“Shaking Out” Entanglement

1. Young Theorists Forum Durham 2011 “Shaking Out” Entanglement Antony Lee University of Nottingham D.E.Bruschi, A.Dragan, I.Fuentes & J. Louko

2. Entanglement • Definition: Separable • A state is said to be separable with respect to two partitions if it can be written as the tensor product of two independent states • Definition: Entangled • If a state cannot be written as separable then it is entangled • Relevance • Way of verifying theoretical predictions • Can be linked to the Dynamical Casimireffect (DCE)

3. Bogoliubov Transformations • QFT • States of fields • Two mode truncation • Validity • Very accurate for low accelerations • Physically reasonable

4. Basic Trajectories

5. “Shaking”

6. Continuous Variables • Definition • Any system whose observables have a continuous spectrum • Collections of molecules, Atoms, lasers etc. • Basics • Any Gaussian state is represented by its first and second moment expectation values

7. Gaussian States • Relevance • Represent the state and the transformations using symplectic matrices • Truncated transformation represented as a change of basis • Multiple “shakes” represented the repeated action of the symplectic transformations i.e.

8. Results • Quantifying entanglement • Many different measures, Negativity, Logarithmic Negativity, Von Neumann entropy • Periodic structure • Entanglement generation rises and lowers • Linear growth • For special fixed parameters • there is unbounded generation of entanglement

9. Conclusions • Entanglement generation • High degrees of entanglement • Use for DCE • Linked to particle creation therefore temperature • Use for QI • Resource of strongly entangled pairs • Further problems • Dissipative systems, different particles

10. Thank You & Questions?