Entanglement of Movable Mirrors in a Correlated Emission Laser

Wenchao Ge, Hyunchul Nha, and M. S Zubairy

Institute for Quantum Science and Engineering, Texas A&M University, College StationTexas A&M University at Qatar, Education City, P.O. Box 23874, Doha, Qatar

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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

down conversion process

beam-splitter process

Radiation Pressure Coupling

Radiation Pressure Coupling

Radiation Pressure CouplingAverage Phonon number versusCooling 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

1 2 3 4 5 0.01

0.020.030.040.05

FF C oupling

•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. Schuessler for a useful

discussion.