Entanglement of Movable Mirrors in a Correlated Emission Laser 1 2 Wenchao Ge, Hyunchul Nha, and M. S Zubairy Institute for Quantum Science and Engineering, Texas A&M University, College Station Texas A&M University at Qatar, Education City, P.O. Box 23874, Doha, Qatar 1 1 2

Contents Motivation Radiation Pressure Coupling Correlated Emission Laser Entangling Movable Mirrors Further Research References

Motivation  

Radiation Pressure Coupling Entanglement generation Laser cooling Optomechanical devices Optomechanically induced transparency Nonlinear effects

Radiation Pressure Coupling    

Radiation Pressure Coupling     small nonlinear term   beam-splitter process down conversion process

Radiation Pressure Coupling  

Radiation Pressure Coupling      

Radiation Pressure Coupling   Average Phonon number versus Cooling driving laser power

Correlated Emission Laser Quantum noise quenching High precision measurements Two-mode field entanglement and squeezing Quantum computing Quantum teleportation

Correlated Emission Laser  

Correlated Emission Laser        

Correlated Emission Laser   Two-mode field Entanglement numerical analytical

Entangling Movable Mirrors The scheme:

Entangling Movable Mirrors Hamiltonian      

Entangling Movable Mirrors Both field-mirror pairs coupled in a DCP Field-mirror pairs coupled one in a DCP and one in BSP or vice verse. No entanglement between movable mirrors because of effective BSP Both field-mirror pairs coupled in a BSP Effective DCP with a large stable region. Entangled!     They do not generate entanglement between mirrors because of instability!      

Entangling Movable Mirrors          

Entangling Movable Mirrors Entanglement of two-mode field

Entangling Movable Mirrors Entanglement of movable mirrors

Entangling Movable Mirrors Normalized field-field coupling strength in the presence of atomic system

Further Research  

References Optomechanical entanglement: D. Vitali et al, Phys. Rev. Lett 98, 030405 (2007) Optomechanical induced transparency: S. Weis et al, Science 330, 1520 (2010) Nanomechanical oscillator cooling: I. Wilson-Rae et al, Phys. Rev. Lett. 99, 093901 (2008); J. Chan et al, Nature 478, 89 (2011) Correlated emission laser: M. O. Scully et al, Phys. Rev. Lett 60, 1832 (1988); X. Han et al, Phys. Rev. Lett. 94, 023601 (2005) Entanglement criterion: X. Wang, Phys. Rev. A 66, 024303 (2002); L.M. Duan et al, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, Phys. Rev. Lett 84, 2726 (2000)

Thank you for your listening and thank Dr Thank you for your listening and thank Dr. Schuessler for a useful discussion.