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.

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 Brian Kennedy, Georgia Institute of Technology. 3. van der Waals interaction in an external field: Quantum reflection in evanescent-wave mirrors: static.vs. dynamic van der Waals (dipole-dipole) potential.

where, DIPOLE-DIPOLE INTERACTION

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

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

A 1D moving optical lattice (with polarization gradient) z x y Θ Θ E1E1 E2E2

Optical potential U +,U - 0 U0U0 2U kLzkLz U-U- U+U+ } Θ=0.1 U-U- U+U+ } Θ=0.25 U-U- U+U+ } Θ=0.5 U-U- U+U+ } Θ=0.25 U-U- U+U+ } Θ=0.1 A 1D moving optical lattice

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

DIPOLE-DIPOLE INTERACTION K1K1 K2K2 Atom 1Atom 2 VACUUM PHOTONS kk Induced dipole - moment.

Selection rules Forbidden Transition probabilities Elastic collisions

Two-qubit: Phase-gate

Elastic collisions, dipole-dipole interaction Interaction energy Spatially modulated losses.

MATRIX ELEMENTS

Interaction energy

Im[Dipole-Dipole interaction potential]

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

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

Remarks 1.Long range potentials rather than s-scattering determine the table of truth of logic gates based on atomic collisions. 2.Logic operations based in the dipole-dipole interaction can not be performed in a time scale shorter than that of the spatially modulated losses. 3.Dissipation diminishes fidelity and does not allow for successive quantum operations. 4.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.

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

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

ALKALI ATOMS & GOLD SURFACE Exp. [1] Theor. [2] Cs Rb K [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) [3]

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

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

DIPOLE-DIPOLE INTERACTION

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. Atomic levels J=0 M=-1M=0 M=1 Dissipation Dynamic Potential

Dissipation due to the interaction through the vacuum

Dynamic van der Waals potential Static van der Waals potential

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

Quantum reflection Evanescent waves. A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, Phys. Rev. Lett. 77, 1464 (1996). E 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/

Quantality of the potentials q Quantum region

Remarks 1.Atom-wall and atom-atom van der Waals potential in external fields relate to the dynamic rather than to the static polarizability. 2.The shape of the reflecting potential is not controlled by S 0 alone. Variations in field intensity scale the potential but variations in detuning shift the maximum. 3.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. 4.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).