Diapositive%201

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Decoherence of Josephson Qubits
-during free evolution -during driven evolution
TowardsQND readout
A -meter
G. Ithier et al. Decoherence in a quantum bit
superconducting circuit, PRB 2005
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DECOHERENCE DURING FREE EVOLUTION
dephasing
DEPHASING
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Decoherence sources in the quantronium circuit
d
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Decoherence in the Quantronium
d
Relaxation
if balanced junctions !
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Model for dephasing charge and phase noise
d
DNg ou Dd
(linear coupling)
Spectral density
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Relaxation of the Quantronium
P0
T10.5µs
T1 0.3-2 ms
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Free evolution coherence time T2 Ramsey
interferences
Ramsey interferences reveal decoherence of
free evolution during the delay
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Characterizing dephasing 1) decay of Ramsey
fringes
best ones
nRF 16409.50 MHz
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Fit with the linked cluster expansion
static approximation for noise during each pulse
sequence ( Makhlin Shnirman, Paladino, Falci)
typical sample
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Comparing envelope fits
static approximation ( Makhlin Shnirman,
Paladino, Falci)
Simple exponential
gaussian noise
500 ns
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Coherence away from optimal point
P0 Ng1/2 d0
Ramsey oscillations
d0
Ng1/2
time
100 ns
Ng
d
d
Ng
Delay between p/2 pulses (ns)
Delay between p/2 pulses (ns)
best coherence at optimal point
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Characterizing dephasing 2) phase detuning
pulses
Dt1
At optimal point
p/2X
p/2X
Dt2
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Characterizing dephasing 2) charge detuning
pulses
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Characterizing decoherence 3) resonance linewidth
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5) Probing the dynamics spin echo experiments
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Direct mapping of echo amplitude
low frequency noise
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Echo decay away from optimal point
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Closer look at charge and phase spectral
densities
Phase noise
Charge noise
Partly external
Cut-off at .5 MHz !!
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Decoherence in phase Qubits (at UCSB)
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Level-crossings with two level systems
Martinis et al (2003)
spectroscopy
p1
w/2p (GHz)
Oxyde? Tunnel junction? Relation to charge
noise?
2 level systems couple to qubit!
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Decoherence and Materials
Theory Martin et al Yu UCSB group
Wheres the problem?
Two Level States (TLS)
Dielectric loss in x-overs
TLS in tunnel barrier
a-Al2O3
Ime/Ree d 1/Q
future a-
New design
xtal Al2O3
ltV2gt1/2 V
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Spectroscopy
2
6
P1 grayscale
saturate
Imw
few TLS resonances
Ip
meas.
Microwave frequency (GHz)
w10(I)
Bias current I (au)
T1 still short 100-150 ns
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New Qubit design
SiNx capacitor
60 ?m
(loss of SiNx limits T1)
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Rabi oscillations
P1 (probability)
tRabi (ns)
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New junction technology ?
II Epitaxial Materials
(NIST)
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DECOHERENCE IN FLUX QUBITS At NEC
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Relaxation T1 measurement
p
p 4ns
readout pulse
delay
initialization to ground state is always better
than 90 ? relaxation dominant ? classical noise
is not important at qubit frequency
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T1 vs f
p 4ns
delay
readout pulse
??
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?1 vs ?E Comparison of two samples
sample5
sample3
Random high-frequency peaks. Broad low-frequency
structure and high-frequency floor.
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?1 vs DE (sample3)
positive and negative side coincide
assuming flux noise
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Dephasing T2Ramsey, T2echo measurement (sample5)
correspond to detuning
Ramsey interference
p/22ns
p/2
readout pulse
t
spin echo
p/2
p 4ns
p/22ns
readout pulse
t/2
t/2
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T2 vs f, vs Ib (sample5)
IbIb
ff
Notice fitted with exponential decay
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T1 and T2echo at IbIb, ff (sample5)
T1545?16ns
Echo decay time is limited by relaxation
Pure dephasing from high frequency noise (gtMHz)
is negligible
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Echo at IbIb, f?f
assuming 1/f flux noise
do not fit
does not fit
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Ramsey
ExpGauss
Exp
Extract flux noise
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Ramsey signal
Ib0
Ib-0.2
Also exponential decay (more or less)
Ib-0.4
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Estimation of Ib noise amplitude
Increase Ib-Ib ?Introduce Ib noise coupling
relaxation
dephasing assuming ohmic noise (cf. Yu.
Makhlin PRL92, 178301 (2004))
From the fitting
For T0.1K, modeled environment
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Decoherence of a qubit
-during free evolution -during driven
evolution -at readout
A -meter
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Decoherence driven evolution versus free
evolution
Bloch-Redfield description
Free
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Spin locking
Determination of T1
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Determination of T2
Decay of Rabi oscillations with Rabi frequency
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Decay of Rabi oscillations with frequency
T2 480 ns
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decoherence in the rotating frame ?
lab frame
Ramsey decay
T2300ns
rotating frame
T2480 ns
Conclusion more robust qubit encoding in the
rotating frame, but limited use.
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CONCLUSIONS
Framework for understanding decoherence large
decoherence Coherence times up to 500
ns Microscopic decoherence sources
?? Decoherence can be fought QND readout
achievable quantum computing applications present
ly beyond reach
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The work on
the
Quantronium
dc
gate
dc
gate
µw
qp
box
trap
A -meter
readout
junction
1µm
SPEC
Appl. Physics
YALE
G. ITHIER E. COLLIN N. BOULANT D. VION P. ORFILA
P. SENAT P. JOYEZ P. MEESON D. ESTEVE
I. SIDDIQI F. PIERRE E. BOAKNIN L. FRUNZIO
A. SHNIRMAN G. SCHOEN Y. MAKHLIN F. CHIARELLO
R. VIJAY C. RIGETTI M. METCALFE M. DEVORET
Karlsruhe Landau
Roma
SQUBIT
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NEC / Japan
Thanks to
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Towards QND readout at optimal point
flux qubit
charge qubit
charge-phase qubit
Quantum capacitance
0
C/CJ
1
SQUID inductance
quantum capacitance
readout junction inductance
TU Delft
Yale, Saclay
Chalmers, Helsinki
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dc versus ac readout in the quantronium
PULSE IN
PULSE OUT
rf readout (M. Devoret, Yale)
U
d
RF pulse
dc pulse
? switching
? d dynamics in anharmonic potential

• simple, but
• -fidelity 40
• qubit reset NOT QND

more complex, but -better fidelity ? -no
reset possibly QND
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Towards non destructive readout at optimal
point with an AC drive
M. Devoret team at Yale I. Siddiqi et al., (2004)
Similar dispersive methods developed for other
qubits
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M. Devoret team at Yale I. Siddiqi et al., (2004)
The Josephson Bifurcation Amplifier
Enhanced
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Quantronium JBA SETUP
NO bifurcation
300 K
4 K
0.6 K
Quantronium from Yale
30 mK
bifurcation
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Rabi oscillations with the JBA
JBA pulse
Contrast 50

(Saclay exprt)
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Quantum Non Demolition ? read twice
gate
JBA readout
100ns
p
125ns
20ns
5ns
10ns
40ns
100ns
A
B
p
correlations
Note results for flux-qubit now available
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Dispersive readout of the flux qubit
A. Lupascu et al. TU DELFT
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Activation rates for different detuning values
F 775 MHz Fres822 MHz
Iac,bifurcation2
slopeudyn/(kT)
Thy M. Dykman
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Activation rates for different detuning values
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Optimal qubit manipulation and readout
87
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Rabi oscillations with optimal settings
Dt length of MW pulse
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Ramsey oscillations with optimal settings
Rabi oscillation
Ramsey frequency vs detuning
Ramsey wge-wmw 69 MHz
Relatively strong low frequency fluctuations
visible in the drift of the Ramsey frequency.
QND data analysis in progress
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Experiments in Cavity QED with Superconducting
Circuits
Rob Schoelkopf
Depts. of Applied Physics Physics Yale
University
expt. Andreas Wallraff David Schuster Luigi
Frunzio
theory Steve Girvin Alexandre Blais Ren-Shou
Huang
And discussions w/ J. Zmuidzinas M. Devoret
Merci to D. Esteve co. for assistance!
Packard Foundation
Keck Foundation
Funding
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A Circuit Analog for Cavity QED
2g vacuum Rabi freq.
k cavity decay rate
g transverse decay rate
out
L l 2.5 cm
transmissionline cavity
Cooper-pair box atom
10 mm
10 GHz in
Blais, Huang, Wallraff, Girvin RS,
cond-mat/0402216 to appear in PRA
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Cavity QED with a Cooper pair box first
dispersive readout
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Dressed Artificial Atom Resonant Case
? T
2g
T
1
vacuum Rabi splitting
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Rabi Oscillations of Qubit
Prf 6 dB
Prf 0 dB
Prf 18 dB
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Coherence time measurements with 2 pulse Ramsey
sequence