1. QUEST - Centre for Quantum Engineering and Space-Time Research 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 for Fysik og Astronomi, Aarhus Universitet, 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. QUEST - Centre for Quantum Engineering and Space-Time Research A typical interferometer Counter | α > θ θ est | 0 > N -1 N +1 π2π2π 3π3π θ S θ est 2

3. QUEST - Centre for Quantum Engineering and Space-Time Research The origin of shot noise -5 -3 -1 +1 +3 +5 counts 76543217654321 N +1 - N -1 3

4. QUEST - Centre for Quantum Engineering and Space-Time Research The origin of shot noise +1 +1 +3 counts 76543217654321 N +1 - N -1 -5 -3 -1 +1 +3 +5 4

5. QUEST - Centre for Quantum Engineering and Space-Time Research The origin of shot noise counts 76543217654321 +1 +1 N +1 - N -1 -5 -3 -1 +1 +3 +5 5

6. QUEST - Centre for Quantum Engineering and Space-Time Research The origin of shot noise counts 76543217654321 N +1 - N -1 -5 -3 -1 +1 +3 +5 6

7. QUEST - Centre for Quantum Engineering and Space-Time Research Shot noise limited sensitivity π2π2π 3π3π θ S θ est 7

8. QUEST - Centre for Quantum Engineering and Space-Time Research How can you beat this limit? uncorrelated particles shot-noise limit entangled particles Heisenberg limit 8

9. QUEST - Centre for Quantum Engineering and Space-Time Research Twin-Fock interferometer Introduction outline Fock state interferometer 9

10. QUEST - Centre for Quantum Engineering and Space-Time Research Spin dynamics as a source of entanglement m F : -1 0 +1 2nd quantization 1st quantization 10

11. QUEST - Centre for Quantum Engineering and Space-Time Research Measuring sub shot-noise fluctuations shot noise detection noise total number of atoms standard deviation /2 7dB below shot noise @ 8000 atoms detection noise σ(J z ) = 20 atoms 11

12. QUEST - Centre for Quantum Engineering and Space-Time Research σJ z Φ J z = (N -1 - N +1 )/2 σΦσΦ JxJx J y Representation on the generalized Bloch sphere RF Entangled Twin-Fock state produced using spin dynamics 12 coherent superposition produced using rf preparation JzJz JxJx JyJy σJ z =0

13. QUEST - Centre for Quantum Engineering and Space-Time Research Uncorrelated input vs. Twin-Fock input 13

14. QUEST - Centre for Quantum Engineering and Space-Time Research Output signal 14

15. QUEST - Centre for Quantum Engineering and Space-Time Research Sensitivity 15

16. QUEST - Centre for Quantum Engineering and Space-Time Research Twin-Fock interferometer Introduction outline Fock state interferometer 16

17. QUEST - Centre for Quantum Engineering and Space-Time Research Counter 17

18. QUEST - Centre for Quantum Engineering and Space-Time Research Does it work with two different Fock states? J z = (N +1 - N -1 )/2 counts J z = (N +1 - N -1 )/2 18

19. QUEST - Centre for Quantum Engineering and Space-Time Research 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 19

20. QUEST - Centre for Quantum Engineering and Space-Time Research Measuring a single output port Counter counts N +1 N θ = 0 N +1 N θ<< π N +1 N Θ = π |α|²

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

22. QUEST - Centre for Quantum Engineering and Space-Time Research Thank you for your attention. 22 W.ErtmerI.GeiselC.KlemptJ.Peise B.LückeJ.MahnkeS.Coleman

23. QUEST - Centre for Quantum Engineering and Space-Time Research Phase estimation for θ=π/2 counts J z = (N +1 - N -1 )/2 counts J z = (N +1 - N -1 )/2 coherent input stateTwin-Fock input state

24. QUEST - Centre for Quantum Engineering and Space-Time Research Phase estimation for θ=π/2 counts J z = (N +1 - N -1 )/2 counts J z = (N +1 - N -1 )/2 coherent input stateTwin-Fock input state

25. QUEST - Centre for Quantum Engineering and Space-Time Research Phase estimation for θ=π/2 counts J z = (N +1 - N -1 )/2 counts J z = (N +1 - N -1 )/2 coherent input stateTwin-Fock input state

26. QUEST - Centre for Quantum Engineering and Space-Time Research Actual measurement 0 +1+1 6 4 2 0 coherent input stateTwin-Fock input state 1 (N +1 - N -1 )/N

27. QUEST - Centre for Quantum Engineering and Space-Time Research JzJz JyJy JxJx The gerneralized Bloch sphere Multi particle Bloch sphere: J x (a † b + a b † )/2 J y =-i (a † b - a b † )/2 with J z = (N +1 - N -1 )/2 J z (a † a - b † b)/2

28. QUEST - Centre for Quantum Engineering and Space-Time Research Expension of the state reveals its entanglement Why is this state not entangled? Because… In 1st quantization: