Decoherence issues for atoms in cavities & near surfaces Peter Knight, Imperial College London work with P 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

height Cold surface Mirror qed Dielectric layer Multilayer PBG JCM limit

Drexhage/Kuhn from late 60’s

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

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

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

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

Cqed good cavity fundamentals Slide from Tom Mossberg

Cqed fundamentals Slide from Tom Mossberg

Two atoms in a cavity: entanglement via decay 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 M.B. Plenio et al, Phys. Rev. A 59, 2468 (1999)

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

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

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

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

Light-induced lattices

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

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

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

Optical Lattices Mott Register Physical System Raman transition: Optical lattice model Tunnelling transitions (J) and collisions (U) Hamiltonian: gaga gbgb e

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

Population Sites Superfluid phase

Mott insulator Population Sites

Population Sites Mott insulator

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

Coherent Interactions Consider the occupational state of two lattice sites: a b 1 2 Atomic Raman trans. a b Tunnelling trans. 1 2 gaga gbgb

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 H eff =-K(|10> <10|) J<<U

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 H eff =-K(|10> <10|) J<<U

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

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.

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

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

Basic idea

Numerical results Copper core, radius a microns plus 55 micron radius a 2 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…

conclusions –Quantum information with optical lattices and atom chips has great potential –Quantum optics techniques on atom chips can probably make basic gates –Decoherence is an interesting problem: heating rates of seconds gives loads of time for gates. –Quantum memories are harder to realize: few qubit applications? Funding: