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Quantum-limited measurements: One physicist’s 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 I. Introduction View from Cape Hauy Tasman Peninsula Tasmania Quantum information science A new way of thinking Computer science Computational complexity depends on physical law. New physics Quantum mechanics as liberator. What can be accomplished with quantum systems that can’t 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 Old physics Quantum mechanics as nag. The uncertainty principle restricts what can be done. Metrology Taking the measure of things The heart of physics 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 physics Quantum mechanics as nag. The uncertainty principle restricts what can be done. Old conflict in new guise II. Squeezed states and optical interferometry Oljeto Wash Southern Utah (Absurdly) high-precision interferometry Hanford, Washington The LIGO Collaboration, Rep. Prog. Phys. 72, 076901 (2009). Laser Interferometer Gravitational Observatory (LIGO) 4 km Livingston, Louisiana (Absurdly) high-precision interferometry Initial LIGO Hanford, Washington Laser Interferometer Gravitational Observatory (LIGO) 4 km Livingston, Louisiana High-power, FabryPerot-cavity (multipass), powerrecycled interferometers (Absurdly) high-precision interferometry Advanced LIGO Hanford, Washington Laser Interferometer Gravitational Observatory (LIGO) 4 km Livingston, Louisiana High-power, FabryPerot-cavity (multipass), powerand signal-recycled, squeezed-light interferometers Mach-Zender interferometer C. M. Caves, PRD 23, 1693 (1981). Squeezed states of light Squeezed states of light Groups at ANU, Hannover, and Tokyo continue to push for greater squeezing at audio frequencies for use in Advanced LIGO, VIRGO, and GEO. Squeezing by a factor of about 3.5 G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471 (1997). Quantum limits on interferometric phase measurements Quantum Noise Limit (Shot-Noise Limit) As much power in the squeezed light as in the main beam Heisenberg Limit III. Ramsey interferometry and cat states Truchas from East Pecos Baldy Sangre de Cristo Range Northern New Mexico Ramsey interferometry N independent “atoms” Frequency measurement Time measurement Clock synchronization 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 2π/N N cat-state atoms Optical interferometry Ramsey interferometry Quantum Noise Limit (Shot-Noise Limit) Heisenberg Limit Something’s going on here. Optical interferometry Between arms (wave entanglement) Ramsey interferometry Entanglement? Between photons (particle entanglement) Between atoms (particle entanglement) Between arms (wave entanglement) IV. Quantum information perspective Cable Beach Western Australia Quantum information version of interferometry Quantum noise limit Quantum circuits cat state N=3 Heisenberg limit Fringe pattern with period 2π/N Cat-state interferometer State preparation Singleparameter estimation Measurement 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). Separable inputs Generalized uncertainty principle Cramér-Rao bound Achieving the Heisenberg limit cat state Is it entanglement? It’s 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. V. Beyond the Heisenberg limit Echidna Gorge Bungle Bungle Range Western Australia 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. Improving the scaling with N Cat state does the job. Metrologically relevant k-body coupling S. Boixo, S. T. Flammia, C. M. Caves, and JM Geremia, PRL 98, 090401 (2007). Nonlinear Ramsey interferometry 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 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]. Improving the scaling with N without entanglement. Two-body couplings Super-Heisenberg scaling from nonlinear dynamics, without any particle entanglement S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, and C. M. Caves, PRL 101, 040403 (2008). Bungle Bungle Range Western Australia Appendix. Two-component BECs Pecos Wilderness Sangre de Cristo Range Northern New Mexico Two-component BECs S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, and C. M. Caves, PRL 101, 040403 (2008). Two-component BECs J. E. Williams, PhD dissertation, University of Colorado, 1999. Two-component BECs Renormalization of scattering strength Let’s start over. Two-component BECs Renormalization of scattering strength Integrated vs. position-dependent phase Two-component BECs for quantum metrology ? Perhaps ? With hard, low-dimensional trap Losses ? Counting errors ? Experiment in H. Rubinsztein-Dunlop’s group at University of Queensland Measuring a metrologically relevant parameter ? 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). Appendix. Quantum and classical resources San Juan River canyons Southern Utah 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 Physics perspective Platform independence Distinctions between different physical systems 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 Physics perspective Platform independence Distinctions between different physical systems Making quantum limits relevant. One metrology story A. Shaji and C. M. Caves, PRA 76, 032111 (2007). Using quantum circuit diagrams Cat-state interferometer 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].