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Title: Progress in Quantum Electromechanics Continuous Position Detection Near the Quantum Limit


1
Progress in Quantum ElectromechanicsContinuous
Position Detection Near the Quantum Limit
  • Keith Schwab, Laboratory for Physical Sciences
  • National Security Agency
  • August 2004
  • schwab_at_lps.umd.edu

This work is supported entirely by NSA
2
My Group and Collaborators
Laboratory for Physical Sciences (LPS) Marc
Manheimer NSA Carlos Sanchez UMCP-grad
student Akshay Niak UMCP-grad student Ben
Palmer NSA Elinor Irish Rochester-grad
student Olivier Buu post doc Matt LaHaye
UMCP-grad student Patrick Truitt UMCP-grad
student Benedetta Camarota post doc Alex
Hutchinson post doc Harish Bhaskaran UMCP-grad
student Dan Stick Univ. Michagan-grad
Cooper-Pair Box
Nanomechanics
Atomic Traps
Collaborators Michael Roukes and his group
Caltech Chris Hammel and Denis Pelekhov Ohio
State Miles Blencowe Dartmouth Andrew Armour
Nottingham Asa Hopkins, Kurt Jacobs, and Salman
Habib LANL Ivar Martin LANL Halina
Rubinsztein-Dunlop Univ. of Queensland Chris
Monroe Univ. of Michigan Kamil Ekinci Boston
University Pierre Echternach JPL / Caltech
3
Examples of Nanomechanical Devices
Quantized Thermal Transport
MRFM detectors
Simple Nanomechanical Resonators
Integrated rf SET
Atomic Traps
4
Quantum limits of position detection
There are two pieces to this system which have
quantum limits Massive resonator Amplifier
k
M
Dx
For one instantaneous measurement no limit
detector
5
How close have other come?
2 Ton Acoustic Resonators-Auriga
Single-Spin Microscopes
4 km Interferometers - LIGO
SETNanomechanics
6
Energy Quantization - Freeze-Out
Oscillator occupation number T(mK) n(1kHz) n(10
MHz) n(100MHz) n(1GHz) 1000 2 107 2070 207 20
100 2 106 207 20.7 1.6 10 2 105
20.8 1.6 0.008 1 2 104 1.6 0.008 10-21 0.
50 1 104 0.6
7
SET Position Measurement
Energy sensitivity of rf SET has been
demonstrated to be 4.8 ? (not including back
action) Assime APL 2001.
Coupling
J
J
island
Blencowe and Wybourne, APL 77, 3845 (2000)
8
SET IVs and Modulation
Fix VG, measure IDS vs VDS
Fix VDS, measure IDS vs VG
Conductance of SET is depends upon applied charge
9
Back-action from SET
Physical Circuit
Noise in Electrical Circuits
Electro-Mechanical Circuit
Vds
Vn
G
e
In
Z
Sff
Cg(x)
e
Cj
SI
G
Vg
IDS
Korotkov, PRB (1994).
10
Complete Noise Model
Read-out noise due to shot noise
SET island
SQ
G
SV
Cm
Cg
2CJ
Back action voltage fluctuations
Lm
RJ
Rm
SThermal
Mechanical Resonator
11
Displacement Resolution at the Sweet Spot
Quantum Back action
12
RF SET coupled to Nanomechanics
L
C
SETmechanics on SiN membrane
13
RF SET coupled to Nanomechanics
14
RF SET coupled to Nanomechanics
gate
20 MHz resonator
SET
15
Recent Devices-RF SET coupled to Nanomechanics
200nm
Au
100 nm SiN
16
Cryogenic and electronicsetup
17
(No Transcript)
18
(No Transcript)
19
Resonance Detection with rf SET
Vdrive
VG
mwave reflectometry
Mechanical resonance detected by
electrostatically driving beam.
20
Thermal Motion of Nanomechanics
Equipartion Theorem
Noise Temperature of our system with VG2V
Thermal Motion 5.4 10-13mRMS _at_ 500mK 2.4
10-13mRMS _at_ 100mK
21
Nanomechanical Noise Thermometry
22
Detection Noise Temperature
TN/TQ33
Dx/DxQL5.8
23
Measured Displacement Resolution
Quantum Back action
LaHaye, et al, Science, 2 April 2004
24
Nanomechancis at Freeze-Out
freeze-out to 1D phonon channels
Measurement of the quantum of thermal
conductance K. Schwab, E.A. Henriksen, J.M.
Worlock M.L. Roukes NATUREVOL 40427 APRIL 2000
25
Strong Coupling Experiments
Classical dynamics of a nanomechanical resonator
coupled to a single-electron transistor, A. D.
Armour, M. P. Blencowe, and Y. Zhang, Phys. Rev.
B 69, 125313 (2004)
26
Strong Coupling Experiments
Mechanical Mode
Phonon Bath
SSET
Classical dynamics of a nanomechanical resonator
coupled to a single-electron transistor, A. D.
Armour, M. P. Blencowe, and Y. Zhang, Phys. Rev.
B 69, 125313 (2004)
27
Q vs Temperature
Q reached 200,000 for low SET coupling voltages
28
Active Cooling to the Ground State
Feedback Cooling of a Nanomechanical Resonator
Jacobs, Hopkins, Habib, and Schwab, PRB 68,
235328 (2004). Quantum Squeezing through
Feedback, Korotkov and Schwab, in preparation
Calculations using a model of continuous quantum
measurement, includes all sources of quantum
noise (including quantum projection noise and
quantum amplifier noise) feedback cooling to
N1-0.1 is possible.
29
Feedback Cooling-Recent Experiments
30
Warming and Cooling
Feedback on
Feedback off
Thermodynamics of a single degree of freedom
31
Cooling in Phase Space
32
What can we do with QL continuous position
measurement?
  • rf SSET coupled to a 20 MHz resonator
  • search for higher order modes
  • achieve freeze-out, deviation
  • from classical equipartition
  • N f l
  • 1 20 MHz 8 mm
  • 3 110 MHz 3.4 mm
  • 5 270 MHz 2.1 mm
  • 7 500 MHz 1.6 mm
  • 9 800 MHz 1.3 mm
  • rf SSET coupled to a 1 MHz resonator
  • increase coupling by reducing gap,
  • observe back action fluctuations
  • (Armour and Blencowe, Martin and Mozyrsky )
  • drive dc current through resonator
  • observe mech. noise from impact of electrons
  • (Shytov, et al. PRL 2002) TN100mK 1K

33
Back-Action Physics
Coupling to SET will cause a damping and
fluctuations
See A. Armour and M. Blencowe,
\condmat0307528 Mozyrsky and Martin, PRL 89,
018301 (2003). recent work of A. Clerk.
34
Mind the Gap
Resonator
100-75 nm Gap
Au Gate
35
Please make 4,000 samples
5mm chip
150 mm dia. Coil
1mm wide lines-photolithography
Samples fabricated by MEMS-Exchange
36
Coupling to Coherent Quantum Devices
Quantum Two Level System Nuclear Spin Electron
Spin Charge on Cooper-Pair Box Flux in a SQUID
ring ..
10-21 Nt . 10-18 Nt. 10-13
Nt.. 10-9 Nt..
Schrodingers Cat Situation Macroscopic state
depends on microscopic quantum state Schrodi
ngers Whisker
Armour, Blencowe, and Schwab, Phys. Rev. Lett.
88, 148301 (2002).
37
Coherence times of the mechanics
Lifetime for number state
Decoherence time for superposition of coherent
states
Zurek, Habib, Paz, PRL 70, 1187 (1993).
38
Quantum Electro-Mechanics
Mirror
Interaction is through capacitance
Armour, Blencowe, Schwab, PRL 88, 148301
(2001). Armour, Blencowe, Schwab, Physica B 316,
(2002). Irish and Schwab, PRB 68, 15531 (2003).
39
Energy Scales and Linewidths
100 MHz - 1 GHz linewidth 1 kHz - 1 MHz
Mechanical States
2-50 GHz linewidth 0.5 - 3 MHz
Charge States
40
Mechanical Cooling Through Laser Cooling of
Qubit?
Decay of charge state without change in
mechanical state
Ground State Cooling of mechanical resonators,
Martin, Shnirman, Tian, and P. ZollerPhys.
Rev. B 69, 125339 (2004)
41
Conclusions
  • Closest approach to the Uncertainty Principle, lt
    10 DxQL
  • Back action of SSET at 20 MHz is near ideal
  • Back action at 50 GHz is terrible! (CPB
    experiments)
  • Observed resonator cooled to N 58 hw
  • Starting feedback cooling thermal relaxation of
    single mode
  • Entanglement with solid state qubits looks
    possible mechanical superpositions
  • Nanomechanical QED experiments look promising
  • Are mechanical resonators useful as a quantum bus
    for charge qubits?

This work is supported by National Security
Agency (NSA) Our Motto Putting the Spook in the
Spooky actions at a distance
schwab_at_lps.umd.edu
42
Calculated Dynamics
Initial state
Intermediate state
Probability Density
After one period
1.10-13 m
43
Cavity Quantum Electro-Dynamics
Mirror
Atom
Mode
44
Cavity QED analog QEM
Quantum Electro-Mechanics
Quantum Electro-Dynamics
Armour, Blencowe, Schwab, PRL 88, 148301
(2001). Armour, Blencowe, Schwab, Physica B 316,
(2002). Irish and Schwab, PRB 68, 15531 (2003).
45
Second Order Shift of Energy Levels
Treat HI as a perturbation
Quantum Measurement with a coupled
Nanomechanical ResonatorCooper Pair Box System,
E. Irish and K. Schwab, Phys. Rev. B 68, 155311
(2003)
46
Mechanical Dressed States
Hamiltonian
Ignoring HI we find the unperturbed energy
47
Nanomechanical Quantum Bus
For a 1 mm wide Diamond beam (E1000GPa) 1 GHz l
6 mm 10 GHz l 2 mm For a 1 mm wide Silicon
beam (E110GPa) 1 GHz l 3.5 mm 10 GHz l
1.2 mm
What is the Q of these higher order modes? What
is the effect of the other modes? Possible
source of decoherence? Advanced materials
Piezoelectric or nanotubes?
Coupling strength
48
Penrose Proposal
Low photon pressure requires very soft cantilever
(even after amplify dwell time with cavity) Very
soft cantilever has very low frequency
1KHz Low frequency cantilever has very low
freezeout temperature 60mK
49
Support

50
C60fF
L150nH
BOX
2e-charge states Good!
SET Gate
1µm
quasi-particle poisoning Bad!
SET
51
Spectroscopy of Box
52
Coherent oscillations
?t
  • Send pulses continuously
  • Measure staircase with SET

Tr500ns
53
Coherent Single ElectronicsCooper-Pair Box
Ultra-small capacitance (lt10-15 F)
--------- charge eigenstates Superconducting
--------- follows Josephson equations of
motion
Cooper Pair Binding energy D230mV Charging
energy Ec e2/2C 100mV Josephson energy EJ
50-10mV Thermal energy T 3mV (30 mK) D
gt Ec gtEJ gtkBT
54
Energy Spectrum of Cooper-Pair Box
At level crossing, states are superposition of
charge states.
DE50-1 GHz Decoherence time measured to be
t20.5msec And excited state lifetime of
t12msec. Vion, et al, Nature 2002.
55
Coherence time of position-superposition states
Decoherence time
Typical resonator decay time Number of Coherent
Oscillations For 100 MHz at 10 mK.
Zurek, Habib, Paz, PRL 70, 1187 (1993).
56
Who is interested in Quantum Limits of motion?
Gravitational Wave Detectors
Interferometers-LIGO
Mechanical Resonators-Auriga
Looking for displacements on the order of
Dl/l10-21 Quantum Limits of the Mega-world.
57
Temperatures?
Clearly the thermal bath which determines f and Q
is different than the mode temperature.
58
Charge States Coulomb Staircase
Measure response at SET
Sweep Box gate Voltage
59
Reality Check A typical fabrication result!
60
Shift of the CPB by Resonator Fock States
Mechanical Lamb shift Mechanical Lamb-shift
analogue for the Cooper-pair box, A.D. Armour,
M.P. Blencowe, and K.C. Schwab,
By driving transitions in the Box, one should be
able to prepare a mechanical number
state perform QND measurement of number using
Ramsey interferometry (Vion, 2002)
61
Shift of the Resonator frequency by the CPB
wm300MHz, l0.1hwm, EJ4mV, EC100mV
By measuring the mechanical frequency we can know
the state of the phase states of the box.
62
Quantum Phenomena in Mechanical Structures
First kind Uncertainty Principle-Limited
Detection
Second kind Energy Level Quantization
Third kind Superpositions and Coherent
Evolution
Fourth kind Controlled Entanglement with
other quantum systems
63
What is Quantum Electro-Mechanics?
  • Single Electron Transistors
  • Cooper-Pair Box
  • Quantum Dots
  • Quantum Point Contacts
  • SQUIDs
  • Single electron spins
  • ..

kBThn just a few quanta tDgt 1/n long
coherence times
Exploit the quantum electronics to both detect
and generate the quantum nature of the mechanical
device.
64
Magnetomotive Readout of Nanomechanics
R
TN
B
Sensitivity of Magnetomotive? Not
very! TN30K
Fabrication by LaHaye and Hutchinson
65
Back action of the SSET onto the CPB
Back-action from phonons or photons emitted when
quasi particles in SET recombine?
Can we engineer D?
66
Can we detect the Thermal Motion?
Amorphous Silicon Nitride resonator
Conditions f0 23MHz Q 104 T
4.2K B9T Thermomechanical Noise xRMS 2 pmRMS
gt 8 nVRMS XRMS (4.2K) 1.4 pm 60 XSQL
To approach quantum limits motion we need a
quantum limited linear amplifier SQUIDs and SETs
67
Displacement Resolution Sweet Spot
Quantum Back action
Shot Noise
Back Action Noise
68
Recent Devices-RF SET coupled to Nanomechanics
1 mm
SET island
junctions
69
Mechanical Entanglement
Idea Use the superposition available in a
Cooper-pair box to place a mechanical system in a
superposition For two different charge states of
the box, the position of the resonator can change
by as much as 12pm gt xSQL100fm
What will the effect of the mechanical mode on
the Cooper-pair box? How long will a
superposition survive? Armour, Blencowe, and
Schwab, Phys. Rev. Lett. 88, 148301 (2002).
70
Can we make the resonator interfere with itself?
You Bet!, send a p/2 pulse to the box after the
systems have entangled This produces states like
Interference terms
By measuring Box, we can create mechanical
superposition states
Probability Density
1.10-13 m
71
Decoherence and Recoherence
Envelope on Ramsey interference experiment
should reveal entanglement with mechanics
Armour, Blencowe, and Schwab, PRL 88, 148301
(2002).
Mixed state
Total State
Expectation Value
72
What can we learn?
  • This teaches us how to engineer quantum limited
    detection where hw is growing smaller and smaller
    (attempt at MHz) on systems that have huge
    numbers of degrees of freedom that must be
    controlled.
  • This forces us to consider carefully the
    interaction between the measuring device and the
    measured quantum system. These studies will
    teach us intelligent measurement strategies (QND,
    indirect measurement, stroboscopic..) (Quantum
    Engineering)
  • Reveals the physics of decoherence and
    entanglements, relevant to the engineering of
    quantum coherent solid state devices (Quantum
    Computers?)
  • This work will push the boundary between the
    classical world that we live in and the bizarre
    behavior that underlies reality (Foundations of
    Physics).

Will Quantum Mechanics break-down on large length
scales?
73
Ramsey Interference Experiments
Interaction Region
State Measurement
p/2 pulse
p/2 pulse
State Preparation
Space or Time
74
Traps for BEC Univ. of Queensland
Fabricated by Ashley Carter
13 mm thick Al film
30 mm wide etched gap
15-30 mm wide wires
75
Microfabricated Ion Traps Univ. of Michigan
Top view
First etch into GaAs
10mm
View behind chip
Fabricated by Dan Stick
76
RF -SET Nanomechanics
See Adrian Cho, Science 299, 36 (2003).
77
Can we exploit what is known from atomic physics?
Laser Cooling Atom in crossed laser field, red
tuned from transition
When atom moves, it encounters light on
resonance, absorbs photon and re-radiates this
into 4p. Kinetic Energy -gt Radiation into cold
reservoir
Nanomechanical Cooling Can we engineer a
situation where the motion of a nanomechanical
device leads to a force, pushing it back towards
equilibrium? By interaction with an SET, a
quantum dot, ect?
78
Frequency and Q Tuning Using an SET
What will happen if we place the SET island on
the nanomechanical resonator and place this
system in a large magnetic field? We can tune the
frequency and adjust the damping.. Schwab,
Appl. Phys. Lett. 80, 1276 (2002).
B
When SET moves, current changes resulting in a
change in the Lorentz force---- will add spring
constant When SET moves, voltage is developed
(Lenzs Law) resulting in a change in SET
current, resulting in a change in the Lorentz
force ----- will add damping constant
79
Lorentz Spring Constant
80
Losses Q modification
Plot for 10MHz Si resonator (7mm X 50nm X50nm)
Emf generated will give an additional damping
force to resonator, depending on VG.
81
The numbers..
Table I silicon (Si), single wall nanotubes
(SWNT), nanotube bundles (B-SWNT), with length l,
width w, thickness t, mass m, resonant frequency
wo, mechanical spring constant kM, maximum bias
voltage VMAX, Lorentz spring constant kL, range
of frequency tuning Dwo/wo, and least upper bound
on quality factor QL, For the nanotube
resonators, it is assumed that the density is
1100 Kg/m3, Youngs modulus 1000 GPa, CG10 aF,
CJ10 aF.
 
82
Suggestions to approach quantum limits
  • Must incorporate detection with mechanical device
    to overcome ultra(high/low) output impedance of
    nanomechanics-detection schemes with noise
    temperature TNlt1K
  • High frequencies gt100MHz
  • to avoid 1/f or similar noise in detector or
    background forces
  • to approach thermal freeze-out to ground state
  • to have long decoherence times
  • Stiff-low density materials Diamond and Silicon
    Carbide
  • need to routinely approach 1GHz- couple well to
    qubit energies
  • Integrate magnetic materials for force
    sensing-Magnetic microscopy
  • Exploit recent developments in solid state
    Quantum Computing coherent electronic devices
  • Engage theorist to guide these experiments and to
    produce measurement strategies (squeezing,
    entanglement, non-classical state formation.)

83
Questions
  • Can we generate an approximation to an arbitrary
    wave function of resonator by coherent control of
    two level system (CPB)?
  • Can we exploit this for metrology? Single spin
    detection? Weak force detection beyond Standard
    Quantum Limit?
  • Can we test Quantum Mechanics, (and how do we
    distinguish new physics from bad experimental
    technique?)

84
Why is there no interference?
System state
Incoherent Sum of Probability Distributions
Physics of decoherence by entanglement with
environment.
85
Control of the Wavefunctions
Uncoupled systems
Coupled and Entangled systems
86
Signature of the Entanglement
Expect to see a modulation on the coherent
oscillations of the Cooper-Pair box at the
resonator frequency (N.B. no fancy detectors
needed to monitor the mechanical resonator.)
Nanomechanical resonator is an engineered
environment Similar to other proposed schemes
with electro-magnetic resonators Marquardt and
Bruder, Phys. Rev. B, vol. 63, 054514-1
(2001) Buisson and Hekking, cond-mat/0008275
87
Some References on SETs
SET Single Charge Tunnelling, edited by Devoret
and H. Grabert, (Plenum, New York,
1992). Single-electron transfer in metallic
nanostructures, M. Devoret, et al., Nature 360,
547 (1992). Instrinsic Noise of a single
electron transistor, A. Korotkov, Phys. Rev. B
49, 10381 (1994). Charge sensitivity of a single
electron transistor, U. Hanke, et al., Appl.
Phys. Lett. 65, 1847 (1994). Charge sensitivity
of superconducting single-electron transistor,
A. Korotkov, Appl. Phys. Lett. 69, 2593
(1996). Take a look at more references from
Korotkov for calculations of fluctuations and
sensitivity of SETs.  Quantum-Limited
Electrometer based on Single Cooper-Pair
tunneling, A. Zorin, Phys. Rev. Lett. 76, 4408
(1996). Highly sensitive electrometer based on
single cooper pair tunneling, A. B. Zorin, et
al., J. Appl. Supercon 12, 747 (1999). This is
a more advanced SET which looks sort-of-like an
electrostatic SQUID. The most interesting
feature is that the tunneling is coherent
Josephson tunneling which produces a sinusoidal
back-action (as opposed to the white noise
spectrum of the backaction in a normal SET.
) The radio frequency single electron transistor
(RF-SET)a fast and ultrasensitive electrometer,
Science 280, 1238 (1998). Amplifying quantum
signal with the single electron transistor, M.
Devoret and R. Schoelkopf, Science 19, 19
(2000). Radio Frequency single-electron
transistor, P. Wahlgreen, el al., J. Supercond.
12, 741 (1999). Radio-frequency single-electron
transistor Toward the shot-noise limit, A.
Aassime, et al., Appl. Phys. Lett. 79, 4031
(2001). SET and nanomechanics Sensitivity of a
micromechanical displacement sensor based on the
radio-frequency single electron transistor, M.
Blencowe and M. Wybourne, Appl. Phys. Lett. 77,
3845 (2000). They did not include the SET
backaction onto the nanomechanical
resonator. Intrinsic noise of a micromechanical
displacement detector based on the
radio-frequency single-electron transistor,Yong
Zhang and Miles P. Blencowe, J. Appl. Phys. 91,
4249 (2002). Quantum Measurement with
Nanomechanical Systems, K. Schwab, submitted to
the International Conference on Solid State
Implementations of Quantum Computing, Sydney,
Australia, January 2001. Here I estimatedthe back
action from the SET. A nanometre-scale
mechanical electrometer, A.N. Cleland, M.L.
Roukes, Nature 392, 160 (1998).
88
References
Quantum Effects in Mechanical Measurement Quantum
Measurement,Braginsky and Khalili, Cambride
University Press, 1992. On the detection of a
weak classical force coupled to a
quantum-mechanical oscillator. I. Issues of
principle, Caves, et al., Rev. Mod. Phys. 52,
341 (1980). Quantum Non-Demolition measurements
the route from toys to tools, V.B. Braginsky and
F. Ya. Khalili, Rev. Mod. Phys. 68, 1 (1996). On
the measurement of a weak classical force coupled
to a harmonic oscillator M. Boco and Roberto
Onofrio, Rev. Mod. Phys. 68, 755
(1996).  Scheme to probe the decoherence of a
macroscopic object, S. Bose, K. Jacobs, and P.
Knight, Phys. Rev. A 59, 3204 (1999).  Quantum
squeezing of mechanical motion for micron-sized
cantilevers, M.P. Blencowe, M. Wybourne, Physica
B 280, 555 (2000).  Schroedinger Cat
formation.. G. Berman, xxx.lanl.gov Mechanical
Lamb-shift analogue for the Cooper-pair box,
A.D. Armour, M.P. Blencowe, and K.C. Schwab, to
appear in Physica B from the proceedings of
Phonons 2001, held at Dartmouth. The noise in
gravitational-wave detectors and other
classical-force measurements is not influenced by
test-mass quantization, V.B. Braginsky, et al.,
xxx.lanl.gov, gr-qc/0109003 Dynamics of damped
cantilever, S. Rast, et al., Rev. Sci. Inst. 71,
2772 (2000). Quantized Thermal Transport-Freeze
Out to 1D D.E. Angelescu, M.C. Cross, and M.L.
Roukes, Superlattices and Microstructures 23,
(1998). Luis G.C. Rego and George Kirczenow,
Phys. Rev. Lett. 81, 232 (1998). Miles Blencowe,
Phys. Rev. B 59, 4992 (1999). Measurement of the
quantum of thermal conductance, K. Schwab, E.A.
Henriksen, J.M. Worlock M.L. Roukes, Nature
404, (2000). Thermal conductance through
discrete quantum channels, K. Schwab, W. Fon,
E.A. Henriksen, J.M. Worlock, M.L. Roukes,
Physica E 9, 60-68 (2001). Elastic wave
transmission at an abrubt junction in a thin
plate with the application to heat transport and
vibrations in mesoscopic systems, M.C. Cross and
Ron Lifshitz, Phys. Rev. B 64, 085324
(2001). Thermal conductance of nanostructured
phononic crystals, A.N. Cleland, D.R. Schmidt,
C.S. Yung, Phys. Rev. B 64, 172301
(2001). Yactocalorimetry phonon counting in
nanostructures, M.L. Roukes, Physica B 263, 1
(1999). by interaction with a Cooper pair box.
89
More References.
Cooper-Pair Box and Entanglement with Resonators
of various kinds Quantum Dynamics of a
Cooper-Pair Box Coupled to a Micromechanical
Resonator, A.D. Armour, M.P. Blencowe, and K.
Schwab, Phys. Rev. Lett. 88, 148301 (2002).
Coherent control of macroscopic quantum states
in a single-Cooper-pair box Y. Nakamura, et al.,
Nature 398, 786 (1999) Quantum state engineering
with Josephson-junction devices,
cond-mat/0011269, Yuriy Makhlin, Gerd Schoen,
Alexander Shnirman This reference is really an
excellent description of the cooper-pair
qubit. Superposition of two mesoscopically
distinct quantum states Coupling a Cooper-pair
box to a large superconducting island, F.
Marquardt and C. Bruder, Phys. Rev. B 63, 054514
(2001). Buisson and Hekking, cond-mat/0008275
90
Single electronics and Nanomechanics
100 nm SiN membrane
50 nm Au
Fabrication by Matt LaHaye and Alex Hutchinson
Tunnel Junctions and SET island
50 nm Al
91
How cold will they get?
Nano-electronic devices rarely ever get below
30mK due to the very weak coupling between
electrons and phonons. (See Roukes, et al., PRL,
(1985).)
Celect
Where W is the volume and S is the
electron-phonon coupling 2 109 W/m3/K5 for
Au. For example it will only take 10-15 W to
hold a 1mm3 of Au at 50mK with phonons at
T0. However, for a mechanical (phonon) device,
the connection to the bath is much stronger..
Coupled by 4 Sch-Roukes!
92
Thermal Circuit
Confidence in this estimate High See Matter
and Methods of Low Temperatures, Pobell
Confidence in this estimate High See Schwab, et
al. Nature, 404, (2000).
Thermal situation for metal on top of mechanical
resonator.
Confidence in this estimate probably totally
wrong (Re-p should diverge as dimensionality is
reduced. ldomgtl,w,h). See Roukes, PRL (1985).
93
Experimental Limits to Electrical and Mechanical
Noise Temperatures
Mechanical noise temperature of a 290nm thick,
3.9 mm wide, 260 mm long cantilever, no5kHz,
Q150,000. Notice saturation in TN at 100mK --
could be fm/hz1/2 vibrations limiting noise
temperature. (should not be a problem for MHz
resonators)
Electrical noise temperature of a 30nm thick, 2
mm wide, 4 mm long Au resistor. Measured with
ultra-low power dc SQUID setup and with extensive
filters to room temperature connections. Notice
saturation in noise temperature at 80mK.
Current best is TNlt30mK (J. Hanolka, et al.,
Caltech).
Mamin and Rugar, APL 79, 3358 (2001).
Schwab, et al, Physica E 9, 60 (2001).
94
Some Useful SET Approximations
Current through the SET, measured at Blockade
voltage VDSe/CS
Transfer function of SET
Spectral density of the current noise through the
SET (about half that of shot noise)
Spectral density of the SET island potential
fluctuations (this is where the back-action
comes from)
Both equations are for wltt, where tRJCS See
Korotkov, PRB (1994).
95
Single Electron Transistor
Criteria for operation Thermal for 50nm X
50nm junctions, C10-15 F, so T ltlt
1K Quantum For island to be in a well defined
number state dnltlt1 charging time, t
RtunnellingC from uncertainty, we know dE t gt
h rearranging we find,
96
SET Fabrication
  • Pattern with electron microscope
  • Evaporate Al island
  • Oxidized Al to form barriers
  • Evaporate leads to island
  • Junctions are typically 50nm X 50nm 10-16
    -10-15 F
  • Fulton and Dolan, PRL 59, 109 (1987).

97
Fancy SETs Josephson Electrometer
  • Zorin, Phys. Rev. Lett. 76, 4408 (1996).
  • Zorin, J. of Supercon. 12, 747 (1999).
  • Work with device in superconducting state
  • with Junction resistance RQ
  • And the environment seen by the device
  • Must be much lower than RQ
  • Advantages
  • Josephson tunneling is non-dissipative so island
    heating is not a problems
  • Voltage oscillations on the island are coherent
    and at the Josephson frequency
  • Deterministic
  • Monochromatic
  • Reduced amplitude of charge fluctuations
  • Sensitivity can be equal to that of normal state
    SET 1me/rtHz
  • Lower impedance can be easier to read-out with
    high frequency electronics
  • Disadvantages
  • Most carefully engineer junction resistance and
    environment

98
Josephson Electrometer Backaction
Charge oscillations of the island are at the
Josephson frequency (As opposed to white noise
from normal state SET)
With amplitude of e/C
Low frequency voltage oscillations of island from
Johnson noise of shunt
Improvement of factor of 20 over normal state SET.
Bottom line Total integrated noise power in both
cases is similar, difference is in spectral
distribution. Does this mean that we will be
limited only by the uncertainty principle of the
resonator mass?
99
Can we engineer the backaction?
Measure Here
Since the backaction of a Josephson electrometer
is dominated by a harmonic component at the
Josephson frequency, can we tune this to hit an
anti-resonance of the resonator? Then we will be
limited only by the white floor which is much
smaller. Can we take advantage of the coherent
tunneling to achieve parametric amplification?
Coupling to only one quadrature component of the
mechanical oscillation? Will it electrometer
SQUEEZE the resonator? Is there any effect at
w0 from mixing when wmwJ?
wJ
Backaction here
Dynamics of damped cantilever, S. Rast, et al.,
Rev. Sci. Inst. 71, 2772 (2000).
100
First LPS Nanomechanics
Silicon Nitride beams with Au electrodes 200 nm X
150 nm X 15 mm -gt 5 MHz Fabrication by Matt LaHaye
101
Thermal Motion of Resonator
f0 23MHz Q 104 T 4.2K XRMS 1.4 pm 60
XSQL B9T VRMS/rtHz 250 pVRMS /rtHz
Magneto-motive Readout Amorphous Silicon Nitride
resonator 8mm X 200nm X 150nm
102
rf SET Performance
Reflection Spectrum vs Gate voltage
1 MHz, 0.1 eRMS signal to gate
Recently demonstrated rf SET technique Charge
sensitivity 70 me/rtHz Bandwidth 50
MHz Carlos Sanchez
103
rf SET at LPS
Microfabricated microwave resonators
SET IV curves T20mK
LC-resonance at 1.3 GHz. Carlos Sanchez, Matt
LaHaye
104
SET Fabrication
Al-AlO-Al Tunnel Junctions
Single Electron Transistor
Carlos Sanchez (UMCP)
105
Sketch of Noise Analysis
106
DC Response of SETs
I-V curves for different VG
Modulation I-VG
107
Cooper-Pair Box
Coplanar Waveguide
Control Lines
Nb Capacitor
25 Turn Nb Inductor
108
Cooper-Pair Box
109
Nanomechanical Resonators
200 nm X 100 nm x 16-6 mm 50 nm of Au on 100 nm
of SiN Resonance of 10-100 MHz Matt LaHaye and
Alex Hutchinson
110
Coherent Single ElectronicsCooper-Pair Box
Ultra-small capacitance (lt10-15 F)
--------- charge basis is good QM
description Superconducting --------- follows
Josephson equations of motion
Vg
111
Quantum Effects in Mechanics
What behavior is possible???
  • Position Detection limited by the Uncertainty
    Principle (Force detection)
  • Energy quantization and freeze-out to the quantum
    ground state
  • Quantized energy and zero-point fluctuations
    Fock states and Lamb shifts
  • Superposition and Entangled states

..it all seems possible!
112
Schwab Group at LPS
  • Cooper-Pair Box Qubits
  • Exploration of coherent two-level electronic
    system qubit
  • - Single-shot readout
  • Nanomechanics
  • rf SET position detection-approaching the
    Standard Quantum Limit
  • Mesoscopic fluctuations with nano-mechanical
    detection
  • Coupling to Cooper-Pair Box-superpositions and
    coherent effects
  • Diamond NEMS (NRL and Cornell)
  • Ultra-sensitive cantilevers for MRFM (Ohio
    State-Caltech)
  • Nanofabrication for Atomic Physics
  • Surface traps for BEC (Univ. of Queensland)
  • GaAs devices for ion traps (Monroe-Univ. of
    Michigan)
  • Ultra-sensitive Superfluid gyroscopes
    (NASA/Goddard)
  • Using rf SET and nanostructures to read-out
    superfluid SQUIDs
  • Understanding limits of superfluid rotation
    detection

113
Mechanics and detection at the Quantum Limit
The Fundamental Quantum Condition
Uncertainty Principle leads to Standard quantum
limit for simple harmonic oscillator
See Braginsky, Khalili, Thorne, Quantum
Measurement
See Heffner, Proc. IRE 50, 1604
(1962). Giffard, Phys. Rev. D 14, 2478 (1976).
For continuous measurement including amplifier
back action
See C. Caves, et al., RMP 1982
114
Time Domain Experiments
T1.2K
104 cycles
digital scope
Free decay
TN
B
pulser
R
115
RF -SET Nanomechanics
100 mm
116
Recent Devices-RF SET coupled to Nanomechanics
117
Nanomechanics at the Quantum Limit
DilutionDemag Fridge
3He Fridge
Dilution Fridge
What refrigeration technology is necessary to get
to freezeout?
Freeze-out
118
Standard Quantum Limit
Measure average position of particle by two
consecutive measurements.
M
Before first measurement
After first measurement
Before second measurement
which minimizes when
119
Quantum Limit for Linear Amplifier
Ideal Detector
Linear Amplifier
See Heffner, Proc. IRE 50, 1604
(1962). Giffard, Phys. Rev. D 14, 2478 (1976). C.
Caves, et al., RMP 1982
120
Nanomechanical Noise Thermometry
Saturation does not seem to be from SET, but from
some other thermal source.
121
Recent SET results
VG
VDS
IDS
122
Mechanical detection of two-level systems
Forces are at the 10-18-10-21 Nt range
Scanned Magnetic Resonance Tool
F
Resonant Spins
Cantilever with magnet
Experiments of Rugar and Mamin and Hammel,
Pelekov, and Roukes
Quantum Limits of the Micro-world following the
dynamics of single engineered quantum systems
123
RFSET
  • Operating frequency 1.5GHz
  • Bandwidth 30MHz
  • Sensitivity 8x 10-6 e/(Hz)1/2

124
staircase
  • 1-e periodic at high Vds
  • Quasi particle poisoned 2-e staircase at low Vds
  • Worked with dc SET to avoid back action

125
Spectroscopy
126
?t
Tr
Refcond-mat/0305433, Duty et. al.
127
Summary
  • Spectroscopy of the box
  • Coherent oscillation in the box
  • T1 350ns
  • Future work
  • Measure T2,T1
  • Single shot measurement of charge states

128
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129
?t
Not for presentation
Tr
130
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131
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132
CPB-rf SSET Experiments
CPB
F
CPB-Gate
SET-Gate
SET
133
Traps for BEC Univ. of Queensland
13mm thick Al carried 3A
134
Traps for Ions Univ. of Michigan
Epitaxial doped GaAs/AlGaAs
135
Sympathetic Cooling of Mechanical Mode
Rate at which quanta enter resonator from thermal
bath
Rate at which quanta are exchanged between
resonator and ion
Rate at which quanta are removed from ion
Quantum-limited cooling and detection of
radio-frequency oscillations by laser-cooled
ions, D. J. Heinzen and D. J. Wineland, Phys.
Rev. B 42, 2977 (1990).
136
from The Onion
137
Whats nano got to do with it?
t
l
Maximize E/r ? Diamond See Dissipation in
Nanocrystaline Diamond Nanomechanical
Resonators, Hutchinson, et al. APL, Feb. 2004.
138
Advanced Materials Diamond (NRL, Cornell, LPS)
E1TPa
Hutchinson, et al, APL 84, 972 (2004)
139
Back-action in an optical Interferometer
Fixed mirror
Pondermotive noise from radiation pressure
Shot noise of photon current
140
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141
Isolating the mechanics from dissipation in the
SET
.
Q
1 pW
142
Outline
  • Intro and motivation
  • Quantum limit of continuous position measurement
  • Issues of principle
  • Experimental approach - rf SSET coupled to a 20
    MHz nanomechanical resonator
  • Our recent results
  • Approach to within 4.3 of Uncertainty Principle
  • Freeze-out to T 56 mK, NTH 58
  • Beginning to Feedback cool 250mK -gt 70mK
  • Future directions
  • Feedback cooling to ground state and quantum
    squeezing
  • Detection and freeze-out of higher order modes
  • Resonator coupled to CPB Quantum
    Electro-Mechanics

143
Improvements to fabrication
Use dry process to undercut no membrane Move
all photo lithography to foundry saves 4 layers
of litho
SiN
Au
Si
144
SET Primer
Ids
Vds
IDS
nCgVg/e
145
Superconducting SET
146
rf SET-Ideal Amplifier for Nanomechanics
Impedance of SET is monitored by measuring
microwave reflections Microwave tank transforms
50kW impedance to 50W
Charge sensitivity 5 m e/ rtHz Band
width 75 MHz 1/f knee 10,000 Hz
Schoelkopf, et al, Science 280, 1238
(1998). Wahlgreen, el al, J. Supercond. 12, 741
(1999).
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