Coherent quantum phase slip, Nature, 484, 355 (2012). RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. Tsai Rutgers: L. B. Ioffe Jyv ä skyl ä : K. Yu. Arutyunov Weizmann: D. Shahar, O. Cohen. Coherent Quantum Phase Slip. Oleg Astafiev
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Coherent quantum phase slip, Nature, 484, 355 (2012)
RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. Tsai
Rutgers:L. B. Ioffe
Jyväskylä: K. Yu. Arutyunov
Weizmann: D. Shahar, O. Cohen
Coherent Quantum Phase Slip
Oleg Astafiev
NEC Smart Energy Research Laboratories, Japanand
The Institute of Physical and Chemical Research (RIKEN), Japan
Coherent Quantum Phase Slips (CQPS)
Cooper pair tunneling
Flux tunneling
Space
Superconductor
Superconductor
Superconductor
Space
Space
Superconducting
Wire
Insulating
Barrier
Space
Superconductor
2e
F0
Josephson Effect: tunneling of Cooper pairs
CQPS: tunneling of vortexes (phase slips)
Thermally activated phase slips
Superconductivity does not exist in 1Dwires:
Width coherence length
Phaseslips at T close to Tc are known for long time
V
Phase can randomly jump by 2
I
Thermally activated and Quantum phase slip
Thermally activated phase slips
Are phase slips possible at T = 0?
V
Signature of QPS?
T
Quantum phase slip
kT
At T = 0: Phase slips due to quantum fluctuations(?)
Quantum Phase Slip (QPS) Coherent QPS
Incoherent quantum process coherent quantum process
incoh<
Spontaneous emission:
Open space infinite number of modes
Dissipative transport measurements:
P = IV
I
Coherent coupling to a single mode:
Resonator, twolevel system single mode
Nanowire in a closed superconducting loop
Duality between CQPS and the Josephson Effect
Mooij, Nazarov. Nature Physics2, 169172 (2006)
Josephson junction
Phaseslip junction
Z Y L C 0 2e
The CQPS is completely dual to the Josephson effect
Mooij, Nazarov. Nature Physics2, 169172 (2006)
[nq,f] = i
nq = normalized charge alongthe wire
f = Phase across junction
CQPS Voltage: Vc sin(2pnq)
Kinetic Capacitance: 2e(2p Vc cos(2pnq))1
Shapiro Step: DI =n2en
Josephson Current: Ic sinf
Kinetic Inductance: F0(2pIc cosf)1
Shapiro Step: DV =nF0n
Shapiro Step
Shapiro Step
IC
VC
Supercurrent
CQPS voltage
(PS qubit proposed by Mooij J. E. and Harmans C.J.P.M）
Flux is quantized: N0
Hamiltonian:
The loop with phaseslip wire is dual to the charge qubit
Degeneracy
1
0




EL
>> ECQPS
+
+
+
+
1
0
E
0
1
2
3
4
ext
Magnrtic energy:
EL
>> kT
ECQPS
Phaseslip energy:
CQPS qubit:
L C 0 2e extqext
Cg
Cg
Box
C
Vg
EJ
Reservoir
Charge is quantized: 2eN
Hamiltonian:
The loop with phaseslip wire is dual to the charge qubit
106
105
Sheet resistance R□ ()
104
103
102
101
0
5
10
15
T (K)
Superconductorinsulator transition(SIT)
Requirements: high sheet resistance > 1 k
InOx, TiN, NbN
High resistance high kinetic inductance
The materials demonstratingSIT transition are the most promising for CQPS
N0
(N+1)0
E
Amorphous InOx film:
R□ = 1.7 k
Es
ext
(N+1/2)0
MW in
Gold groundplanes
InOx
MW out
0.5 mm
InOx
Stepimpedance resonator:
High kinetic inductance
40 nm
5 m
Network
Analyzer
output
input
4.2 K
1 K
Low pass filters
Isolator
20 dB
40 mK
20 dB
Isolator
resonator
Phaseslip qubit
Coil
Transmission through the stepimpedance resonator
Z0
Z0
Z1
Current field the resonator
2nd
Current amplitudes: maximal for evenzero for odd modes
Z1 >> Z0
1st
Transmission at 4th peak
4
3
5
250 MHz
We measure transmission through the resonator at fixed frequency fres Another frequency fprobe is swept
f =
260 MHz
arg(t) (mrad)
0
5
The fitting curve: Ip = 24 nA, ES/h = 4.9 GHz
The result is well reproducible
Three identical samples show similar behaviorwith energies 4.9, 5.8 and 9.5 GHz
After “annealing” at room temperature InOxbecomes more superconducting.
The samples were loaded three times with intervals about 1 months. Es is decreased with time.
D
E
/
h
(
)
2
+
2
d
F
2
I
E
p
s
=
h
Wide range spectroscopy
2 fprobe + fres
(3photons)
fprobe + fres
(2 photons)
fprobe
Linear inductance!
Gaussian peak
low frequency noise
f =
260 MHz
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?
R 2 k
In MW measurements Tc 5 K
L 1.6 nH/sq
20 different loops with wires of 2050 nm width
Many qubits can be identified
General tendency: the higher resistance, the higher ES