle in a radio frequency Paul trap. We adopt non-perturbative treatment based on the quantized Floquet formalism together with the resonating averages method (RAM). We prove that we can develop solutions of the time-dependent Schrödinger equation of such a system, in terms of the simple harmonic oscillator wave functions. Numerical simulations of the analytical results are performed to show the coherence and the squeezed proprieties of the wave-packet of this system.
Highlights
Numerous mathematical and physical studies have been devoted to the construction of robust framework for solving the time-dependent Schrödinger equation of quantum systems [1] [2]
We study the evolution in time of the quantum Mathieu oscillator (QMO), according to the motion of a charged particle in a radio frequency Paul trap
We adopt non-perturbative treatment based on the quantized Floquet formalism together with the resonating averages method (RAM)
Summary
Numerous mathematical and physical studies have been devoted to the construction of robust framework for solving the time-dependent Schrödinger equation of quantum systems [1] [2]. In the regime of strong laser-matter interaction problems, a non-perturbative approach, based on the quantization version of the Floquet theorem has been established and applied to schemes of physical systems with periodic Hamiltonians [7] [8] [9]. This was used to give explanation of multiphoton processes in intense laser fields [10], selective excitation of molecu-. These quantum steady states or Floquet states constitute the most probable states, and provide a useful dynamical description induced by the time-periodic interaction
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