Quantum simulations: solid state devices

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Quantum simulations solid state devices
Max-Planck Institut für Quantenoptik Tutorial
talk _at_ Ringberg December, 10th, 2007 Matteo
Rizzi
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Outline

• 0. Basic motivations why a q-sim is more
  feasible than a q-comp?
• Solid state device I Josephson Junction Arrays
• Quantum phase model definition
• Frustration effects
• Other implementable models
• Experimental techniques (hints)
• Solid state device II Quantum Dot Arrays
• Experimental Realization
• Fermi Hubbard mapping
• Experimental techniques (hints)
• Brief comparison with Cold Atoms in Optical
  Lattices

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Basic motivations
Well known difficulties in Classical Computers
(expon. scaling) ? e.g. 200 spins requires as
many coefficients as protons in the universe !
Universal Q-Comp requires 103 bites 102
ancillas each will be optimistically feasible
in 20 years ! ?
and not every problem is polynomial (e.g. 2D
Hubb spectrum) ?
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Basics Shortcut to quantum simulations
Liquid NMR 4He (hard-core bosons)
SOLID STATE (Josephson Junctions Quantum
dots) Hubbard models (with frustration), Spin
models, Dissipation,
Optical lattices Hubbard, Spin, High Tc
BEC sound waves Black holes
Coupled cavities Dirac equations
Ion Traps Cosmological creation
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Device 1 Josephson Junctions
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D1 JJ arrays definitions
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D1 JJAs Quantum phase model
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D1 JJAs frustration effects (electric)
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D1 JJAs frustration effects (magnetic)
Magnetic frustration
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D1 JJAs other models
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D1 JJAs experimental detection
Basic technique is current-voltage transport
through lattice
Much more interesting physics can be done with
JJAs quantized vortices, dissipation effects,
some kind of Hall regime,
R. Fazio, H. van der Zant, Phys. Rep. 355 235334
(2001)
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Device 2 Quantum dot arrays
T. Byrnes, N.Y. Kim, K. Kusudo, and Y. Yamamoto,
arXiv0711.2841v2 quant-ph (dec. 2007)

• List of ingredients to get a Fermi-Hubbard
  simulator
• 2DEG at semiconductors inteface
• GG global gate to tune population screen
  Coulomb
• MG mesh gate to get periodic potential
• INSulator strip to make GG MG independent !
• Source S Drain D to make transport measures

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D2 QDAs important features
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D2 QDAs Fermi-Hubbard mapping (1)
get a local effective Hamiltonian, and then
include site-site terms
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D2 QDAs Fermi-Hubbard mapping (2)
Outer shell is the important one !
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D2 QDAs tunability requirements
choosing the right band, and tuning V0 , one
should get MI-SF transition
AF visible T lt 0.1 t // d-wave SC T lt 0.02 t
T 10 mK 1 meV is OK !
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D2 QDAs exp. detection models
Cooper pairs Magn.Capac. Oscill. Period
AF nature T-varying Magn.Suscept.
Scaling theory of quantities even far from QPT
Phase-breaking length Magnetoconductance
Any other kind of transport property btw. Source
Drain
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Solid state vs. Optical Lattices
Solid state devices Optical lattices
Phase coherence direct observation ? ?
Diagonal order (2-part. Correl) ? ? (noise-noise)
Transport properties ? ?
Different geometries non periodic ? ?
Single site addressability ? ?
Tunability during experiment ? QDAs / ? JJAs ?
Frustrations (elec magn) ? QDAs / ? JJAs ? (rotations)
Temperature KBT ? well defined controlled ? great controversy !