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Single mode squeezing for Interferometry beyond shot noise

Single mode squeezing for Interferometry beyond shot noise . Bernd Lücke J. Peise , M. Scherer, J. Kruse, O. Topic, W. Ertmer , C. Klempt Institute of Quantum Optics, Leibniz Universität Hannover, Germany G. Gebreyesus , F. Deuretzbacher , L. Santos

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Single mode squeezing for Interferometry beyond shot noise

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  1. Single mode squeezing for Interferometry beyond shot noise Bernd Lücke J. Peise, M. Scherer, J. Kruse, O. Topic, W. Ertmer, C. Klempt Institute of Quantum Optics, Leibniz Universität Hannover, Germany G. Gebreyesus, F. Deuretzbacher, L. Santos Institute of Theoretical Physics , Leibniz Universität Hannover, Germany J. Arlt QUANTOP, Institut forFysikogAstronomi, AarhusUniversitet, Denmark P. Hyllus, A. Smerzi INO-CNR BEC Center and Dipartimento di Fisica, Universita‘ di Trento, Italy L. Pezze Laboratoire Charles Fabry, Institut d’Optique, 91127 Palaiseau, France

  2. A typicalinterferometer | α > N+1 S θ N-1 | 0 > Counter θest θest < N+1 - N-1 > 2 3π π 2π θ

  3. 7 6 5 4 3 2 1 The originofshotnoise counts -5 -3 -1 +1 +3 +5 N+1 - N-1

  4. +1 7 6 5 4 3 2 1 +1 The originofshotnoise counts +1 -1 +1 -5 -3 -1 +1 +3 +5 N+1 - N-1 +3

  5. -1 7 6 5 4 3 2 1 -1 The originofshotnoise counts +1 -1 +1 -5 -3 -1 +1 +3 +5 N+1 - N-1 -1

  6. 7 6 5 4 3 2 1 The originofshotnoise counts -5 -3 -1 +1 +3 +5 N+1 - N-1

  7. Shotnoise limited sensitivity S θest < N+1 - N-1 > 7 3π π 2π θ

  8. How can you beat this limit? uncorrelated particles shot-noise limit entangled particles Heisenberg limit

  9. Introduction outline Twin-Fock interferometer Fock state interferometer

  10. Spin dynamics as a source of entanglement mF: -1 0 +1 2nd quantization 1st quantization

  11. Measuring sub shot-noise fluctuations /2 shot noise standard deviation detection noise total number of atoms • 7dB below shot noise@ 8000 atoms • detection noise σ(Jz) = 20 atoms

  12. Representation on the generalized Bloch sphere coherent superposition produced using rf preparation Entangled Twin-Fock state produced using spin dynamics Jz= (N-1 - N+1)/2 Jz Φ RF Jy Jx Jy Jx σJz σJz=0 σΦ

  13. Uncorrelated input vs. Twin-Fockinput

  14. Output signal

  15. Sensitivity

  16. Introduction outline Twin-Fock interferometer Fock state interferometer

  17. -1 0 +1 Counter Counter

  18. Does it work with two different Fock states? counts Jz = (N+1 - N-1)/2 Jz = (N+1 - N-1)/2

  19. Does it work with a coherent and a Fock input state? Counter Ultrasensitive Atomic clock with single-mode number-squeezing, L. Pezzé and A. Smerzi, arXiv:1004.5486v1

  20. Measuring a single output port counts Counter Θ = π θ<< π θ = 0 N+1 N+1 N+1 |α|² N N N

  21. For sub shot-noise sensitivity entanglement is necessary summary • Sub shot-noise sensitivity can be achieved with Twin-Fock states produced by spin dynamics • A single Fock state and an coherent input state are also suitable for sub shot-noise interferometry

  22. Thank you for your attention. W.Ertmer I.Geisel C.Klempt J.Peise B.Lücke J.Mahnke S.Coleman

  23. coherentinputstate Twin-Fock inputstate Phase estimationforθ=π/2 counts counts Jz = (N+1 - N-1)/2 Jz = (N+1 - N-1)/2

  24. coherentinputstate Twin-Fock inputstate Phase estimationforθ=π/2 counts counts Jz = (N+1 - N-1)/2 Jz = (N+1 - N-1)/2

  25. coherentinputstate Twin-Fock inputstate Phase estimationforθ=π/2 counts counts Jz = (N+1 - N-1)/2 Jz = (N+1 - N-1)/2

  26. coherentinputstate Twin-Fock inputstate Actualmeasurement 6 4 2 0 -1 0 1 (N+1 - N-1)/N +1

  27. The gerneralized Bloch sphere Jz Multi particle Bloch sphere: Jx (a† b + a b†)/2 Jy = -i (a† b - a b†)/2 with Jz = (N+1 - N-1)/2 Jz (a† a - b† b)/2 Jy Jx

  28. Expensionofthestaterevealsitsentanglement Whyisthisstate not entangled? Because… In 1st quantization:

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