Nanomechanically Induced Transparency

TL;DR

Addresses realizing nanomechanically induced transparency (NIT) by coupling a nanoelectromechanical system to a trapped ion, exploiting quantum interference between absorption paths in a driven open system. Uses the Lamb-Dicke approximation and rotating-wave approximation to derive a driven-dissipative effective Hamiltonian with cross-mode coupling λ and qubit–motion coupling g, and solves the master equation to obtain steady-state responses ⟨a⟩_ss, ⟨b⟩_ss, and ⟨σ_-⟩_ss. Finds tunable transparency windows and the possibility of a Fano-type resonance near g ≈ 3λ, with central peak strength limited by dissipation rates κ_a, κ_b, γ, γ_φ. This work expands nanoscale electromagnetically induced transparency (EIT) analogs, with potential applications in quantum information processing and precise control of light–matter–motion interactions.

Abstract

In this paper, we investigate a nanomechanically induced transparency (NIT) effects that arises from the coupling of a nanoelectromechanical system and a trapped ion. By confining the ion in mesoscopic traps and capacitively coupling it with a nanoelectromechanical system suspended as electrodes, the research is intricately focussed on the implications of including the ion's degrees of freedom. The Lamb--Dicke approximation is crucial to understanding the effects of phonon exchange with electronic qubits and revealing transparency phenomena in this unique coupling. The results underline the importance of the Lamb--Dicke approximation in modelling the effects of transparency windows in nanoelectromechanical systems.

Figures (3)

• Figure 1: Schematic model of experiment: vibrational mode of trapped Ion interacting with the electric field of a laser, and electrostatically with a nanoelectromechanical system.
• Figure 2: Absorption $Im \left \langle a \right \rangle_{ss}$ (red dashed line) and dispersion $Re \left \langle a \right \rangle_{ss}$ (blue solid line) of the cavity mode $a$ when coupled to trapped ion and cavity mode $b$ as a function of the normalized detuning $\Delta_p/\kappa_a$. In this case we use the parameters: a) $\left |\epsilon \right | = 0.03\kappa_a, \lambda = g = 0.5 \kappa_a, \kappa_b = 10^{-3}\kappa_a, \gamma = \gamma_\phi =10^{-3} \kappa_a$; b) $\left |\epsilon \right | = 0.03\kappa_a, \lambda = 1.0\kappa_a, g = 0.15 \kappa_a, \gamma = \gamma_\phi =10^{-3} \kappa_a$.
• Figure 3: Absorption $Im \left \langle a \right \rangle_{ss}$ (red dashed line) and dispersion $Re \left \langle a \right \rangle_{ss}$ (blue solid line) of the cavity mode $a$ when coupled to trapped ion and cavity mode $b$ as a function of the normalized detuning $\Delta_p/\kappa_a$. In this case we use the parameters: a) $\left |\epsilon \right | = 0.03\kappa_a, \lambda = g = 0.5 \kappa_a, \kappa_b = 10^{-3}\kappa_a, \gamma = 10^{-2} \kappa_a, \gamma_\phi =10^{-1} \kappa_a$; b) $\left |\epsilon \right | = 0.03\kappa_a, \lambda = g = 0.5 \kappa_a, \gamma = 10^{-1} \kappa_a, \gamma_\phi = 1.0\kappa_a$.