Preventing Multipartite Disentanglement by Local Modulations

An entangled multipartite system coupled to a zero-temperature bath undergoes rapid disentanglement in many realistic scenarios due to local, symmetry-breaking differences in the particle-bath couplings. We show that locally controlled perturbations, addressing each particle individually, can impose a symmetry allowing the existence of decoherence-free multipartite entangled systems.

Figure 1

Two 3-level particles in a cavity, coupled to the cavity modes (thin lines) and subject to local control fields (thick lines). (a)–(c) Frequency domain overlap of coupling spectrum (dotted line) and modulation matrix elements (solid line), resulting in modified decoherence matrix elements (shaded area), for: (a) global modulation, (b) cross-decoherence elimination (IIP symmetry), and (c) IIT symmetry. (d) IIT symmetry scheme.

Figure 2

Fidelity as a function of time [in units of $(10\gamma {)}^{-1}$]: (a) overall fidelity, (b) correlation preservation, and (c) population preservation. (i) Global $\pi$-phase flips impose no symmetry (dashed line) (${\tau }_{j,n}=1.1$, ${\theta }_{j,n}/\pi =1.0$). (ii) IIP symmetry (dotted line) [${\tau }_{j,n}=(0.75,0.85,0.95,1.05)$, ${\theta }_{j,n}/\pi =(0.834,0.806,0.836,0.82)$]; (iii) IIT symmetry (solid line) ${\tau }_{j,n}=(0.85,0.85,1.05,1.05)$, ${\theta }_{j,n}/\pi =(0.924,0.9,0.945,0.91)$]. Top right: Decoherence matrix elements at time $t=100$. The parameters are ${\omega }_1=0.5$, ${\omega }_2=0.6$, $\gamma =0.1$, $k_0{r}_{\min }=1.0$, $t_{j,n}=(0.7,1.0,1.06,1.1)$, $r_j=(0.0,0.1)$, and ${\eta }_n/\pi =(0.0,0.1)$.