Cluster States from Quantum Logic Gates with Trapped Ions inThermal Motion

Abstract

Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86(2001) 910], a procedure is proposed for one-step realizing quantumcontrol phase gates with two trapped ions in thermal motion. It is shownthat the scheme can also be used to create a new special type ofentangled states, i.e., cluster states of many trapped ions. In thescheme the two-trapped ions are simultaneously excited by a single laserbeam and the frequency of the laser beam is slightly off resonance withthe first lower vibration sideband of the trapped ions. The distinctadvantage of the scheme is that it does not use the vibrational mode asthe data bus. Furthermore, our scheme is insensitive to both the initialmotional state and heating (or decay) as long as the system remains inthe Lamb–Dicke regime.