Effects of boundary conditions on quantum nanoresonators: decoherence-free subspaces

TL;DR

The paper develops a semiclassical quantization of the Euler-Bernoulli nanobeam to study how boundary conditions affect quantum behavior and decoherence. It reveals a phonon Casimir-like vacuum energy requiring renormalization, and shows that boundary conditions induce (quasi-)degeneracies in the mode spectrum, which can give rise to decoherence-free subspaces under dispersive phase-damping baths. For hinged-hinged beams exact degeneracies produce DFS, while other BCs yield near-degeneracies that still extend decoherence times, suggesting design pathways for robust quantum nanomechanical devices. The work highlights both fundamental Casimir-like vacuum effects in mechanical systems and practical implications for quantum information processing with nanomechanical resonators.

Abstract

The Euler-Bernoulli beam model has been studied classically and semi-classically. The semi-classical quantization is done in an analogous way to the quantization of the electromagnetic field, and we found an effect that is similar to the Casimir effect, which is the photonic Casimir effect. The Casimir force, by unit area, is proportional to the first mode energy divided by the volume of the beam. For the hinged-hinged boundary condition, degenerate states were found. These degenerate pairs form decoherence-free subspaces for dispersive thermal reservoirs. For other boundary conditions, there are also subspaces with lower decoherence rates, which occur for quasi-degenerate states.

Figures (4)

• Figure 1: Euler-Bernoulli beam schematic model.
• Figure 2: Roots of $F_{j}$ as function of $k$ for $L=1$.
• Figure 3: Ratio of $\frac{\omega_i}{\omega_0}$ as function of $k$, and $\omega_0(k)=\frac{ \pi^{2}}{L^{2}} \sqrt{\frac{\rho A}{EI}} \, k^{2}$.
• Figure 4: Time evolution of linear entropy of the state \ref{['psi_D']} for $a=b=\frac{1}{\sqrt{2}}$, $j=1$ and $k=2$. The values of $(m,n)$ are given in the legend. The others constants are chosen as $\frac{\rho A}{EI}=1$, $\hbar=1$, and $\Lambda=\frac{1}{(10\pi)^2}$. The beam contour condition is clamped-hinged.