Coherent Quantum Phase Slip

1
Coherent Quantum Phase Slip
Oleg Astafiev NEC Smart Energy Research
Laboratories, Japanand The Institute of Physical
and Chemical Research (RIKEN), Japan
2
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

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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)

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What is phase slip?
Flux tunneling
Cooper pair tunneling
Superconductor
Space
Superconductor
Superconductor
Space
Space
Superconducting Wire
Insulating Barrier
Superconductor
Space
Josephson Effect tunneling of Cooper pairs
CQPS tunneling of vortexes (phase slips)
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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?
I
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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(?)
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Quantum Phase Slip (QPS) ? Coherent QPS
Incoherent quantum process ? coherent quantum
process
??incoh lt ??
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
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Duality between CQPS and the Josephson Effect
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
Josephson junction
Phase-slip junction
Z ? Y L ? C ?0 ? 2e
The CQPS is completely dual to the Josephson
effect
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Exact duality
Mooij, Nazarov. Nature Physics 2, 169-172 (2006)
nq,f -i
nq normalized charge alongthe wire
f Phase across junction
Josephson Current Ic sinf Kinetic Inductance
F0(2pIc cosf)-1 Shapiro Step DV nF0n
CQPS Voltage Vc sin(2pnq) Kinetic Capacitance
2e(2p Vc cos(2pnq))-1 Shapiro Step DI n2en
Shapiro Step
Shapiro Step
IC
VC
Supercurrent
CQPS voltage
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A loop with a nano-wire
(PS qubit proposed by Mooij J. E. and Harmans
C.J.P.M)
Flux is quantized N?0
Hamiltonian
The loop with phase-slip wire is dual to the
charge qubit
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The Phase-Slip Qubit
E
0
2
3
1
4
?ext
Magnrtic energy
gtgt kT
EL
ECQPS
Phase-slip energy
CQPS qubit
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Duality to the charge qubit
L ? C ?0 ? 2e ?ext?qext
Cg
Cg
Box
C
Vg
EJ
Reservoir
Charge is quantized 2eN
Hamiltonian
The loop with phase-slip wire is dual to the
charge qubit
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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

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Superconductor-insulator transition(SIT)
Requirements high sheet resistance gt 1 k?
InOx, TiN, NbN
High resistance ? high kinetic inductance
The materials demonstratingSIT transition are
the most promising for CQPS
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The device
N?0
(N1)?0
E
Amorphous InOx film R? 1.7 k?
Es
?ext
(N1/2)?0
MW in
Gold ground-planes
InOx
MW out
0.5 mm
InOx
Step-impedance resonator High kinetic inductance
40 nm
5 ?m
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Measurement circuit
Network Analyzer
output
input
4.2 K
1 K
Low pass filters
Isolator
-20 dB
40 mK
-20 dB
Isolator
resonator
Phase-slip qubit
Coil
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Transmission through the step-impedance resonator
Z0
Z0
Z1
Current field the resonator
2nd
Current amplitudes maximal for evenzero for
odd modes
Z1 gtgt Z0
1st
Transmission at 4th peak
4
3
5
250 MHz
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Two-tone spectroscopy
We measure transmission through the resonator at
fixed frequency fres Another frequency fprobe is
swept
?f 260 MHz
0
arg(t) (mrad)
-5
The fitting curve Ip 24 nA, ES/h 4.9 GHz
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Current driven loop with CQPS
ES
1?
0?
RWA
Transitions can happen only when ES ? 0
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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 InOx
becomes more superconducting. The samples were
loaded three times with intervals about 1
months. Es is decreased with time.
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Wide range spectroscopy
2 fprobe fres (3-photons)
fprobe fres (2 photons)
fprobe
Linear inductance!
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Decoherence
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?
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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
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NbN qubits
Transmission amplitude
f (GHz)
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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