Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving

TL;DR

This paper investigates the feasibility of maintaining entanglement at high temperatures in parametrically driven quantum oscillators, revealing that while hot entanglement can occur in unstable regimes, it requires exponential power, making it practically unfeasible.

Contribution

It provides a detailed analysis of hot entanglement in driven quantum oscillators, showing instability is necessary but not sufficient, and highlights the impractical energy costs involved.

Findings

Hot entanglement occurs only in unstable regimes.

Instability is necessary but not sufficient for hot entanglement.

Power required increases exponentially in unstable regimes.

Abstract

Entanglement being a foundational cornerstone of quantum sciences and the primary resource in quantum information processing, understanding its dynamical evolution in realistic conditions is essential. Unfortunately, numerous model studies show that degradation of entanglement from a quantum system's environment, especially thermal noise, is almost unavoidable. Thus the appellation `hot entanglement' appears like a contradiction, until Galve et al [Phys. Rev. Lett. \textbf{105} 180501 (2010)] announced that entanglement can be kept at high temperatures if one considers a quantum system with time-dependent coupling between the two parties, each interacting with its individual bath. With the goal of understanding the sustenance of entanglement at high temperatures, working with the same model and set up as Galve et al, namely, parametrically-driven coupled harmonic oscillators interacting with their own Markovian baths, this work probes into the feasibility of `hot entanglement' from three aspects listed in the subtitle. Our findings show that 1) hot entanglement functions only in the unstable regimes, 2) instability is a necessary but not sufficient condition, and 3) the power intake required by the drive operating in the unstable regime to sustain entanglement increases exponentially. The last factor indicates that hot entanglement under this modeling is theoretically untenable and its actual implementation likely unattainable.