Decoherence Issues for Atoms in Cavities & Near Surfaces

1. Decoherence issues for atoms in cavities & near surfacesPeter Knight, Imperial College Londonwork withP K Rekdal,Stefan Scheel, Almut Beige, Jiannis Pachos, Ed Hinds and many others • Cold surfaces: cqed in bad and good cavity limits? • Warm surfaces & cold atoms: Atom chips, Mott transition & registers and spin flips

2. height Cold surface Mirror qed Dielectric layer Multilayer PBG JCM limit

3. Drexhage/Kuhn from late 60’s

4. cavities • Barton Proc Roy Soc 1971 • Milonni & Knight, 1973 • Kleppner • Hinds, Haroche, Mossberg, • Kimble • And now with ions in Innsbruck and Munich

6. Dielectric output coupler • Dutra & Knight, Optics Commun 117, 256, 1995; Phys Rev A53, 3587, (1996); • Neat Bessel beam output for microcavity

7. Put single atom or dot source in PBG or Bragg Stack • Rippin & Knight, J Mod Opt 43, 807, (1996) Bragg stack • Scheel, Dowling, PLK et al quant-ph0207075 • Does it work?

8. Beige, Knight, Tregenna, Huelga, Plenio, Browne, Pachos… how to live with noise, and use of decoherence-free subspaces

9. Cqed good cavity fundamentals Slide from Tom Mossberg

10. Cqed fundamentals Slide from Tom Mossberg

11. Two atoms in a cavity: entanglement via decay M.B. Plenio et al, Phys. Rev. A 59, 2468 (1999) Cavity in vacuum state, with two atoms in their ground state. Excite one atom! Exchange of excitation between the atoms and the cavity mode. No jump detection and Bell states

12. Entanglement between distant cavities. S. Bose, P.L. Knight, M.B. Plenio and V. Vedral, PRL 58, 5158 (1999); Browne et al (2003/4) D + Bob D - Beam splitter destroys which-path information! A detected photon could have come from any cavity. Alice

13. Cold atoms and warm surfaces • Atom chip guides: Ed’s talk • Atom registers made via Mott Transition from BEC • Addressing & gates • Heating and decoherence

14. dissipation in surface fluctuation of field heating and spin flips Spin flip lifetime above a thick slab/wire height spin flip frequency skin depth metal slab Henkel, Pötting and Wilkens Appl. Phys B 69,379 (1999);Scheel, Rekdal, PLK & Hinds Warm surfaces: em field noise above a metal surface: Ed reprise resistivity of metal

15. electrostatic wires trapping light BEC Mott insulator There can be exactly 1 atom per lattice site (number squeezing) Ed’s vision: An atomic quantum register integrated fiber

16. Light-induced lattices

17. Atom number distribution after a measurement Superfluid Limit Atoms aredelocalized over the entire lattice!Macroscopic wave function describes this state very well. Poissonian atom number distribution per lattice site n=1

18. Atom number distribution after a measurement Atomic Limit of a Mott-Insulator Atoms are completely localized to lattice sites ! Fock states with a vanishing atom number fluctuation are formed. n=1

19. Quantum gates with neutral atoms • Bring atoms into a superposition of internal states • Move atoms state selectively to neighbouring site • Interaction phase (Collisions or Dipole-Dipole) • Create large scale entanglement • Ising model • Hamiltonian simulations • Multi-particle interferometer D. Jaksch et al., PRL 82,1975(1999), G. Brennen et al., PRL 82, 1060 (1999)A. Sorensen et al., PRL 83, 2274 (1999)

20. Optical Lattices Mott Register Physical System e • Raman transition: • Optical lattice model • Tunnelling transitions (J) and collisions (U) • Hamiltonian: gb ga

21. PHASE TRANSITION 8 atoms in 10 sites Superfluid phase Population Sites In harmonic potential V~U

22. Superfluid phase Population Sites

23. Mott insulator Population Sites

24. Mott insulator Population Sites

25. For U/J>11.6 approximately one atom per lattice site is obtained. For J=0 we obtain Fock states. Mott insulator Population Sites Use it as a register: one atom per site in a or b mode is a qubit in |0> or |1> state.

26. Coherent Interactions • Consider the occupational state of two lattice sites: a b 2 1 • Atomic Raman trans. • a b ga gb • Tunnelling trans. • 1 2

27. Exchange Interaction • Consider the evolution of the state |01;10> and |10;01> when we lower the potential of both a and b-modes. They are coupled to |00;11> and |11;00> by |11;00> |00;11> |01;10> |10;01> • Evolution: effective exchange interaction • Heff =-K(|10><01|+|01><10|) J<<U

28. Exchange Interaction • Consider the evolution of the state |01;10> and |10;01> when we lower the potential of both a and b-modes. They are coupled to |00;11> and |11;00> by |11;00> |00;11> |01;10> |10;01> • Evolution: effective exchange interaction • Heff =-K(|10><01|+|01><10|) J<<U

29. Quantum Computation • One qubit gate by Raman transitions between the states |0>=|ga > and |1 >=|gb >. • Two qubit gates by modulations of lattice potential • Conditional Phase gate: |11> |11> • : |01> (|01>+i|10>)

30. Gates • “Charge based” quantum computation with Optical Lattice. • Mott Insulator of 1 atom/site serves as a register. Two in-phase lattices trap two ground states of the atom [logical |0> and |1>]. • One qubit gates by Raman transitions |0> |1>. • Two qubit gates [control phase-gates or ] performed by exchange interactions in one or both of the optical lattices, respectively. • Can perform multi-qubit gates in one go.

31. 2. What about decoherence? (A) Technical noise in the em field Above current-carrying wires audiofrequency vibrates the trap heating radiofrequency excites spin flips loss In a far-detuned light trap fluctuations of intensity, phase, polarization heating and loss In permanent magnet traps We are just learning how to control technical noise in microtraps time scale ~ 1-100s is there technical noise?

32. Heating rate calculations: Rekdal, Scheel, Knight & Hinds (2004)

34. Basic idea

49. Numerical results • Copper core, radius a1 185 microns plus 55 micron radius a2 Al layer • Use quoted resistivities to get skin depths delta of 85 microns for Cu and 110 microns for Al at frequency 560 kHz used by Ed’s group • One conclusion: Ed is a bit more wiry than slabby…