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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 Cold surface Mirror qed Dielectric layer Multilayer PBG JCM limit ? kT height ? kT Drexhage/Kuhn from late 60’s cavities Barton Proc Roy Soc 1971 Milonni & Knight, 1973 Kleppner Hinds, Haroche, Mossberg, Kimble And now with ions in Innsbruck and Munich Dielectric output coupler Dutra & Knight, Optics Commun 117, 256, 1995; Phys Rev A53, 3587, (1996); Neat Bessel beam output for microcavity 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? 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 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 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- Alice Beam splitter destroys whichpath information! A detected photon could have come from any cavity. Cold atoms and warm surfaces Atom chip guides: Ed’s talk Atom registers made via Mott Transition from BEC Addressing & gates Heating and decoherence Warm surfaces: em field noise above a metal surface: Ed reprise resistivity of metal dissipation in surface fluctuation of field heating and spin flips Spin flip lifetime above a thick slab/wire height skin depth metal slab spin flip frequency Ed’s vision: An atomic quantum electrostaticregister wires integrated fiber trapping light BEC Mott insulator There can be exactly 1 atom per lattice site (number squeezing) 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 Atoms are completely localized to lattice sites ! Fock states with a vanishing atom number fluctuation are formed. n=1 Atom number distribution after a measurement 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 QuickTime™ and a Microsoft Video 1 decompressor are needed to see this picture. •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) Optical Lattices Mott Register Physical System e •Raman transition: •Optical lattice model * J iR a b 2 a ga b gb Tunnelling transitions (J) and collisions (U) •Hamiltonian: [ai , a j ] [bi , bj ] ij H (Jia ai ai1 Jib bibi1 JiR aibi H.c.) i U aa U bb 2 2 2 2 ai ai U ab ai aibi bi bi bi 2 i 2 i i PHASE TRANSITION 8 atoms in 10 sites Superfluid phase Population Sites In harmonic potential V~U Superfluid phase Population Sites Mott insulator Population Sites Mott insulator Population Sites 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. Coherent Interactions | 10;01 •Consider the occupational state of two lattice sites: a b | n1a nb1 ; na2 nb2 •Atomic Raman trans. a b •Tunnelling trans. 1 2 ga JR 1 gb 2 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 U ab a J H2 b J 0 J 0 a 0 Jb J 0 b 0 Ja |11;00> 0 b J a J U ab U ab Jb a J J K 2 U ab b J<<U Jb Ja •Evolution: effective exchange interaction Heff =-K(|10><01|+|01><10|) |00;11> Kt |01;10> 0 .5 4321 SWAP |10;01> 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 U ab a J H2 b J 0 J 0 a 0 Jb J 0 b 0 Ja |11;00> 0 b J a J U ab U ab Jb a J J K 2 U ab b J<<U Jb Ja •Evolution: effective exchange interaction Heff =-K(|10><01|+|01><10|) |00;11> Kt |01;10> 876 10.9 SWAP |10;01> Quantum Computation • One qubit gate by Raman transitions between the states |0>=|ga > and |1 >=|gb >. • Two qubit gates by modulations of lattice potential i Conditional Phase gate: |11> e |11> SWAP : |01> (|01>+i|10>) / 2 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>. SWAP ] • 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? (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 is there technical noise? We are just learning how to control technical noise in microtraps time scale ~ 1-100s Heating rate calculations: Rekdal, Scheel, Knight & Hinds (2004) Basic idea 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… 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: