1. NANOMECHANICAL SYSTEMS APPROACHING THE EXPECTED QUANTUM-CLASSICAL BORDER Nanomechanical oscillators getting lighter and lighter bring us close to the time when quantum signatures, so far seen only on not too big molecules, become visible on the motion of man-made objects, by coupling them to various quantum systems, including light, reflected from attached nano-mirrors.

2. Where is the border between quantum and classical? WKB? That does not erase interference! Entanglement with environment → decoherence (Zeh, Zurek) Collapse? Origin of randomness? Where does the macro-world begin? nor a cat… molecules do interfere melons do not interfere

3. nano-(electro-etc.-)mechanical oscillators mass? semiconducting nanostructures size? C molecule interference 60

4. a)cantilever+single- electron transistor (20 MHz) b)magnetic force sensor, detecting spin of 1 electron c)torsion resonator, to measure Casimir force and eventual short- range gravity d)amplifier of mechanical motion by factor of 1000 e)cantilever + single-electron transistor (116 MHz) f)tunable carbon nanotube resonator (3-300 MHz)

5. Since the turn of the millennium: QUANTUM BEHAVIOUR OF NANOMECHANICAL DEVICES? oscillators close to the ground state: kT/ħω ~1 high frequency– little cooling, low frequency – much cooling - no remedy to everything! Tiny displacements have to be detected! OPTOMECHANICS: NANO-OSCILLATOR -- PHOTON COUPLING

6. optical sensing of motion also used in the Atomic Force Microscope (AFM) semiconductor single-electron transistor: SET (or: quantum dot QD in capacitive coupling) THERE IS MORE: 2-level quantum systems (QUBITs) two states with charge quantization: with 0 or 1 electron in it

7. that’s what it looks like in reality…

8. …, Armour, Clerk, Blencowe, Schwab Nature 2006 szept. cooling by quantum measurement back-action, to ½ Kelvin Superconducting single-electron transistor sensing the vibration of a nanomechanical oscillator (charge quantization, capacitive coupling)

9. Cooper-pair box controlling the state of a nanomechanical oscillator alternative: in big superconducting circuits magnetic flux gets quantized, not the charge (the two can be combined)

10. Mirror-photon coupling momentum transferred repetition frequency work done by light pressure! the mirror is vibrating C.K.Law 1994 int Can be much stronger … see later

11. The Marshall-Shimon-Penrose-Bouwmeester project photon-mirror coupling B A PRL 91, 130401 (2003)

12. thermal narrowing (Bose, Jacobs, Knight; reconsidered by Bernád-Diósi-TG: PRL, 2006 december) 1.For strong coupling, soft oscillator is needed, difficult to cool 2.There are visibility returns at high temperatures, by purely classical mechanism 3.Not even entanglement is fully quantum: can reduce to classical correlation „visibility” of interference Project advancing towards better cooling …

13. Critical task #1 is COOLING! Velocity dependent light pressure~ damping, without heating!

14. retardation, not memory! 1 Friction caused by retarded light response Metzger & Karrai 2004 (not only light) cantilever position light li light

15. Doppler cooling Γ Ω ω ω v ħKħK Ω<ωΩ<ω laser Ion trap: SIDEBAND COOLING translation becomes quantized vibration, electron levels acquire vibrational sub-levels Laser cooling of atoms - ions: Absorbed energy has to be irradiated by spontaneous emission, momentum decreases 543210543210 543210543210 STIMULATED RAMAN: detuned from resonance, with immediate rebound 2 lasers needed, ~10 Ghz, sharp to 100 Khz! GHz („carrier”): hyperfine sub-levels vibration: ~10 MHz energy is also decreasing Nanomechanics: momentum is primary, but it’s vibration

16. Sideband cooling in optomechanics Schliesser et al (Max Planck, Garching, Nature Phys. 2008) Excited optical mode depleted to environment; cooled mechanical mode heated by environment… it works classically too: in Doppler cooling, velocity is oscillating… CAN BE REGARDED AS QUANTUM BACK-ACTION …

17. „ active cooling ” by feedback from motion sensing Maxwell demon

18. Ground-state cooling without laser, helium dilution fridge 6 GHz, 0.25 mK O’Connell et al., Nature 464, 697 (2010, 1 April (!)) no cooling but state preparation and measurement by Josephson phase qubit Resonant energy transfer between qubit and oscillator, read off from qubit Bad news: with classical oscillator it is just as good … Piezoelectric coupling!

19. demonstrates quantum behaviour of ELECTRONS under perturbation of frequency ν, NO PROOF FOR PHOTONS! Here? The Josephson qubit is quantized. The oscillator? WHO KNOWS? Critical task #2 is QUANTUM STATE IDENTIFICATION („RECONSTRUCTION”) AND PREPARATION!

20. ≈ 100 Hz Preparation of non-classical states (Schrödinger cats, squeezed states etc.) needs STRONG COUPLING to succeed before DECOHERENCE takes over For stronger coupling: displace from equilibrium find avoided crossing Sankey, …, Harris: Nature Phys. 6, 707 (2010)

21. A promising (?) scope: to observe subtle qantum correlations between vibrating mirror and optical resonator(s), in the measured fluctuations measurable: 2-resonator optical noise correlations no result so far … why? M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, M. Aspelmeyer Phys. Rev. Lett. 99, 250401 (2007) Phys. Rev. Lett. 99, 250401 (2007) D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. Aspelmeyer Phys. Rev. Lett. 98, 030405 (2007) Phys. Rev. Lett. 98, 030405 (2007) = ENTANGLEMENT

22. various theories … important topic: how harmful the phase noise of lasers can be to cooling? Diósi vs. Aspelmeyer et al.: markovian or non-markovian treatment?

23. Theory for mechanical friction and related noise? ”phonon tunneling” (Wilson-Rae, PRB 77, 245418 (2008), arXiv:1007.4948) FAPP universal ?? Cantilever support acts as a narrow wave guide for phonons sound waves of velocity c through wave guide of diameter d: threshold frequency c/d for wave propagation → energy barrier of ħc/d for phonons Sub-threshold phonons get through by tunneling

24. Trapped cold gases 1. Coupling of trapped cold gases to a nanomechanical oscillator …,Hänsch,…, PRL 99,140403(2007) proposal: BEC with spin, coupled to magnetic tip of a nano-oscillator integrated on an atom chip; the nano-oscillator senses vibrational modes of the condensate The same, arXiv:1003.1126 experiment: surface attraction, no magnetic force Entangling two nano-oscillators by magnetic coupling? arXiv:1006.4036

25. 1. To couple the C.O.M. mode of an atomic cloud (BEC) to a nano-oscillator / micro-membrane by light …,Aspelmeyer,…,Zoller, PRL 102,020501(2008) Paternostro et al., PRL 104, 243602 (2010) …, Zoller, …, Hänsch, PRA 82, 021803 (2010) Some more proposals :

26. 2. C.O.M. of trapped condensate IS the nanomechanical oscillator! BEC: Science 322,235(2008) ETH Zürich

27. 3. LEVITATION of a dielectric sphere (bead) by two-mode Optical Tweezer no mechanical support, but noise from lasers + Casimir force; trapping is weak → soft oscillator Li,Kheifets,Raizen(Austin), arXiv:1101.1283v2 Many theory papers since 2010, most including O. Romero-Isart cooling to 1.5 mK (kT/ħω≈3000)

28. SUMMARY the world of moving objects, lighter than any man-made product so far but heavier than any flying molecule, is not only potentially useful for applications but offers a deeper understanding of the quantum world around us; outstanding laboratories are competing in building lighter and lighter, cooler and cooler oscillators, attaching mirrors, SETs, all kinds of various Josephson qubits to them, to control and observe their motion; legions of curious theoreticians are competing in trying understand how those objects move and how they will move after tomorrow