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Quantum-limited measurements: One physicists crooked path from quantum optics to quantum information I.Introduction II.Squeezed states and optical interferometry III.Ramsey interferometry and cat states IV.Quantum information perspective V.Beyond the Heisenberg limit Carlton M. Caves Center for Quantum Information and Control, University of New Mexico School of Mathematics and Physics, University of Queensland http://info.phys.unm.edu/~caves Collaborators: E. Bagan, S. Boixo, A. Datta, S. Flammia, M. J. Davis, JM Geremia, G. J. Milburn, A Shaji, A. Tacla, M. J. Woolley. Center for Quantum Information and Control Slide 2 I. Introduction View from Cape Hauy Tasman Peninsula Tasmania Slide 3 A new way of thinking Quantum information science Computer science Computational complexity depends on physical law. Old physics Quantum mechanics as nag. The uncertainty principle restricts what can be done. New physics Quantum mechanics as liberator. What can be accomplished with quantum systems that cant be done in a classical world? Explore what can be done with quantum systems, instead of being satisfied with what Nature hands us. Quantum engineering Slide 4 Metrology Taking the measure of things The heart of physics Old physics Quantum mechanics as nag. The uncertainty principle restricts what can be done. New physics Quantum mechanics as liberator. Explore what can be done with quantum systems, instead of being satisfied with what Nature hands us. Quantum engineering Old conflict in new guise Slide 5 II. Squeezed states and optical interferometry Oljeto Wash Southern Utah Slide 6 (Absurdly) high-precision interferometry Laser Interferometer Gravitational Observatory (LIGO) Hanford, Washington Livingston, Louisiana 4 km The LIGO Collaboration, Rep. Prog. Phys. 72, 076901 (2009). Slide 7 Laser Interferometer Gravitational Observatory (LIGO) Hanford, Washington Livingston, Louisiana 4 km Initial LIGO High-power, Fabry- Perot-cavity (multipass), power- recycled interferometers (Absurdly) high-precision interferometry Slide 8 Laser Interferometer Gravitational Observatory (LIGO) Hanford, Washington Livingston, Louisiana 4 km Advanced LIGO High-power, Fabry- Perot-cavity (multipass), power- and signal-recycled, squeezed-light interferometers (Absurdly) high-precision interferometry Slide 9 Mach-Zender interferometer C. M. Caves, PRD 23, 1693 (1981). Slide 10 Squeezed states of light Slide 11 G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471 (1997). Groups at ANU, Hannover, and Tokyo continue to push for greater squeezing at audio frequencies for use in Advanced LIGO, VIRGO, and GEO. Squeezed states of light Squeezing by a factor of about 3.5 Slide 12 Quantum limits on interferometric phase measurements Quantum Noise Limit (Shot-Noise Limit) Heisenberg Limit As much power in the squeezed light as in the main beam Slide 13 III. Ramsey interferometry and cat states Truchas from East Pecos Baldy Sangre de Cristo Range Northern New Mexico Slide 14 Ramsey interferometry N independent atoms Frequency measurement Time measurement Clock synchronization Slide 15 Cat-state Ramsey interferometry J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996). Fringe pattern with period 2/N N cat-state atoms Slide 16 Optical interferometryRamsey interferometry Quantum Noise Limit (Shot-Noise Limit) Heisenberg Limit Somethings going on here. Slide 17 Optical interferometryRamsey interferometry Entanglement? Between arms Between atoms (wave entanglement) (particle entanglement) Between photons Between arms (particle entanglement) (wave entanglement) Slide 18 IV. Quantum information perspective Cable Beach Western Australia Slide 19 Heisenberg limit Quantum information version of interferometry Quantum noise limit cat state N = 3 Fringe pattern with period 2/N Quantum circuits Slide 20 Cat-state interferometer Single- parameter estimation State preparation Measurement Slide 21 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). Generalized uncertainty principle Cramr-Rao bound Separable inputs Slide 22 Achieving the Heisenberg limit cat state Slide 23 Is it entanglement? Its the entanglement, stupid. But what about? We need a generalized notion of entanglement /resources that includes information about the physical situation, particularly the relevant Hamiltonian. Slide 24 V. Beyond the Heisenberg limit Echidna Gorge Bungle Bungle Range Western Australia Slide 25 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. Slide 26 Improving the scaling with N S. Boixo, S. T. Flammia, C. M. Caves, and JM Geremia, PRL 98, 090401 (2007). Metrologically relevant k-body coupling Cat state does the job. Nonlinear Ramsey interferometry Slide 27 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). Product input Product measurement Slide 28 Improving the scaling with N without entanglement. Two-body couplings S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E. Bagan, and C. M. Caves, PRA 77, 012317 (2008); M. J. Woolley, G. J. Milburn, and C. M. Caves, arXiv:0804.4540 [quant-ph]. Slide 29 Improving the scaling with N without entanglement. Two-body couplings S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, and C. M. Caves, PRL 101, 040403 (2008). Super-Heisenberg scaling from nonlinear dynamics, without any particle entanglement Slide 30 Bungle Bungle Range Western Australia Slide 31 Pecos Wilderness Sangre de Cristo Range Northern New Mexico Appendix. Two-component BECs Slide 32 Two-component BECs S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, and C. M. Caves, PRL 101, 040403 (2008). Slide 33 Two-component BECs J. E. Williams, PhD dissertation, University of Colorado, 1999. Slide 34 Lets start over. Two-component BECs Renormalization of scattering strength Slide 35 Two-component BECs Integrated vs. position-dependent phaseRenormalization of scattering strength Slide 36 ? Perhaps ? With hard, low-dimensional trap Two-component BECs for quantum metrology Losses ? Counting errors ? Measuring a metrologically relevant parameter ? Experiment in H. Rubinsztein-Dunlops group at University of Queensland S. Boixo, A. Datta, M. J. Davis, A. Shaji, A. B. Tacla, and C. M. Caves, Quantum-limited meterology and Bose-Einstein condensates, PRA 80, 032103 (2009). Slide 37 San Juan River canyons Southern Utah Appendix. Quantum and classical resources Slide 38 Making quantum limits relevant The serial resource, T, and the parallel resource, N, are equivalent and interchangeable, mathematically. The serial resource, T, and the parallel resource, N, are not equivalent and not interchangeable, physically. Information science perspective Platform independence Physics perspective Distinctions between different physical systems Slide 39 Making quantum limits relevant The serial resource, T, and the parallel resource, N, are equivalent and interchangeable, mathematically. The serial resource, T, and the parallel resource, N, are not equivalent and not interchangeable, physically. Information science perspective Platform independence Physics perspective Distinctions between different physical systems Slide 40 Making quantum limits relevant. One metrology story A. Shaji and C. M. Caves, PRA 76, 032111 (2007). Slide 41 Using quantum circuit diagrams Cat-state interferometer C. M. Caves and A. Shaji, Quantum-circuit guide to optical and atomic interferometry,'' Opt. Comm., to be published, arXiv:0909.0803 [quant-ph].