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Coherent Quantum Phase Slip
Oleg Astafiev
NEC Smart Energy Research Laboratories, Japanand
The Institute of Physical and Chemical Research (RIKEN), Japan
RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. TsaiRutgers: L. B. Ioffe Jyväskylä: K. Yu. ArutyunovWeizmann: D. Shahar, O. Cohen
Coherent quantum phase slip, Nature, 484, 355 (2012)
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Introduction. Phase slip (PS) and coherent quantum phase slip (CQPS)
Duality between CQPS and the Josephson Effect CQPS qubits Superconductor-insulator transition (SIT) materials Experimental demonstration of CQPS
Outline
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Very fundamental phenomenon of superconductivity (as fundamental as the Josephson Effect) Exactly dual to the Josephson Effect
• Flux interference (SQUID) Charge interference• Charge tunneling Flux tunneling
Applications Quantum information
• Qubits without Josephson junctions Metrology
• Current standards (dual to voltage standards)
Coherent Quantum Phase Slips (CQPS)
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Flux tunnelingFlux tunneling
SpaceSpace SpaceSpace
SuperconductorSuperconductor
SuperconductorSuperconductor
SuperconductingSuperconducting WireWire
SuperconductingSuperconducting WireWire
Cooper pair tunnelingCooper pair tunneling
SuperconductorSuperconductor SuperconductorSuperconductor
SpaceSpace
SpaceSpaceInsulating Insulating
BarrierBarrierInsulating Insulating
BarrierBarrier
2e2e
What is phase slip?
Josephson Effect: tunneling of Cooper pairs
CQPS: tunneling of vortexes (phase slips)
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Superconductivity does not exist in 1D-wires:
Thermally activated phase slips
I
V
PSe
h
teV
22
Phase-slips at T close to Tc are known for long time
I
VR
Width coherence length
Phase can randomly jump by 2
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Thermally activated phase slips
Quantum phase slip
V
T
kT
Thermally activated and Quantum phase slip
Signature of QPS?
At T = 0: Phase slips due to quantum fluctuations(?)
Are phase slips possible at T = 0?
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Incoherent quantum process coherent quantum process
Quantum Phase Slip (QPS) Coherent QPS
Spontaneous emission:Open space infinite number of modes
I
Dissipative transport measurements:P = IV
Coherent coupling to a single mode:Resonator, two-level system single mode
Nanowire in a closed superconducting loop
incoh <
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Duality between CQPS and the Josephson Effect
Josephson junction Phase-slip junction
cos0JJ EE qSS EE cos0
02
22
0
~21
JJ
J
EE
L
02
22
~2
21S
q
S
k
EE
eC
The CQPS is completely dual to the Josephson effect
Z Y L C 0 2e
0
2
e
q
2
2
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
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Exact dualityExact duality
Josephson Current: Ic sinKinetic Inductance: (2Ic cos)-1
Shapiro Step: V = n
CQPS Voltage: Vc sin(2nq)Kinetic Capacitance: 2e(2 Vc cos(2nq))-1
Shapiro Step: I = n2e
= Phase across junction = Phase across junction nq = normalized charge alongthe wire
nq = normalized charge alongthe wire
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
IICC
VVCC
Shapiro Step
Shapiro Step
[nq,] = -i
Supercurrent CQPS voltage
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NNNNE
NNEH SN 11
2
Flux is quantized: N0
A loop with a nano-wire
Hamiltonian:
L
NE extN 2
20
The loop with phase-slip wire is dual to the charge qubit
BSext
(PS qubit proposed by Mooij J. E. and Harmans C.J.P.M )
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Magnrtic energy:
Phase-slip energy: ECQPS
E
Degeneracy
>> kT
0 2 31 4
The Phase-Slip Qubit
ext
EL
>> ECQPS
ELCQPS qubit:
0
1 0
1
L
NE extN 2
20
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NNNNE
NNE
H JN 1122
Charge is quantized: 2eN
Duality to the charge qubit
Hamiltonian:
C
qeNE extN 2
2 2
The loop with phase-slip wire is dual to the charge qubit
EJ
Reservoir
BoxC
Cg
Vg
ggext CVq
Cg
L C 0 2e extqext
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Loops of usual (BCS) superconductors (Al, Ti) did not show qubit behavior BCS superconductors become normal metals, when superconductivity is suppressed Special class of superconductors turn to insulators, when superconductivity is suppressed Superconductor-insulator transition (SIT) High resistive films in normal state high kinetic inductance
Choice of materials
R
RaE Q
S exp
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Superconductor-insulator transition
(SIT)
InOx, TiN, NbN
Requirements: high sheet resistance > 1 k
n
k
RL
High resistance high kinetic inductance
107
106
105
104
103
102
101
0 5 10 15
T (K)
Sh
ee
t re
sist
an
ce R
□ (
)
The materials demonstratingSIT transition are the most promising for CQPS
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40 nm
Es
N0 (N+1)0
E
ext(N+1/2)0
Gold ground-planes InOx
5 m
0.5 mmInOx
MW in MW out
Amorphous InOx film:R□ = 1.7 k
The device
Step-impedance resonator:High kinetic inductance
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Measurement circuit
NetworkAnalyzer
-20 dB
-20 dB
Isolator
Isolator
resonator
Phase-slip qubit Coil
Low
pas
s fil
ters
output
input4.2 K
1 K
40 mK
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Transmission through the step-impedance resonator
1st
2nd
Z0 Z1
Z0
Current field the resonator
Current amplitudes: maximal for evenzero for odd modes
6 7 8 9 10 11 120.0
0.5
1.0
t (a.
u.)
f (GHz)
34
5250 MHz
-0.10 -0.05 0.00 0.05 0.100.7
0.8
0.9
1.0
0.0
0.1
0.2
t
Bext
(mT)
arg
(t)
B
Z1 >> Z0
Transmission at 4th peak
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5.0 5.5 6.0-6
-4
-2
0
arg
(t)
(m
rad
)
f (GHz)
f = 260 MHz
0
-5
arg
(t)
(mra
d)
Two-tone spectroscopy
We measure transmission through the resonator at fixed frequency fres
Another frequency fprobe is swept
The fitting curve: Ip = 24 nA, ES/h = 4.9 GHz
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Current driven loop with CQPS
Transitions can happen only when ES 0
M
Ip
I0
|1
|0
tacosa
tIMIE
H axpxS
z cos
22 0
a
Sp
EIMI
0
zH 2int
RWA:
22sa E
tH axza
cos22
ES
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The result is well reproducibleThree identical samples show similar behaviorwith energies 4.9, 5.8 and 9.5 GHz
After “annealing” at room temperature InOx becomes more superconducting.The samples were loaded three times with intervals about 1 months. Es is decreased with time.
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00.0 0.5 1.0
0
20
40
60
80
E/h
(G
Hz)
ext
/
fprobe
2 fprobe + fres
(3-photons)
h
EI
hE
sp22
2
/
fprobe + fres
(2 photons)
Wide range spectroscopy
Linear inductance!
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Decoherence
5.0 5.5 6.0-6
-4
-2
0
arg
(t)
(m
rad
)
f (GHz)
f = 260 MHz
Gaussian peak low frequency noise
k
kSkS e
qiEE
2
2exp
Total PS energy:
Potential fluctuations along the chain of Josephson junctions leads to fluctuations of energy and decoherence
Potential equilibration (screening) in the wire? Mechanism of decoherence?
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L 1.6 nH/sq
NbN thin filmsR 2 kIn MW measurements Tc 5 K
Many qubits can be identified
20 different loops with wires of 20-50 nm width
General tendency: the higher resistance, the higher ES
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NbN qubitsf (
GH
z)
Tra
nsm
issi
on a
mp
litud
e
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Conclusion
We have experimentally demonstrated Coherent Quantum Phase Slip
Phase-slip qubit has been realized in thin highly resistive films of InOx and NbN
Mechanism of decoherence in nano-wires is an open question