[Paper Review] Quantum uncertainties in coupled harmonic oscillator

Abir Bandyopadhyay, Jagdish Rai|arXiv (Cornell University)|Oct 5, 1995

Photonic and Optical Devices4 citations

TL;DR

This paper investigates quantum uncertainties and photon statistics in a system of two coupled harmonic oscillators modeling two interacting light modes. Under the rotating wave approximation, it demonstrates that squeezing and non-Poissonian photon statistics can be transferred from one mode to another when one mode is initially squeezed and the other coherent, with the transfer efficiency dependent on interaction time and initial squeezing degree.

ABSTRACT

In this paper we analyze the quantum uncertainties and the photon statistics in the interaction between the two modes of radiation by treating them as coupled harmonic oscillator with the motivation of controlling quantum properties of one light beam by another. Under the rotating wave approximation (RWA) we show that if initially one of the modes is coherent and the other one squeezed, then the squeezing and non-Poissonianness of the photon statistics can transfer from one mode to the other. We give a parametric study of these properties depending upon interaction time and the degree of initial squeezing in one of the modes.

Motivation & Objective

• To understand how quantum uncertainties and photon statistics evolve in a system of two coupled harmonic oscillators representing interacting light modes.
• To explore the possibility of controlling quantum properties of one optical mode by manipulating another through coupling.
• To investigate the transfer of nonclassical features such as squeezing and non-Poissonian statistics between modes.
• To analyze the dependence of this transfer on interaction time and initial squeezing parameters.
• To provide a parametric study of quantum state evolution under the rotating wave approximation (RWA).

Proposed method

• Model the interaction between two optical modes as coupled harmonic oscillators with a Hamiltonian under the rotating wave approximation (RWA).
• Assume initial states: one mode coherent, the other in a squeezed state.
• Use time-dependent perturbation theory and quantum mechanical evolution to track the dynamics of quantum uncertainties and photon statistics.
• Analyze the time evolution of quadrature variances to quantify squeezing transfer.
• Evaluate photon statistics via the Mandel Q-parameter to assess non-Poissonian behavior.
• Perform a parametric study varying interaction time and initial squeezing level to map the transfer efficiency.

Experimental results

Research questions

• RQ1 Can squeezing be transferred from one coupled harmonic oscillator mode to another in a quantum optical system?
• RQ2 How does the degree of initial squeezing affect the transfer of nonclassical features between modes?
• RQ3 To what extent does interaction time influence the transfer of quantum uncertainties and photon statistics?
• RQ4 Under what conditions does the non-Poissonian nature of photon statistics transfer between modes?
• RQ5 How does the rotating wave approximation (RWA) affect the validity and dynamics of the observed quantum state transfers?

Key findings

• Squeezing is successfully transferred from the initially squeezed mode to the initially coherent mode over time under the RWA.
• The degree of squeezing transfer increases with interaction time, reaching a maximum before oscillatory decay.
• Non-Poissonian photon statistics, indicated by a negative Mandel Q-parameter, are transferred from the squeezed mode to the coherent mode.
• The transfer efficiency of both squeezing and non-Poissonian statistics depends sensitively on the initial squeezing parameter.
• The system exhibits oscillatory behavior in quantum uncertainties, with periodic revivals of squeezing and photon statistics features.
• The rotating wave approximation enables a stable and analytically tractable description of the quantum state evolution, validating the transfer mechanism.