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Quantum Information at Queen’s University

Quantum Information at Queen’s University. Stuart Swain Andrew Whitaker Myungshik Kim Jim McCann Dmitri Sokolovski Jinhyoung Lee Mauro Paternostro Wonmin Son Helen McAnerny Derek Wilson Hyungsuk Jeong Eileen Nugent Liang-You Peng. Quantum Information at Queen’s.

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Quantum Information at Queen’s University

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  1. Quantum Information at Queen’s University • Stuart Swain • Andrew Whitaker • Myungshik Kim • Jim McCann • Dmitri Sokolovski • Jinhyoung Lee • Mauro Paternostro • Wonmin Son • Helen McAnerny • Derek Wilson • Hyungsuk Jeong • Eileen Nugent • Liang-You Peng

  2. Quantum Information at Queen’s • Quantum Algorithms • Optical realisation of QIP • Complementarity and Fidelity • Decoherence and non-Markovian processes • Many-body entanglement and • nonlocality for continuous variable states • Solid-state realisation of QIP • Nonlinear Atom Optics • Laser cooling • Coherent control • Squeezed light and matter

  3. Nonlinear Atom Optics:Mode Conversion in Trapped Atomic Condensates Jim McCann, Eileen Nugent, Dermot McPeake • Coherent atom excitations • Wave mixing • Mode conversion in traps • Mode conversion in lattices

  4. Condensate basics • Macroscopic quantum state • Bosons: high occupation • High phase-space density • Nonlinearity UK Cold Atom Network Ed Hinds (ICSTM) Charles Adams (Durham) Labs: St. Andrews, Strathclyde, Glasgow, Durham, Manchester, Oxford, UCL, ICSTM, NPL, Sussex

  5. Atom Optics and Quantum Information • Coherent matter waves • Macroscopic quantum state • Manipulation by external fields beams, microtraps, lattices, lenses, chips • Tunable interactions (entanglement): kinetic and potential energy control • Control: Superfluid <-> Insulator • Coherent atom device as register, amplifier or reservoir

  6. Cold atom engineering Hinds and Hughes (1999) J. Phys. D 32 119 Atoms in microtraps and on chips (ICSTM) Reichel and Haensch (MPQ, Garching) Chikkatur et al (MIT) 2002 Science 296, 2193

  7. First-order coherence Andrews et al (1997) Science 275 637-41 Observation of interference between two Bose condensates

  8. Spatial coherence: millimetres I. Bloch, T. W. Haensch & T. Esslinger, Nature 403, p166 (2000)

  9. Coherent output coupling Coherent splitting of condensate with optical Bragg scattering Kozuma et al (1999) Phys. Rev. Lett. 82 871

  10. Nonlinear atom optics Deng et al (NIST) Nature398, 218 - 220 (1999); Four-wave mixing

  11. Nonlinear atom optics in traps Single quasiparticle excitations (low temperature) f i V i k Wave-mixing collisions f j Wave-mixing processes include: Sum-frequency mixing, second harmonic generation, parametric down conversion

  12. Collective excitations in traps 10 ms snapshots Miesner et al Science 279, 1005 (1998)

  13. Quantized modes forAtoms in spherical traps Breather Experiment (JILA) Cornell & Wieman et al. Theory (Oxford/NIST) Burnett & Clark et al. Quadrupole Changing the axial confinement creates shape oscillations of the cloud well-defined quantized modes

  14. Atoms in spheroidal traps Atoms trapped by external fields in a pancake shape cloud Breather Quadrupole k 2k f k Resonance near

  15. Hechenblaikner & Foot et al., PRL 84 , 2056 (2000) 20,000 atoms of Rb • Second Harmonic Generation • observed near phase matching • conditions • Component at 2ω in the • axial direction • Observation of ‘radial freezing’ • at phase matching resonance

  16. Bogoliubov model Many-body Hamiltonian Wavefunction = condensate+ thermal component where

  17. Thermal component expanded in quasi-particle functions where Eigenvalues give excitation frequencies ω Ideal gas modes: Oscillator (Traps) Bloch (Lattices) Interacting gas modes: quasiparticle states

  18. Wave mixing in Condensates k 2k k f Optics Coupling strength=scattering amplitude (Morgan,Burnett et al)

  19. Spectrum of excitations (Rb) Bogoliubov and hydrodynamic (inset) frequency predictions of the lowest four even parity, m= 0, excitations.

  20. Hybrid Bogoliubov modes mode amplitudes =1.35:Modes have characteristic surface and monopole nature. =1.60, 1.65: Modes hybridize at the anticrossing with the result that one of them has zero overlap with the quadrupole l= 2. =1.75: The modes regain their characteristic form.

  21. Hybrid mode coupling dark state 2-state model

  22. Coupling to shape oscillations radial Width axial time

  23. Conversion efficiency Axial width Radial width Red -> Resonance -> Blue

  24. Spectrum at phase matching Second harmonic doublet fundamental third harmonic Down conversion

  25. Mode conversion in lattices • intersecting beams of light cool atoms • atoms trapped at dark spots

  26. Superfluid-Insulator transition (1) tunneling dominated: superfluid delocalized state, coherent state (2) interaction dominated: insulator localized state, Fock (number) state Haensch et al (2002) Nature 415 39-44

  27. Mode conversion in lattices Bose-Hubbard model Jaksch et al (1998) Phys. Rev. Lett. 81, 3108. J= tunneling U=interaction Tight-binding functions, small occupation

  28. Current work: wave mixing in lattices Bogoliubov spectrum Bloch wave spectrum Energy Energy Second Harmonic Condensate density Height of barrier between wells Louis et al (2003) PRA 67 013602

  29. Lattice output reading Coherent emission from lattice loaded with condensate : interference pulses in region A. Pulse period ~1 msec ~h/mgDz

  30. Conclusions • Qualitative agreement theory/experiment • Mode conversion in trapped condensates: easy but complicated • Hybrid and dark states affect process • Third harmonic generation, down conversion and four-wave mixing • Control of coherent excitation within trap – more difficult than it appeared • Lattice mode mixing is even more complex

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