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.

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 interferemelons do not interfere

nano-(electro-etc.-)mechanical oscillatorsmass?

semiconducting nanostructures

size?

C molecule interference60

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)

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

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

that’s what it looks like in reality…

…, 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)

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)

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

The Marshall-Shimon-Penrose-Bouwmeester project

photon-mirror coupling

B

A

PRL 91, 130401 (2003)

thermal narrowing (Bose, Jacobs, Knight; reconsidered by Bernád-Diósi-TG: PRL, 2006 december)

1. For strong coupling, soft oscillator is needed, difficult to cool2. There are visibility returns at high temperatures, by purely classical mechanism3. Not even entanglement is fully quantum: can reduce to classical correlation

„visibility” ofinterference

Project advancing towards better cooling …

Critical task #1 is COOLING!

Velocity dependent light pressure~ damping, without heating!

retardation, not memory!

1

Friction caused by retarded light response

Metzger & Karrai 2004

(notonlylight)

cantilever position

light lilight

Doppler cooling

ΓΩ ω

ωvħK

Ω<ωlaser

Ion trap: SIDEBAND COOLINGtranslation becomes quantized vibration,

electron levels acquire vibrational sub-levels

Laser cooling of atoms - ions:

Absorbed energyhas to be irradiated byspontaneous emission, momentum decreases

5 4 3 2 1 0

5 4 3 2 1 0

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

Sideband cooling in optomechanicsSchliesser 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 …

„active cooling” by feedback from motion sensing

Maxwell demon

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!

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!

≈ 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)

A promising (?) scope:

to observe subtle qantum correlations

between vibrating mirror and optical

resonator(s),

in the measured fluctuationsmeasurable:2-resonatoroptical noise correlations

no result so far … why?

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, M. AspelmeyerPhys. Rev. Lett. 99, 250401 (2007) 

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. AspelmeyerPhys. Rev. Lett. 98, 030405 (2007)

= ENTANGLEMENT

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?

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

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

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 :

2. C.O.M. of trapped condensate IS the nanomechanical oscillator!

BEC: Science 322,235(2008) ETH Zürich

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)

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