QUEST - Centre for Quantum Engineering and Space-Time Research Spin dynamics and the Quantum Zeno Effect Carst en Klem pt Leibn iz Univ ersitä t Hann over Fresco in the Library of El Escorial, Madrid. Carsten Klempt, Luis Santos, Augusto Smerzi, Wolfgang Ertmer

QUEST - Centre for Quantum Engineering and Space-Time Research 2 Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect Content

QUEST - Centre for Quantum Engineering and Space-Time Research 3 Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect Content

QUEST - Centre for Quantum Engineering and Space-Time Research 4 Zeno of Elea 490 v. Chr v. Chr.

QUEST - Centre for Quantum Engineering and Space-Time Research 5 The paradoxes of Zeno of Elea "not less than forty arguments revealing contradictions" –Proclus Only nine are known First examples of reductio ad absurdum Paradoxes of motion: o The dichotomy paradox o Achilles and the tortoise o The arrow paradox

QUEST - Centre for Quantum Engineering and Space-Time Research 6 The dichotomy paradox That which is in locomotion must arrive at the half- way stage before it arrives at the goal. –Aristotle

QUEST - Centre for Quantum Engineering and Space-Time Research 7 Achilles and the tortoise

QUEST - Centre for Quantum Engineering and Space-Time Research 8 Achilles and the tortoise

QUEST - Centre for Quantum Engineering and Space-Time Research 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

QUEST - Centre for Quantum Engineering and Space-Time Research 10 Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect Content

QUEST - Centre for Quantum Engineering and Space-Time Research 11 Zeno with a quantum arrow Zeno: The spin cannot rotate in the Bloch sphere

QUEST - Centre for Quantum Engineering and Space-Time Research 12 The quantum Zeno setup Zeno: divide time in m small intervals and follow the dynamics at each time step. (total time : t = m τ = π )

QUEST - Centre for Quantum Engineering and Space-Time Research 13 The quantum Zeno effect Peres, Am. J. Phys. 48, 931 (1980). 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

QUEST - Centre for Quantum Engineering and Space-Time Research 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 !

QUEST - Centre for Quantum Engineering and Space-Time Research 15 The quantum Zeno effect in a BEC

QUEST - Centre for Quantum Engineering and Space-Time Research 16 Level scheme F=2 F=1 m F = P 3/2 5S 1/2 6.8 GHz 780 nm

QUEST - Centre for Quantum Engineering and Space-Time Research 17 Pulsed measurements

QUEST - Centre for Quantum Engineering and Space-Time Research 18 Experimental results

QUEST - Centre for Quantum Engineering and Space-Time Research 19 Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect Content

QUEST - Centre for Quantum Engineering and Space-Time Research 20 BEC spin dynamics Idea: Spin dynamics as slow coherent process Prevent spin dynamics by Zeno measurement It is sufficient to measure one ±1 component The creation of the other is blocked by entanglement

QUEST - Centre for Quantum Engineering and Space-Time Research 21 Level scheme F=2 F=1 m F = P 3/2 5S 1/2 6.8 GHz 780 nm ?

QUEST - Centre for Quantum Engineering and Space-Time Research 22 Expected result without Zeno measurements with Zeno measurements

QUEST - Centre for Quantum Engineering and Space-Time Research 23 Level scheme F=2 F=1 5P 3/2 5S 1/2 6.8 GHz 780 nm 10 Hz 10 kHz kHz 6 MHz

QUEST - Centre for Quantum Engineering and Space-Time Research 24 Zeno’s paradoxes The quantum Zeno effect Spin dynamics and the quantum Zeno effect Entanglement and the quantum Zeno effect Content

QUEST - Centre for Quantum Engineering and Space-Time Research 25 Zeno dynamics and entanglement Complicated, extremely entangled, fragile state unwanted state decoherence Is the state intact?

QUEST - Centre for Quantum Engineering and Space-Time Research 26 Entangled states are more difficult to protect!

QUEST - Centre for Quantum Engineering and Space-Time Research 27 Level scheme F=2 F=1 m F = P 3/2 5S 1/2 6.8 GHz 780 nm

QUEST - Centre for Quantum Engineering and Space-Time Research 28 Two-mode squeezed vacuum σ(N -1 – N +1 ) = 0 σ(Φ -1 – Φ +1 )   /  3 N -1, Φ -1 N +1, Φ +1 Barnett & Pegg, Phys. Rev. A 42, 6713 (1990).

QUEST - Centre for Quantum Engineering and Space-Time Research 29 Level scheme F=2 F=1 m F = P 3/2 5S 1/2 6.8 GHz 780 nm

QUEST - Centre for Quantum Engineering and Space-Time Research 30 J z /J +1 0 Rotation angle ↔ Variance Jz2Jz2 ‹J z ›=0 Probability distribution

QUEST - Centre for Quantum Engineering and Space-Time Research 31 Distribution after rotation

QUEST - Centre for Quantum Engineering and Space-Time Research 32 Level scheme F=2 F=1 m F = P 3/2 5S 1/2 6.8 GHz 780 nm

QUEST - Centre for Quantum Engineering and Space-Time Research 33 Expected result Twin Fock state can be protected against rotation Zeno measurements must be fast. They are faster than for a classical state  Entanglement is difficult to protect by Zeno measurements

QUEST - Centre for Quantum Engineering and Space-Time Research 34 Thank you for your attention

QUEST - Centre for Quantum Engineering and Space-Time Research 35

QUEST - Centre for Quantum Engineering and Space-Time Research 36