A qualitative perspective on idempotency defect of a single-Cooper-pair box placed inside a phase-damped cavity

In a recent paper Dajka, et.al., [J. Phys. A 40, F879 (2007)] predicted that some composite systems can be entangled forever even if coupled with a thermal bath. We analyze the transient entanglement of a single-Cooper-pair box biased by a classical voltage and irradiated by a single-mode quantized field and find the unusual feature that the phase-damped cavity can lead to a long-lived entanglement. The results show an asymptotic value of the idempotency defect which embodies entanglement survival, independent of the interaction development by dependent critically on environment. PACS numbers: 03.67.-a; 32.80.Pj; 42.50.Ct; 42.65.Yj; 03.75.-b § E-mail: [email protected] A qualitative perspective on idempotency defect of a ... 2