Gravitationally Induced Entanglement Between Particles in Harmonic Traps: Limits for Gaussian States

TL;DR

This paper investigates the limits of gravitationally induced entanglement between particles in harmonic traps, revealing that entanglement is minimal and challenging to observe experimentally, especially at higher temperatures.

Contribution

It provides a detailed analysis of entanglement limits for Gaussian states in gravitational systems, identifying temperature thresholds and optimal trap frequencies.

Findings

Maximum temperature limits entanglement generation

Optimal trap frequency maximizes entanglement

Entanglement generated is extremely small

Abstract

Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.