Spin dynamics and the Quantum Zeno Effect

1. Spin dynamics and the Quantum Zeno Effect Fresco in the Library of El Escorial, Madrid. Carsten Klempt, Luis Santos, Augusto Smerzi, Wolfgang Ertmer Carsten Klempt Leibniz Universität Hannover

2. Content Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect

3. Content Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect

4. Zeno of Elea 490 v. Chr. - 430 v. Chr.

5. The paradoxes of Zeno of Elea • "not less than forty arguments revealing contradictions"–Proclus • Onlynineareknown • First examplesofreductio ad absurdum • Paradoxes ofmotion: • The dichotomy paradox • Achilles andthetortoise • The arrow paradox

6. The dichotomy paradox That which is in locomotion must arrive at the half-way stage before it arrives at the goal. –Aristotle

7. Achilles and the tortoise

8. Achilles and the tortoise

9. The arrow paradox If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. –Aristotle

10. Content Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect

11. Zeno with a quantumarrow Zeno: The spin cannot rotate in the Bloch sphere

12. The quantum Zeno setup Zeno: divide time in msmall intervals and follow the dynamics at each time step. (total time : t = m τ = π )

13. The quantum Zeno effect Zeno: check at each time step if the spin really rotated: projective measurements The projective measurement has eigenvalues “yes”, “no”. The “yes” projects on the subspace with probability Peres, Am. J. Phys. 48, 931 (1980).

14. Zeno: give a look at the survival probability (the probability that at the final time the spin is still pointing up) The arrow does not rotate if watched !

15. The quantum Zeno effect in a BEC

16. Level scheme 5P3/2 780 nm F=2 6.8 GHz 5S1/2 F=1 -1 0 +2 mF= -2 +1

17. Pulsedmeasurements

18. Experimental results

19. Content Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect

20. BEC spin dynamics -1 0 1 • Idea: • Spin dynamicsasslowcoherentprocess • Preventspindynamicsby Zeno measurement • Itissufficienttomeasureone ±1 component • The creationoftheotherisblockedbyentanglement

21. Level scheme 5P3/2 780 nm F=2 6.8 GHz 5S1/2 F=1 ? -1 0 +2 mF= -2 +1

22. Expectedresult without Zeno measurements with Zeno measurements

23. Level scheme 5P3/2 6 MHz 780 nm 10-100 kHz F=2 6.8 GHz 10 kHz 5S1/2 F=1 10 Hz

24. Content Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect

25. Zeno dynamicsandentanglement Complicated, extremelyentangled, fragile state Isthestate intact? decoherence unwantedstate

26. Entangledstatesaremoredifficulttoprotect!

27. Level scheme 5P3/2 780 nm F=2 6.8 GHz 5S1/2 F=1 -1 0 +2 mF= -2 +1

28. Two-mode squeezed vacuum N-1 , Φ-1 N+1, Φ+1 σ(N-1 – N+1) = 0 Barnett & Pegg, Phys. Rev. A 42, 6713 (1990). σ(Φ-1– Φ+1) /3

29. Level scheme 5P3/2 780 nm F=2 6.8 GHz 5S1/2 F=1 -1 0 +2 mF= -2 +1

30. Rotation angle ↔ Variance ‹Jz›=0 Jz/J +1 Jz2 0 -1 Probability distribution

31. Distribution after rotation

32. Level scheme 5P3/2 780 nm F=2 6.8 GHz 5S1/2 F=1 -1 0 +2 mF= -2 +1

33. Expectedresult • Twin Fock statecanbeprotectedagainstrotation • Zeno measurements must be fast. • Theyarefasterthanfor a classicalstate • Entanglementisdifficult • toprotectby Zeno measurements

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