Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions

Abstract

We investigate the quantum signatures of classical nonlinear resonances by making the analytic connection between the quantum wave functions and the classical periodic orbits for the uncoupled systems. It is found that the highly efficient extension of the localized coherent states within the classical caustics is an intriguing phenomenon in mesoscopic systems with nonlinear resonances. With the theoretical analysis, we experimentally demonstrate that the laser resonator with an intracavity saturable absorber can be employed to visualize the wave patterns analogous to the quantum wave functions associated with Fermi resonance.

Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

“…As shown in Fig. 1(a), the wave patterns corresponding to the Lissajous periodic orbits of two-dimensional (2D) commensurate harmonic oscillators have been confirmed to be the predominant modes in the selectively pumped large-Fresnel-number spherical cavity with astigmatism [31][32][33][34][35]. Furthermore, as shown in Fig.…”

“…In contrast, the emergence of classical features in 2D square billiards is found to arise from the superposition of nearly degenerate eigenstates induced by the tiny damping effect. The present model can provide deep insight into mesoscopic physics [24][25][26][27] and transverse pattern formations in laser resonators [31][32][33][35][36][37][38][39].…”

“…We further verify that the quantum Green's function with an appropriate damping factor can be decomposed to correspond to the individual classical periodic orbit. Since the quantum-classical or ray-wave correspondence has been ubiquitously observed in numerous systems [22][23][24][25][26][27][31][32][33][34][35][36][37][38][39][40], the present analysis can offer important insights into quantum physics, mesoscopic physics, and laser physics.…”

“…Quantum wave functions correlated with classical periodic orbits have been verified to play an important role in explaining the quantum phenomena such as shell effects in nuclei and metallic clusters [22,23], conductance fluctuations in mesoscopic quantum transports [24,25], and oscillations in photodetachment cross sections [26,27]. On the other hand, thanks to Hamilton's ingenious optico-mechanical theory [28][29][30], modern laser resonators have been widely exploited to analogously explore the formation of quantum coherent waves in the mesoscopic regime [31][32][33][34][35][36][37][38][39][40]. As shown in Fig.…”

Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations

“…Spatial structures of laser modes in broad-area resonators have been of interest for a long time because they offer much insight into the pattern formation of natural waves [19][20][21][22][23][24][25][26][27]. More recently, wave patterns of high-order coherent laser modes in various cavities have been generated to manifest the morphologies of quantum coherent states related to periodic orbits [28][29][30]. The most remarkable finding is that the coherent optical waves related to the Lissajous and trochoidal patterns can be geometrically connected through SU(2) transformations [31].…”