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?

molecules do interfere

melons do not interfere nor a cat…

WKB? That does not erase interference!

Entanglement with environment → decoherence

(Zeh, Zurek)

Collapse? Origin of randomness? Where does the macro-world begin?

size?

semiconducting nanostructures

mass?

nano-(electro-etc.-)mechanical oscillators

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)

THERE IS MORE: 2-level quantum systems (QUBITs) semiconductor single-electron transistor: SET

(or: quantum dot QD in capacitive coupling)

two states with charge quantization: with 0 or 1 electron in it

that’s what it looks like in reality…

Superconducting

single-electron transistor sensing the vibration of a nanomechanical oscillator

(charge quantization, capacitive coupling)

…, Armour, Clerk, Blencowe, Schwab

Nature

2006 szept.

cooling by quantum measurement back-action, to ½ Kelvin

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

C.K.Law 1994 the mirror is vibrating

int

momentum transferred repetition frequency

work done by light pressure!

Can be much stronger … see later

The Marshall-Shimon-Penrose-Bouwmeester project

PRL

91,

130401 (2003)

B A

photon-mirror coupling

„visibility” of interference

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 Project advancing towards better cooling …

Critical task #1 is

COOLING!

Velocity dependent light pressure~ damping, without heating!

cantilever position

1

Metzger & Karrai 2004 retardation, not memory!

light

Friction caused by retarded light response

(not only light)

ħK

Laser cooling of atoms - ions:

Doppler cooling

Ω<ω

laser

v

ω Ω

Γ

ω

Absorbed energy has to be irradiated by spontaneous emission,

momentum

decreases

Ion trap: SIDEBAND COOLING translation becomes quantized vibration, electron levels acquire vibrational sub-levels

STI MULATED R AMAN: detuned from resonance, with immediate rebound

5 4 3 2 1 0 GHz („carrier”): hyperfine sub-levels vibration: ~10 MHz

2 lasers needed, ~10 Ghz, sharp to 100 Khz!

5 4 3 2 1 0 energy

is also decreasing

Nanomechanics: momentum is primary, but it’s vibration

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 …

„

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

Piezoelectric coupling!

Resonant energy transfer between qubit and oscillator, read off from qubit

Bad news: with classical oscillator it is just as good …

Critical task #2 is

QUANTUM STATE IDENTIFICATION („RECONSTRUCTION”) AND PREPARATION!

demonstrates quantum behaviour of ELECTRONS under perturbation of frequency

ν, NO PROOF FOR PHOTONS!

Here? The Josephson qubit is quantized.

The oscillator? WHO KNOWS?

Preparation of non-classical states (Schrödinger cats, squeezed states etc.) needs

STRONG COUPLING

to succeed before

DECOHERENCE

takes over ≈ 100 Hz 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 fluctuations

measurable: 2-resonator optical noise correlations M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, M. Aspelmeyer 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)

no result so far … why?

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, magnetic tip

of a nano-oscillator integrated on an atom chip; the nano-oscillator senses vibrational modes of the condensate coupled to The same, arXiv:

1003

.1126

experiment: surface attraction, no magnetic force

Entangling two nano-oscillators by magnetic coupling? arXiv:

1006

.4036

Some more proposals : 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)

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

cooling to 1.5 mK (kT/ħω≈3000)

Many theory papers since 2010, most including O. Romero-Isart

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