Qubit-Coupled Nanomechanics junho suh, michael roukes - caltech Quantum Measurement and Metrology with Solid State Devices keith schwab - caltech & cornell pierre echternach - j p l PBH, Germany 5 Nov. 2009 experiments performed at caltech with: Matt LaHaye ” Syracuse University
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Qubit-Coupled Nanomechanics
junho suh, michael roukes - caltech
Quantum Measurement and Metrology with Solid State Devices
keith schwab - caltech & cornell
pierre echternach - j p l
PBH, Germany 5 Nov. 2009
experiments performed at caltech with:
Matt LaHaye ” Syracuse University
Atoms, Ions, SpinsCasimir Physics
m
(Caltech, Cornell, JPL) NEMS/CPB
(Cornell/Caltech) SMR/NEMS
(Delft):DC-SQUID/NEMS
(Maryland) SSET/NEMS
(JILA): APC/NEMS, SMR/NEMS
(UCSB) SET/NEMS
(UCSB)
(MIT & LIGO)
(Caltech, Max Planck Institute)
(Yale) (Vienna)
(Oregon)
mechanical structures in the quantum regime
Nanoelectromechanical Systems (NEMS)
Optomechanical
Systems
And many others …
(Dartmouth/ Padova) (IBM Almaden)
Atoms, Ions, SpinsCasimir Physics
m
(Caltech, Cornell, JPL) NEMS/CPB
(Cornell/Caltech) SMR/NEMS
(Delft):DC-SQUID/NEMS
(Maryland) SSET/NEMS
(JILA): APC/NEMS, SMR/NEMS
(UCSB) SET/NEMS
(UCSB)
(MIT & LIGO)
(Caltech, Max Planck Institute)
(Yale) (Vienna)
(Oregon)
mechanical structures in the quantum regime
Nanoelectromechanical Systems (NEMS)
Optomechanical
Systems
Interesting review from a few years ago: K. Schwab and Michael Roukes,
Physics Today July 2005
More recently: special issue of the New Journal of Physics on mechanical
systems approaching the quantum regime. September 2008
Gordon Conference 2008 &2010: Mechanical Systems in the Quantum Regime
And many others …
(Dartmouth/ Padova) (IBM Almaden)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany - 05 Nov. 20094
Ideal characteristics: Small mass,
“ Typ. quality factors ~ 104-105,
but demonstrated >106
“ Zero-point motion
“ Energy-level spacing
zpx / 2 ~ 40 fmm
Mo Li, Hong Tang, Michael Roukes, 2007
Estimate for SiC resonator,
.6m x .4m x .07m
Mass ~ 50 fg, f0 ~ 127 MHz
ο Bω k T For 1 GHz resonator
At mK temperatures
Huang, Roukes, 2003
Attainable with dilution fridge.Schwab 2008
Orders of magnitude larger than gram- or kg-scale oscillators
May portend long coherence and
relaxation times (~ sec’s)
high frequency, low dissipation
‚ultimate limit of NEMS is in the quantum regime‛ ” Roukes (2001)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
approaching the quantum limit of NEMS with an RFSET
“ The radio-frequency single-electron transistor (RFSET) as
a quantum-limited displacement detector (proposed by
Blencowe and Wybourne, APL 2000)
Demonstrated sensitivity using superconducting SET (SSET) near
(~4x) the quantum limit for continuous linear detection. SSET a
near-ideal linear detector: =15 /2
Observation of low nanoresonator thermal occupation Nth= KT/ (~25).
Observed SSET quantum back-action on the NEMS; measured asymmetry
In SSET noise spectrum; performed back-action cooling of NEMS
“Potential for interesting future experiments
Gate of SET
NR GateSSET
NR
1m
VNR
M. LaHaye, O. Buu, B. Camarota,
K. Schwab, Science 2004
A. Naik, O. Buu, M. LaHaye, A. Armour, M.
Blencowe, A. Clerk, K. Schwab, Nature 2006
(Ground-state cooling) A. Hopkins, K. Jacobs, S. Habib & K. Schwab, PRB (2003).
(Squeezing) R. Ruskov, A. Korotkov & K. Schwab, IEEE Trans. Nano., (2005).
(Micro-maser analog) D. Rodrigues, J. imbers & A. Armour (2007).
VNR
VNR
19.7 MHz Resonator
20 MHz
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
approaching the quantum limit of NEMS with an RFSET
Demonstrated sensitivity using superconducting SET (SSET) near
(~4x) the quantum limit for continuous linear detection. SSET a
near-ideal linear detector: =15 /2
Observation of low nanoresonator thermal occupation Nth= KT/ (~25).
Observed SSET quantum back-action on the NEMS; measured asymmetry
In SSET noise spectrum; performed back-action cooling of NEMS
“ Other linear displacement detectors developed
Gate of SET
NR GateSSET
NR
1m
VNR
M. LaHaye, O. Buu, B. Camarota,
K. Schwab, Science 2004
A. Naik, O. Buu, M. LaHaye, A. Armour, M.
Blencowe, A. Clerk, K. Schwab, Nature 2006
(Normal SET) R. Knobel & A. Cleland, Nature 424 , 291 (2003).
(APC) N. Flowers-Jacobs, D. Schmidt & K. Lehnert, PRL 98, 096804 (2007)
(DC SQUID) S. Etaki et al., Nature Physics 4, 785 (2008)
VNR
VNR
19.7 MHz Resonator
20 MHz
“ The radio-frequency single-electron transistor (RFSET) as
a quantum-limited displacement detector (proposed by
Blencowe and Wybourne, APL 2000)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany - 05 Nov. 2009
Notes: Model convolved with 0.1 CPrms charge noise, and includes thermal population of CPB excited state
dispersive interaction: measurement vs. model
Note: Magnetic field applied on top of ~ 100 G οJJ πEE Φ/Φcosmax,
Flux Periodicity:Applied Magnetic Field (A.U.)
f N
EM
S(H
z)
-200
-100
Vg (mV)-10 -5 0 5 10
0
2
3
1
4
ng (2e)
Flux (A.U.)
f N
EM
S(H
z)
-1.0 -0.5 0.0 0.5 1.0
-200
-100
0Model
Exp. 65
fN
EM
S(H
z)
-1.0 -0.5 0.0 0.5 1.0
-15
-10
-5
0
5
10
15
-250
-200
-150
-100
-50
0
Vg
(mV
)
1 2
5
Flux (o)-0.5 0.0 0.5
0.0
-200
-150
-100
-50
fN
EM
S(H
z)
3 4
0
6-0.5
0.5
1515
3 41 2
5 6
With coupling strength, proposals suggest that it should be possible to
implement single qubit ‚lasing‛, ground-state cooling, squeezing of NEMS, (Lasing) J. Hauss,, A. Federov, C. Hutter, A. Shnirman, G. Schon, PRL. 100, 037003 (2008)
(Ground-state Cooling) I. Martin, A. Shnirman, L. Tian, P. Zoller, Phys. Rev. B 69, 125339 (2004).
(Squeezing) P. Rabl,, A. Shnirman, P. Zoller. Phys. Rev. B 70, 205304 (2004).
From M.D. LaHaye et al., Nature 459 , 960 (2009).
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
DEVICE SCHEMATIC
CPB ENERGY BAND DIAGRAM
APPLY MICROWAVES THAT ARE RESONANT
WITH CPB SPLITTING.
EXPECTED NEMS FREQUENCY SHIFT
NEMS-based spectroscopy of CPB
f N
EM
S(H
z)
EJ/h = 13.0 GHz
p-=p+
13 GHz applied
0 0.2 0.4 0.6 0.8 1
-400
-300
-200
-100
0
no microwaves
13 GHzd/2=13 GHz
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
10
20
30 C+(EJ,Ng)
C-(EJ,Ng)
ng (2e)
E c
pb/h
(GH
z)
EJ/h= 13 GHz
CPB
Resonator
CNR
d
Gate
VNR
Vg(t)=Vg0+Vcosdt
d=(E/)
Vg(t)
ng (2e)
AVERAGE NEMS FREQUENCY SHIFT
Δ Δ Δ 0NEMS NEMS NEMSf p f p f
p- = p+ as given by Bloch equations
Δ ΔNEMS NEMSf f
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
DEVICE SCHEMATIC
CPB ENERGY BAND DIAGRAM
NEMS-based spectroscopy of CPB
d/2=13 GHz
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
10
20
30 C+(EJ,Ng)
C-(EJ,Ng)
E c
pb/h
(GH
z)
EJ /h= 9 GHz
13 GHZ
0 0.2 0.4 0.6 0.8 1-600
-500
-400
-300
-200
-100
0
f N
EM
S(H
z)
9 GHz applied
no microwavesEJ/h = 9.0 GHz
p-=p+
APPLY MICROWAVES THAT ARE RESONANT
WITH CPB SPLITTING.
CPB
Resonator
CNR
d
Gate
VNR
Vg(t)=Vg0+Vcosdt
d=(E/)
Vg(t)
ng (2e)
ng (2e)
EXPECTED NEMS FREQUENCY SHIFT
AVERAGE NEMS FREQUENCY SHIFT
Δ Δ Δ 0NEMS NEMS NEMSf p f p f
p- = p+ as given by Bloch equations
Δ ΔNEMS NEMSf f
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
DEVICE SCHEMATIC
CPB ENERGY BAND DIAGRAM
NEMS-based spectroscopy of CPB
d/2=13 GHz
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
10
20
30+(EJ,Ng)
-(EJ,Ng)
E c
pb/h
(GH
z)
13 GHZ
0 0.2 0.4 0.6 0.8 1-600
-500
-400
-300
-200
-100
0
f N
EM
S(H
z)
9 GHz applied
no microwavesEJ/h = 9.0 GHz
p-=p+
(o)
ng
(2e)
-0.5 0 0.5
0
0.2
0.4
0.6
0.8
1 -1000
-800
-600
-400
-200
fNEMS
(Hz)EJ /h= 9 GHz
CPB
Resonator
CNR
d
Gate
VNR
Vg(t)=Vg0+Vcosdt
d=(E/)
Vg(t)
C
CMax EJ
ng (2e)
ng (2e)
EXPECTED NEMS FREQUENCY SHIFT
EXPECTED NEMS FREQUENCY SHIFT
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
Flux (A.U.)
Vg (
mV
)
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U..)
Vg (
mV
)
Microwave Frequency: 20 GHz
-5.79 -5.78 -5.77 -5.76 -5.75 -5.74 -5.73
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 17 GHz
-5.76 -5.75 -5.74 -5.73 -5.72 -5.71 -5.7
-12
-10
-8
-6
-4
-2
0-600
-500
-400
-300
-200
-100
0
100
200
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 16 GHz
-5.74 -5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-12
-10
-8
-6
-4
-2
0
2
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 14.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-12
-10
-8
-6
-4
-2
0
2-700
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 13.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-6
-4
-2
0
2
4
6
8-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 12.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-28
-26
-24
-22
-20
-18
-16
-14
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
increasing microwave frequency
EJ = EJ,max 10.5 GHz 12.5 GHz 13.5 GHz
14.5 GHz 16.0 GHz 17.0 GHz 20.0 GHz
Flux (A.U.)
Vg (
mV
)
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
MW OFF EJ = EJ,max
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
Flux (A.U.)
Vg (
mV
)
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U..)
Vg (
mV
)
Microwave Frequency: 20 GHz
-5.79 -5.78 -5.77 -5.76 -5.75 -5.74 -5.73
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 17 GHz
-5.76 -5.75 -5.74 -5.73 -5.72 -5.71 -5.7
-12
-10
-8
-6
-4
-2
0-600
-500
-400
-300
-200
-100
0
100
200
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 16 GHz
-5.74 -5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-12
-10
-8
-6
-4
-2
0
2
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 14.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-12
-10
-8
-6
-4
-2
0
2-700
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 13.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-6
-4
-2
0
2
4
6
8-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
Flux (A.U.)
Vg (
mV
)
Microwave Frequency: 12.5 GHz
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68
-28
-26
-24
-22
-20
-18
-16
-14
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
increasing microwave frequency
For each value of EJ
Fit the data to
0
5
10
15
20
0.0 0.04 0.08 0.12 0.16 0.20
|Vg /18.7| (2e)
Mic
row
ave F
requency
(G
Hz)
2 2Δ (8 Δ )μ C g Jhf E E n E
10.5 GHz 12.5 GHz 13.5 GHz
14.5 GHz 16.0 GHz 17.0 GHz 20.0 GHz
2|Vg|
|Δ | | .5 |g gn n Wheremax 0cos( Φ /Φ )J JE E πand
13 14 GHz C
E / h and [0,9,10] GHzJE / h ~
max 12.5 13.5GHzJ E / h ~
EJ = EJ,max
Flux (A.U.)
Vg (
mV
)
-5.73 -5.72 -5.71 -5.7 -5.69 -5.68 -5.67
-24
-22
-20
-18
-16
-14
-12
-10
-600
-500
-400
-300
-200
-100
0
fNEMS
(Hz)
MW OFF EJ = EJ,max
From M.D. LaHaye et al., Nature 459 , 960 (2009).
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
NEMS coupled to strongly-driven CPBQubit Landau-Zener interference: see Sillanpaa et al., PRL 96 (2006), Oliver et al., Science 310 (2005) ,
Izmalkov et al., PRL (2008), Sun et al., APL (2009). Similar multi-photon transitions: see Wilson et al., PRL 98 (2007)
ng0
CPB ENERGY BANDS IN ng-SPACE
nRFnRF
Apply periodic modulation ng to CPB gate large enough to sweep CPB through charge degeneracy
EJ
slope~gC
n8Eng(t) = ngo+ nRFsin(RFt)
CPBE
CPBE
JE
RFω
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
NEMS coupled to strongly-driven CPB
ng0
CPB ENERGY BANDS IN ng-SPACE
nRFnRF
Starting in ground state , as approach degeneracy, probability PLZ for CPB to tunnel from to
EJ
)2
exp(2
ν
EπP J
LZ
EnergyVariation rate
RFRFCn8E~ ων
CPBE
CPBE
ng(t) = ngo+ nRFsin(RFt)
Qubit Landau-Zener interference: see Sillanpaa et al., PRL 96 (2006), Oliver et al., Science 310 (2005) ,
Izmalkov et al., PRL (2008), Sun et al., APL (2009). Similar multi-photon transitions: see Wilson et al., PRL 98 (2007)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
NEMS coupled to strongly-driven CPB
ng0
CPB ENERGY BANDS IN ng-SPACE
nRFnRF
After crossing degeneracy, time-dependent phase (t) develops in wave function between and
Wave Function
CPBE
CPBE
ΨΨΨ (t)-ie(t) φ
t
gCPB ))(t'(nΔEdt'1
(t)φ
CPBCPBCPB EEEΔ
Probability Amplitudes
After tunneling
LZPiCΨ
LZPC 1Ψ
)2
exp(2
ν
EπP J
LZ
Ψ
Ψ
Qubit Landau-Zener interference: see Sillanpaa et al., PRL 96 (2006), Oliver et al., Science 310 (2005) ,
Izmalkov et al., PRL (2008), Sun et al., APL (2009). Similar multi-photon transitions: see Wilson et al., PRL 98 (2007)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
NEMS coupled to strongly-driven CPB
ng0
nRFnRF
Return swing: degeneracy crossed, probability for LZ tunneling to occur, interference between tunneling events
)2
exp(2
ν
EπP J
LZ
CPBE
CPBE
Wave Function
Amplitudes
)cos(2 /2e /2-i φPLZ
φ
)2/cos()1(2 φPPi LZLZ
t
gCPB ))(t'(nΔEdt'1
φ
Phase-developed between
first and second LZ events
CPB ENERGY BANDS IN ng-SPACE
CPBCPBCPB EEEΔ
Qubit Landau-Zener interference: see Sillanpaa et al., PRL 96 (2006), Oliver et al., Science 310 (2005) ,
Izmalkov et al., PRL (2008), Sun et al., APL (2009). Similar multi-photon transitions: see Wilson et al., PRL 98 (2007)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
NEMS coupled to strongly-driven CPB
ng0
nRFnRF
After full cycle: if CPB coherence time is longer than cycle period, oscillations in excited state probability with
Probability to
be in
CPBE
CPBE
))cos(1)(1(2 φPP LZLZ
t
gCPB ))(t'(nΔEdt'1
φ
Phase-developed between
first and second LZ events
CPB ENERGY BANDS IN ng-SPACE
CPBCPBCPB EEEΔ
ng(t) = ngo+ nRFsin(RFt)
Qubit Landau-Zener interference: see Sillanpaa et al., PRL 96 (2006), Oliver et al., Science 310 (2005) ,
Izmalkov et al., PRL (2008), Sun et al., APL (2009). Similar multi-photon transitions: see Wilson et al., PRL 98 (2007)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
Vcpb
(mV)
V (
V)
-10.0 -8.0 -6.0 -4.0 -2.0
0.5
1.0
1.5
2.0
2.5
-400 -200 0 200 400 600
NR/2 (Hz)
NEMS as a probe of LZ interferometry
Nanomechanical measurement of LZ interference
t
gCPB ))(t'(nΔEdt'1
φ
Function of ,g0V RFω,RFV
Modulate the CPB gate with large RF
excitation VRF, and track NEMS frequency
shift as a function of Vg0 and VRF
CPB Excited state becomes populated,
changing sign of NEMS frequency shift
Vg0 (mV)GHz0.42/ πωRF
VRF
(Volts)
From M.D. LaHaye et al., Nature 459 , 960 (2009).
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
Vcpb
(mV)
V (
V)
-3
-4
-3-4
-10.0 -8.0 -6.0 -4.0 -2.0
0.5
1.0
1.5
2.0
2.5
-400 -200 0 200 400 600
NR/2 (Hz)
Nanomechanical measurement of LZ interference
t
gCPB ))(t'(nΔEdt'1
φ
Function of ,g0V RFω,RFV
CPB Excited state becomes populated,
changing sign of NEMS frequency shift
Vg0 (mV)
Modulate the CPB gate with large RF
excitation VRF, and track NEMS frequency
shift as a function of Vg0 and VRF
GHz0.42/ πωRF
VRF
(Volts)
NEMS as a probe of LZ interferometry
‚Constructive‛ interference occurs at Vg0 where
= 2n (intersection of black lines in plot ).
))cos(1)(1(2 φPPP LZLZ
Parameters used for contour overlay:
Ec = 15 GHz, Ej=13 GHz
From M.D. LaHaye et al., Nature 459 , 960 (2009).
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
Vcpb
(mV)
V (
V)
-3-4
-3
-4
-8.0 -6.0 -4.0 -2.0 0.0
0.5
1
1.5
2
2.5
-500 0 500 1000 1500
NR/2 (Hz)
-8.0 -6.0 -4.0 -2.0 0.0
0
1000
2000
3000
4000
5000
/2=4.00 GHz
4.83 GHz
5.66 GHz
6.50 GHz
Vcpb
4.0 5.0 6.0 7.0
0.06
0.08
0.10
0.12
NEMS coupled to strongly-driven CPB
Vg0 (mV) GHz5.62
π
ωRF
ng0 conversion: 18.7 mV per 2e
VRF
(Volts)
ng0 (2e)
f N
R(H
z)
ExpectedFringe
spacing:Δ g0 RF
C
n ω4E
From fit
EC/h = 14.9 .6 GHz
ng0
(2e)
RF/2 (GHz)
LZ Fringes at constant VRFEstimate of EC from LZ interference
Fit to straightLine thru origin
ng0
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
-
58.470 58.475 58.480 58.485
5
10
15
20
25
30
35
Frequency (MHz)
Am
plit
ud
e (
V)
58.470 58.475 58.480
-1
0
1
2
Frequency (MHz)
Ph
ase
(R
ad
.)
Off Degeneracy
On Degeneracy1.6 kHz
T ~ 130 mK
VNR= 15 V
prospects for strong dispersive coupling limit
Demonstrated fNEMS NEMS/2
With conservative improvements to sample
geometry, should achieve fNEMS ~ 100’s kHz
Definition of strong coupling limit: Dispersive
interaction exceeds qubit and NEMS linewidth
2
[ , ]2 2
NEMS CPB
J
γ γλ
πE π π
Present Sample: NEMS Linewidth
Present Sample: CPB Linewidth
Present sample: CPB/2fNEMS
However, there is significant room to improve,
e.g. in circuit QED, CPB/2 1 MHz
hN
E N
CPB
)12(
Δ
NEMSfΔ
e.g. see Wallraff et al., Nature 431 (2004)
Quantum Measurement and Metrology with Solid State Devices PBH, Germany ” 05 Nov. 2009
prospects for dispersive CPB-NEMS entangled states