Transcript NANOMECHANIKAI RENDSZEREK OTT, AHOVA A KVANTUM …
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