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
C60 molecule interference
mass?
nano-(electro-etc.-)mechanical oscillators
a) cantilever+singleelectron
transistor (20
MHz)
b) magnetic force
sensor, detecting
spin of 1 electron
c) torsion resonator,
to measure
Casimir force and
eventual shortrange 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)
A
B
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!
Metzger & Karrai 2004
cantilever position
1
retardation, not memory!
light
li
light
Friction caused by retarded light response
(not
only
light)
Laser cooling of atoms - ions:
Doppler cooling
Ω<ω
laser
ħK
v
Absorbed energy
has to be irradiated by
spontaneous emission,
momentum decreases
Γ
ω
Ω
ω
Ion trap: SIDEBAND COOLING
translation becomes quantized vibration,
electron levels acquire vibrational sub-levels
STIMULATED RAMAN: 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 = ENTANGLEMENT
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, 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
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