Response of the Quantum Ground State to a Parametric Drive

TL;DR

This paper investigates the quantum ground state's response to parametric driving, revealing purely quantum effects with no classical analog by analyzing a time-varying quantum harmonic oscillator.

Contribution

It introduces a study of quantum parametric resonance effects on the ground state, highlighting non-trivial evolution absent in classical systems.

Findings

Quantum ground state exhibits non-trivial evolution under parametric drive.

Purely quantum effects observed with no classical counterpart.

Analysis of a time-dependent quantum harmonic oscillator.

Abstract

The phenomenon of Parametric Resonance (PR) is very well studied in classical systems with one of the textbook examples being the stabilization of a Kapitza's pendulum in the inverted configuration when the suspension point is oscillated vertically. One important aspect that distinguishes between classical PR and ordinary resonance is that in the former, if the initial energy of the system is at its minimum (${\dot x}={x}=0$), the system does not evolve. In a quantum system, however, even when the system is in the minimum energy (ground) state, the system has non-trivial evolution under PR due to the delocalized nature of the ground state wavefunction. Here we study the evolution of such a system which exhibits a purely quantum effect with no classical analog. In particular, we focus on the quantum mechanical analog of PR by varying with time the parabolic potential i.e. the frequency of the quantum harmonic oscillator