Upload
katrina-hampton
View
215
Download
1
Embed Size (px)
Citation preview
Two Level Systems and Kondo-like traps as possible sources of
decoherence in superconducting qubits
Lara Faoro and Lev Ioffe
Rutgers University (USA)
Outline
• Decoherence in superconducting qubit [ experimental state of the art ]:• low frequency noise (1/f noise)• high frequency noise (f noise)
• We discuss two possible microscopic mechanisms for the fluctuators• weakly interacting quantum Two Level Systems (TLSs)• environment made by Kondo-like traps
• TLSs model: • significant source of noise• detailed characteristics of the noise power spectrum are in a qualitative and quantitative disagreement with the data
• Kondo-like traps model:• significant source of noise• agreement with most features observed in the experiments
What are the sources of noise?
There are several experiments in different frequency regimes butthe dominant source of noise is yet to be identified!
Electromagnetic fluctuationsof the circuit (gaussian)
Discrete noise due tofluctuating background charges (BC)trapped in the substrate or in thejunction
S
?
1
Experimental picture ofthe noise power spectrum
Zimmerli et al. 1992Visscher et al. 1995 Zorin et al. 1996 Kenyon et al. 2000Nakamura et al. 2001Astafiev et al. 2004 Wellstood et al. 2004
T
Origin of both types of noise are the same ?
Low frequency noise ( 1/f )
• 1/f spectrum up to frequency ~ 100-1000 Hz. [ where is the upper cut-off ??? ] The intensity is in the range of at f=10Hz
• some samples clearly produce a telegraph noise but 1/f spectrum points to numerous charges participating in generating the noise.
• This noise dominates and it is greatly reduced by echo technique.
Hze43 1010
2T
• - Temperature dependence of the noise 2T
S
high frequency noise ( f )
Theoretical analysis
Upper level: use a proper model to study decoherence. “fluctuators model” and not spin boson model Paladino, Faoro, Falci and Fazio (2002) Galperin, Altshuler, Shantsev (2003)
Lower level: understanding which is the microscopic mechanism of decoherence that originate the fluctuators Faoro, Bergli, Altshuler and Galperin (2004)
Faoro and Ioffe (2005)
Quantum TLSs modelxzTLS tEH
4322
1010
de
tt,EP with
eVcm3
2010
i
zii
i ij ij
iijiijjiint pp̂
r
p̂r̂p̂r̂p̂p̂H
34
3
dep
The effective strength of the interactions is controlled by and it is always very weak.
2p
• Many TLSs interacts via dipole-dipole interactions:
23
3
2 prdEP
r
pEE ji
• interaction with low energy phonons T>100 mk
Relaxations for TLSs
Dipole and qubit interaction
L
pVCQ
Q
EpV g
nmL 3
nmL 300
tiggq eQtQdtS 0
iiizii deppp̂
i
tiiz
iz etdtG 0
ixi
izi
iz sincos 22
iii
i
ii
i
ii
tEE
E
tsinθ
E
Eθcos
Each dipole induces a change in the island potential or in the gate charge
i.e.
barrier
substrate
Charge Noise Power Spectrum:
Rotated basis:
+++
---
Q
Dephasing rates for the dipoles
i
ixi
izii
effint sincosthH
ij j
jijci Ecoshcoskh
222 1
Tp
2pure dephasing:
The weak interaction• causes a width in each TLS• at low frequency some of the TLSs become classical
Effective electric field
34
3
ij
jijiijjiij r
pr̂pr̂ppk
N.B: density of thermally activated TLSs enough (Continuum)
T 310
Relaxation rates for the dipoles
Tp
sin ii
2221
jiijj ji
i sinsinkEE
222
221
Fermi Golden Rule
0 ji EE
But in presence of large disorder, some of TLSs:
These dipoles become classical and will be responsible for 1/f noise
qS at high frequency
22
2
20
i
iii
tiiz
iz
EsinetdtG
222
2
eLe
VpSq
white!
Tp
2
In the barrier...3
710
AV The density of TLSs ~ too low! K/.10
Astafiev et al. 2004
Edet
EnE
HHHH
zxzxJ
zgC
ITLSQ
22
214
22 tedEE
eVEE
GHzEeVEnm.d
E
E
L
dEE
optopt
optC
opt
Coptopt
2
3013010
12
1
1
2
2
2
12
Strongly coupled TLS21gn
23gn
E
gn
In the substrate...
3910
AV
222
2
eLe
VpSq
HzeSq
21817 1010
• Comparison with experiments :
Astafiev et al. 2004
mKTC 120
2862
1010 eSq 2
Hze
TS
Cq
217152
1010
qS at low frequency
21
2
12 20
i
i
iii
tiiz
iz cosetdtG
222
2
eT
Le
VpSq
• it has a 1/f dependence for
• it has only linear dependence on Temperature
• it has intensity in agreement with experimental data
T310
What did we learn from the dipole picture?
qS
f1
2T dependence
Search for fluctuators of different nature ...
CT
eVcm3
2010
Number of thermally activated TLSs
T
eVWVW
TnTLS 10
NW
TnTLS
2
dependence
VVT
WN 0
60 10
Andreev fluctuators model
qubit
v
• correlations are short range• amplitude of oscillations increases with increasing
Faoro, Bergli, Altshuler and Galperin (2004)
ccccTHccH
HT
T~ccvH
TE
zTI
0
0
2
0
2 gdg 2T dependence
T 110 06
0 VVW
TN mKT 20
Kondo-like traps model
dididi
i kdikkisd
dii
didii
didd
kkkkk
kkBCS
sddBCS
ccn
.c.hccVH
nnUccH
.c.hccccH
HHHH
0
Uexp
UT d
i
d
ii
iK
00
122
202 ii VN
Kondo Temperature
U
0d
Properties of the ground state and the localized excited state
30.TTT *K
*KKK
KT KT
Weak coupling Strong coupling
KT
ds EE
doublet
singlet
0sHd 30.T *
K
“Physics” of the Kondo-like traps
*K
*KK
K
KKKK
T
TTT
dTd
0
0
0
0
0
242
3
220 10
1 *K
*K
Al
*K TTTA
r
eAA
0
Slow processes
Fast processes
0d
KTw
barrier
superconductor
Superconductor coherence lenght
Density of states closeto the Fermi energy
bare density
weight of the Kondo resonance
L
HzW
Hz.T *K
14
10
10
1030
ji tjit
ATransition amplitude:
at high frequency qS
2
cothRS
20
2
021 AT
VweGR
*K
• This noise is dominated by fast tunneling processes between traps• effectively the motion of electrons between trap acts as resistor R
From the conductance G we calculate the resistance R
The noise power spectrum raises linearly with the frequency!
NB: Andreev fluctuators have the same but … and
12
1 2
at low frequency qS
22
02
2 T
T
V
L
rweS
*K
q
*KT
TV
L
rw
0
410w
e32 1010
e43 1010
• in the barrier :
3710
AV
22
2
0i
i
i
tiggq L
rweeQtQdtS
HzA?,d
Ai
iii
80 10 but maxmin
g
33
0 10
A
experimental value:
estimates :
• We have discussed a novel microscopic mechanism (Kondo-like traps) that might be the dominant source of noise for dephasing
• But the “physics” of the device is complex : Kondo-like + TLSs
• TLSs are “killed” by the T-dependence!
• Our analysis cannot be done in greater details, due to the lack of an analytical theory of kondo-like impurites with superconductor
• Try to measure 1/f noise after suppressing the superconductivity. We expect reduction of 1/f noise
• Reasonable level of noise even only in the barrier. • Different substrates no changes in the intensity of the noise (NEC)• relevant for phase qubit.
Conclusions