A study of quantum decoherence in a system with Kolmogorov-Arnol'd-Moser tori

A quantum Kolmogorov-Arnold-Moser theorem in the anisotropic Dicke model and its possible implications in the hybrid Sachdev-Ye-Kitaev models

The classical Kolmogorov-Arnold-Moser (KAM) theorem provides the underlying mechanism for the stability of the solar system under some small chaotic perturbations. Despite many previous efforts, any quantum version of the KAM theorem remains elusive In this work, we provide a quantum KAM theorem in the context of the anisotropic Dicke model which is the most important quantum optics model. It describes a single mode of photons coupled to $ N $ qubits with both a rotating wave (RW) term and a counter-RW (CRW) term. As the ratio of the CRW over the RW term increases from zero to one, the systems…

用于量子参数估计的非柯尔莫哥洛夫-阿诺德-莫泽（KAM）量子传感器

Non-Kolmogorov-Arnold-Moser Quantum Sensors for Quantum Parameter Estimation

本研究提出利用非KAM系统的共振敏感性作为量子传感器，通过计算量子费舍尔信息，发现其在满足共振条件时QFI显著增强，可实现优于混沌辅助等传感的计量性能。

Quantum Kicked Dynamics and Classical Diffusion

We consider the quantum counterpart of the kicked harmonic oscillator showing that it undergoes the effect of delocalization in momentum when the classical diffusional threshold is obeyed. For this case the ratio between the oscillator frequency and the frequency of the kick is a rational number, strictly in analogy with the classical case that does not obey the Kolmogorov-Arnold-Moser theorem as the unperturbed motion is degenerate. A tight-binding formulation is derived showing that there is not delocalization in momentum for irrational ratio of the above frequencies. In this way, it is stra…

Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics

We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.

Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems

This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered, those satisfying the classical Kolmogorov-Arnol'd-Moser scenario and those which not. The experimental realization of some of these systems using atom-optics methods will be mentioned.

Wannier basis method for KAM effect in quantum mechanics

The effect of Kolmogorov-Arnold-Moser (KAM) theorem in quantum systems is manifested in dividing eigenstates into regular and irregular states. We propose an effective method based on Wannier basis in phase space to illustrate this division of eigenstates. The quantum kicked-rotor model is used to illustrate this method, which allows us to define the area and effective dimension of each eigenstate to distinguish quantitatively regular and irregular eigenstates. This Wannier basis method also allows us to define the length of a Planck cell in the spectrum that measures how many Planck cells the…