Abstract
The generation and detection of entanglement between mesoscopic systems would have major fundamental and applicative implications. In this work, we demonstrate the utility of continuous variable tools to evaluate the Gaussian entanglement arising between two homogeneous levitated nanobeads interacting through a central potential. We compute the entanglement for the steady state and determine the measurement precision required to detect the entanglement in the laboratory.
Highlights
Introduction anAbstractThe generation and detection of entanglement between mesoscopic systems would have major fundamental and applicative implications
We further explore the entanglement in the steady state by plotting the logarithmic negativity EN for noisy dynamics in Fig. 4a for a range of interaction strengths α ∈
We derived the Hamiltonian matrix for a linearised potential and investigated the entanglement arising between two initially squeezed states given unitary and noisy dynamics
Summary
We begin by considering two spheres trapped next to each other as per Figure 1. We introduce the 4×4 two-mode covariance matrix σ, which consists of all second moments of the Gaussian state ρG (t) It is defined as σ(t) = Tr {r, r T } ρG (t) ,. (i) cri pt and where H0 = 14 is the 4 × 4 identity matrix that governs the free evolution and HI denotes the Hamiltonian matrices responsible for the interaction. We note that HI is of the form of two-mode squeezing, which implies that the corresponding closed system will not display periodic behaviour With these rescaled quantities, the evolution is encoded as.
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