Dipole-dipole interaction in quantum logic gates and quantum reflection

1. Dipole-dipole interaction in quantum logic gates and quantum reflection Angela M. Guzmán Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia, and visiting Professor, School of Physics, The Georgia Institute of Technology, Atlanta, GA 30332, USA. angela.guzman@guzgon.com.

2. Outline 1. Quantum dipole-dipole interaction 2. Controlled collisions between neutral atoms. s-scattering .vs. dipole-dipole interaction in a phase gate. Marco Dueñas, Universidad Nacional de Colombia • 3. van der Waals interaction in an external field: • Quantum reflection in evanescent-wave mirrors: • static .vs. dynamic van der Waals (dipole-dipole) • potential. • Brian Kennedy, Georgia Institute of Technology.

3. where, DIPOLE-DIPOLE INTERACTION

4. DIPOLE-DIPOLE INTERACTION Controlled collisions between adjacent atoms in an optical lattice • Atom-wall interaction in quantum reflection Cold atoms Wannier functions

5. Two-qubit:Phase-gate s-scattering (Fermi Potential) D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller. Phys. Rev. Lett. 82,1975 (1999).

6. x Θ E2 E1 Θ z y A 1D moving optical lattice (with polarization gradient)

7. A 1D moving optical lattice }Θ=0.1 }Θ=0.1 U- U- U+ U+ }Θ=0.25 }Θ=0.25 U- U- U+ U+ }Θ=0.5 U- U+ Optical potential U+,U- 2U0 U0 0 0 0.8 1.6 kLz

8. Sinusoidal variation of the angle: with Operation time Adiabaticity Controlled Collisions CONTROLLED COLLISION

9. DIPOLE-DIPOLE INTERACTION Atom 1 Atom 2 K2 K1 k k VACUUM PHOTONS Induced dipole -moment.

10. Forbidden Selection rules Transition probabilities Elastic collisions

11. Two-qubit:Phase-gate

12. Two-qubit:Phase-gate Elastic collisions, dipole-dipole interaction Interaction energy Spatially modulated losses.

13. MATRIX ELEMENTS

14. Interaction energy

15. Im[Dipole-Dipole interaction potential]

16. Relative phase difference with respect to ORDERS OF MAGNITUDE • The probability losses(probability of having the • atoms in the original two-qubit state) Adiabatic criterion

17. For c=0.4: Phase Logic Gate Probability losses of 84% Using a commutation frequency b=3

18. Remarks • Long range potentials rather than s-scattering determine thetable of truth of logic gates based on atomic collisions. • Logic operations based in the dipole-dipole interaction can not be performed in a time scale shorter than that of the spatially modulated losses. • Dissipation diminishes fidelity and does not allow for successive quantum operations. • Same limitations apply to schemes with enhanced dipole-dipole interaction [G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, Phys. Rev. Lett. 82, 1060 (1999)], unless special bichromatic engineering is used to balance losses.

19. Perfect conductor r r r Image dipole dipole Atom-wall interaction in atomic reflection & the dipole-dipole interaction J.E. Lennard-Jones, Trans. Faraday Soc. 28,33 (1932). Perfect conductor Perfect conductor Perfect conductor r r r r r r r r

20. & retardation effects EM Vacuum EM Vacuum Perfect conductor Perfect conductor • H.B. Casimir and D. Polder, Phys. Rev. 73, 360 (1948). Radiative corrections

21. ALKALI ATOMS & GOLD SURFACE [3] [1] A. Shih, V.A. Parsegian , Phys. Rev. A 12, 835 (1975) [2] A. Derevianko, W. R. Johnson, M. S. Safranova, J. F. Babb Phys. Rev. Lett. 82, 3589 (1999). [3] F. Shimizu, Phys. Rev. Lett. 86, 987 (2001) (Neon)

22. QUANTUM REFLECTION Na BEC T. A. Pasquini, Y-I Shin, C. Sanner, M. Saba, A. Schirotzek, D.E. Pritchard, and W. Ketterle, arXiv.org/cond-mat/0405530.

23. EVANESCENT-WAVE ATOMIC MIRRORS M. Kasevich, K. Moler, E. Riis, E. Sunderman, D. Weiss, and S. Chu, Atomic Physics 12, AIP Conf. Proc. 233, 47 (1991). A means of measuring atom-surface forces

24. DIPOLE-DIPOLE INTERACTION

25. Atomic levels M=1 M=-1 M=0 J=0 Dynamic van der Waals potential between a ground state atom and a dielectric surface in the presence of an evanescent wave and the EM vacuum. Dissipation Dynamic Potential

26. Dissipation due to the interaction through the vacuum

27. Dynamic van der Waals potential Static van der Waals potential

28. Effective potential Optical potential Dynamic van der Waals potential Effect of van der Waals potential

29. Quantum reflection E • Evanescent waves.A. Landragin, J.-Y. Courtois, G.Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, Phys. Rev. Lett. 77, 1464 (1996). From a solid surface at normal incidence. T. A. Pasquini, Y-I Shin, C. Sanner, M. Saba, A. Schirotzek, D.E. Pritchard, and W. Ketterle, arXiv.org/cond-mat/0405530.

30. Quantum region Quantality of the potentials q

31. Remarks • Atom-wall and atom-atom van der Waals potential in external fields relate to the dynamic rather than to the static polarizability. • The shape of the reflecting potential is not controlled by S0alone. Variations in field intensity scale the potential but variations in detuning shift the maximum. • Quantum reflection from solid surfaces occurs only for atomic velocities close to zero (heating has been observed). Quantum reflection from evanescent-wave atomic mirrors occurs at finite energies, but the reflectivity will be less than one because of dissipative effects. • Applications in atomic funnels, quantum reflection engineering, optical traps for quantum gases, Rydberg atoms in optical lattices (a power dependent line width of the fluorescence spectrum has already been observed, FiO 2004).