Quantum metrology:

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• Quantum metrology
• dynamics vs. entanglement
• APS March Meeting
• Pittsburgh, 2009 March 16
• Ramsey interferometry and cat states
• Quantum information perspective
• Beyond the Heisenberg limit
• Two-component BECs
• Appendix. Quantum metrology and resources
• Carlton M. Caves
• University of New Mexico
• http//info.phys.unm.edu/caves
• Quantum circuits in this presentation were set
  using the LaTeX package Qcircuit, developed at
  the University of New Mexico by Bryan Eastin and
  Steve Flammia. The package is available at
  http//info.phys.unm.edu/Qcircuit/ .

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I. Ramsey interferometry and cat states
Herods Gate/King Davids Peak Walls of Jerusalem
NP Tasmania
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Ramsey interferometry
Frequency measurement Time measurement Clock
synchronization
Shot-noise limit
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Cat-state Ramsey interferometry
Fringe pattern with period 2p/N
J. J. Bollinger, W. M. Itano, D. J. Wineland, and
D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
Heisenberg limit
Its the entanglement, stupid.
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II. Quantum information perspective
Cable Beach Western Australia
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Quantum information version of interferometry
Shot-noise limit
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Heisenberg limit
S. L. Braunstein, C. M. Caves, and G. J.
Milburn, Ann. Phys. 247, 135 (1996). V.
Giovannetti, S. Lloyd, and L. Maccone, PRL 96,
041401 (2006).
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Achieving the Heisenberg limit
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Its the entanglement, stupid.
Is it entanglement?
We need a generalized notion of entanglement that
includes information about the physical
situation, particularly the relevant Hamiltonian.

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III. Beyond the Heisenberg limit
Echidna Gorge Bungle Bungle Range Western
Australia
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Beyond the Heisenberg limit
The purpose of theorems in physics is to lay out
the assumptions clearly so one can discover which
assumptions have to be violated.
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Improving the scaling with N
S. Boixo, S. T. Flammia, C. M. Caves, and JM
Geremia, PRL 98, 090401 (2007).
Nonlinear Ramsey interferometry
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Improving the scaling with N without entanglement
S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E.
Bagan, and C. M. Caves, PRA 77, 012317 (2008).
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Improving the scaling with N without
entanglement. Two-body couplings
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Improving the scaling with N without
entanglement. Two-body couplings
Super-Heisenberg scaling from nonlinear dynamics,
without any particle entanglement Scaling robust
against decoherence
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IV. Two-component BECs
Pecos Wilderness Sangre de Cristo Range Northern
New Mexico
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Two-component BECs
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Two-component BECs
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Two-component BECs
Renormalization of scattering strengths
Lets start over.
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Two-component BECs
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Two-component BECs
Two-body elastic losses
Imprecise determination of N
? Perhaps ? With hard, low-dimensional trap
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Appendix. Quantum metrology and resources
Cape Hauy Tasman Peninsula
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Making quantum limits relevant
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Making quantum limits relevant. One metrology
story
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One metrology story
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One metrology story