Coherent Quantum Phase Slip
Oleg Astafiev
NEC Smart Energy Research Laboratories, Japan
and
The Institute of Physical and Chemical Research (RIKEN), Japan
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
Outline
 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
Coherent Quantum Phase Slips (CQPS)
 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)
What is phase slip?
Cooper pair tunneling
Space
Flux tunneling
Superconductor
F0
2e
Superconductor
Space
Superconductor
Insulating
Barrier
Space
Space
Superconductor
Superconducting
Wire
Josephson Effect: tunneling of Cooper pairs
CQPS: tunneling of vortexes (phase slips)
Thermally activated phase slips
Superconductivity does not exist in 1D-wires:
Width  coherence length 
Phase-slips at T close to Tc are known for long time
V
Phase can randomly jump by 2
 
h
V
 PS
2e t
2e
I
V
R
I
Thermally activated and Quantum phase slip
Thermally activated phase slips
Are phase slips possible at T = 0?
V
Signature of QPS?
Quantum phase slip
T
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, two-level system  single mode
Nanowire in a closed
superconducting loop
Duality between CQPS and the Josephson Effect
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
Josephson junction
EJ  EJ 0 cos
2
Phase-slip junction
2F
F0
1  2   2 ES

~ ES 0

2
Ck  2e   q
2
1  2   E J

 
~ EJ 0
2
LJ  F 0  
2
ZY
ES  ES 0 cos q
2q
2e
LC
F0  2e
The CQPS is completely dual to the Josephson effect
Exact duality
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
f = Phase across junction
Josephson Current: Ic sinf
Kinetic Inductance: F0(2Ic cosf)-1
Shapiro Step: DV = nF0
[nq,f] = -i
nq = normalized charge along
the wire
CQPS Voltage: Vc sin(2nq)
Kinetic Capacitance: 2e(2 Vc cos(2nq))-1
Shapiro Step: DI = n2e
Shapiro Step
Shapiro Step
IC
VC
Supercurrent
CQPS voltage
A loop with a nano-wire
(PS qubit proposed by Mooij J. E. and Harmans C.J.P.M）
Fext  BS
Flux is quantized: NF0
Hamiltonian:
EN
2

NF 0  F ext 

2L
ES
 N N 1  N 1 N
H  EN N N 
2

The loop with phase-slip wire is dual to the charge qubit
The Phase-Slip Qubit

F ext  NF 0 

2
EN
2L
Degeneracy
E
0
1
2
3








Magnrtic energy: EL >> kT
Fext
1
0
0
1
Phase-slip energy: ECQPS
CQPS qubit:
4
EL >> ECQPS
Duality to the charge qubit
LC
F0  2e
Fextqext
Cg
C
Cg
Box
EJ
Vg
qext  Vg Cg
Reservoir
Charge is quantized: 2eN
Hamiltonian:
EN
2

2eN  qext 

2C
EN
EJ
 N N 1  N 1 N
H
N N 
2
2

The loop with phase-slip wire is dual to the charge qubit
Choice of materials
 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

RQ 

ES  D exp  a


R



Superconductor-insulator transition
(SIT)
107
Requirements: high sheet resistance > 1 k
Sheet resistance R□ ()
106
InOx, TiN, NbN
105
High resistance  high kinetic inductance
104
Rn
Lk 
D
103
102
101
0
5
10
T (K)
15
The materials demonstrating
SIT transition are the most
promising for CQPS
The device
NF0
Amorphous InOx film:
R□ = 1.7 k
(N+1)F0
E
Es
(N+1/2)F0 Fext
MW in
Gold ground-planes
InOx
0.5 mm
InOx
Step-impedance resonator:
High kinetic inductance
40 nm
5 m
MW out
Measurement circuit
input
output
4.2 K
1K
Isolator
-20 dB
40 mK
-20 dB
Isolator
resonator
Phase-slip qubit
Coil
Low pass filters
Network
Analyzer
Transmission through the step-impedance resonator
Z0
Z0
Z1
Current field the resonator
2nd
Z1 >> Z0
1st
Current amplitudes:
maximal for even
zero for odd modes
Transmission at 4th peak

5
250 MHz
1.0
0.2
0.9
0.1
t
t (a.u.)
1.0
4
3
0.5
0.8
0.0
6
0.7
7
8
9
f (GHz)
10
11
12
0.0
-0.10
-0.05
0.00
Bext (mT)
0.05
0.10
arg(t)
DB
Two-tone spectroscopy
We measure transmission through the resonator
at fixed frequency fres
Another frequency fprobe is swept
-5
arg (t) (mrad)
0
arg(t) (mrad)
0
Df =
260 MHz
-2
-4
-6
5.0
The fitting curve: Ip = 24 nA, ES/h = 4.9 GHz
5.5
f (GHz)
6.0
Current driven loop with CQPS
 cosat
Ip
|1
a

M
|0
I0


ES
H   z 
 x  MI p I 0 x cos a t
2
2
 a

H 
z 
 x cos a t
2
2
RWA: H int


z
2
a   2  Es2
ES
  MI p I 0
a
Transitions can happen only when ES  0
ES
The result is well reproducible
Three identical samples show similar behavior
with 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.
Wide range spectroscopy
80
2 fprobe + fres
(3-photons)
DE/h (GHz)
60
40
fprobe + fres
(2 photons)
20 D E / h 
2 I d F  E
2

0
p
2
s
fprobe
h
0.0
0.5
1.0
Fext/F0
Linear inductance!
Decoherence
Df =
260 MHz
0
arg (t) (mrad)
Gaussian peak 
low frequency noise
-2
-4
-6
5.0
5.5
6.0
f (GHz)
 2qk 
ES   ESk exp i

 2e 
k
Potential fluctuations along the chain of Josephson junctions
leads to fluctuations of energy and decoherence
Total PS energy:
Potential equilibration (screening) in the wire?
Mechanism of decoherence?
NbN thin films
R  2 k
In MW measurements Tc  5 K
L  1.6 nH/sq
20 different loops with wires of 20-50 nm width
Many qubits can be identified
General tendency: the higher resistance, the higher ES
Transmission amplitude
f (GHz)
NbN qubits
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