University of Oslo
Physics
Structural
AMCS
Chemistry
Electronics
Advanced Materials &
Complex Systems
Superconductivity
Mesoscopic physics
Complex
Nuclear
Complex group
People
Professors:
Tom Henning
Johansen
Superconductivity
and
Michael Bazilevich
post-docs
Joakim Bergli
Hongqi Chen
Daniel V. Shantsev
Vitaliy Yurchenko
Yuri
Galperin
Mesoscopic Physics: Theory
PhD students
Dmitry Denisov
Oleg Fefelov
Øyvind Haugen
Sanyalak Niratisairak
Åge Andreas Falnes Olsen
Jørn Inge Vestgården
Superconducting magnets
zero resistance
persistent currents
large magnetic fields ~ R
Jc
Superconducting magnet can trap
> 17 Tesla (2004)
Magnetic Levitation Train
Miyazaki Maglev Test Track
501 km/h
581 km/h
Measuring Levitation
Experimental setup & Theory
for lateral levitation force
Magneto-striction
Field distribution
Ba
f
J
Jc
f = JB
Bz
[T]0.4
... and so they crack
0.3
0.2
Bz / T
Lorentz force:
0.1
25
20
15
y / m 10
m
5
15
0
0
5
10
x / mm
20
25
0.0
Practical ways
steel tube
YBCO
Smart ways
to calculate stress distribution
3 cm
and optimize magnet activation process
M
Review in SuST 2000
Phys. Rev. Lett. 1998
Phys. Rev. B 1999
Phys. Rev. B 1999a
………..
Bp
-Bp
Ba
Magneto-Optical Imaging
mirror
image
q F(H)
Faraday-active crystal
A
Linearly
polarized
light
small
large
qF
P
H
2 qF
Magnetic field
light source
Double Faraday rotation
MO indicator
mirror
N
S
small
Magnetic card
MO-crystal
MO image
Magneto-optical indicator films: Garnets
Bi:FG indicator film
LPE furnace
(Bi,Y/Lu)3(Fe,Ga)5O12
single-crystal film
grown by LPE
substrate; GGG
~ 0.5 mm thick
substrate
melt
Pt crucible
furnace
substrate holder
Some grown films, Ø = 30 mm
Film thickness ~ 1- 5 m
In-plane films
we don’t want
“out-of-plane” films
Ms
f
Bi:FG
B
Faraday rotation:
through x’ed P & A:
Ms
qF  Ms sinf
I  sin2qF
Typical MOI setup
magnetic field
cold stage
View through crossed P & A
Ampere's law:  0 J = dB / dx
•
The Bean model: linear B-profile, constant Jc, but:
1. Jc=Jc(B)
2. Shape effects: non-local J(B) for thin films
3. Creep effects at J<Jc
In general, we need to know
• the material law E=E(j,B,T), and
• Bio-Savart B(r)= K(r,r’)J(r’)
MO images of various superconductors
Hg-based ceramic
coherence length
 ~ 10 A
YBaCuO film:
heavy-ion irradiation
1 mm
BiSrCaCuO-tape
Melt-textured NdBaCuO
Macroturbulence of magnetic flux
+
_
1 mm
A hydrodynamic theory for the vortex-antivortex system with anisotropic
viscosity can explain such behavior
Phys. Rev. Lett. 87, 247005 (2001), Phys. Rev. Lett. 2004
Dendritic flux instability
100 km/sec
MgB2 film
T=10K
Local threshold field
- Phys.Rev.B 2003
Dendrites induced by current pulse
- Appl.Phys.Lett. 2002
Dendrites and gradual penetration
- Sup.Sci.Tech. 2003
Dendrites avoid crossing
- Sup.Sci.Tech. 2001
Scientific American, June 2001
Irreproducibility
3 identical experiments: field ramp from 0 to 13.6 mT for 10 sec
the nucleation place:
the exact flux pattern:
well reproduced
never reproduced
D=1.05
D=1.35
D=1.65
D=1.75
Tthresh ~ 10K
1) Flux motion releases heat
2) T rise weakens flux pinning
Thermal diffusion + electrodynamics
T0  Jc    Q  T > T0
Thermal runaway
z
j,E
y
H
0
Linear Analysis
x
l
penetrated
by flux
no flux
unstable if Re  > 0
non-uniform if
ky0
The instability increment
Fastest
growth:
0.0
Re

0.5
-0.5
Ba
-1.0
0
3
6
ky
Only when
9
H(E) stability diagram
H
Fingering is not sensitive to
• initial T(x,y), E(x,y)
• boundary conditions
• Jc(B) dependence
Uniform
jumps
dynamic
criterion
Fingering
adiabatic criterion
Hadiab
S
t
Ec/n
a
b
l
Ec
e
E ~dH/dt
Uniform
jumps
H
Hadiab
Fingering
dynamic adiabatic criterion
criterion
S
t
a
b
l
e
slab
Stable
strip
E ~ dH/dt
Thin films are
* more unstable (avalanches occur at smaller H, dH/dt)
* stronger tendency for dendritic pattern (it forms at smaller dH/dT)
Can magneto-optics resolve individual flux quanta?
garnet indicator
Vortex imaging essentials
GGG
Bi:FGF
Al
Ti3N4
• Modulation of magnetic field
- minimize gap, h
Bk(h) = e-kh Bk(0)
At h=a; damping of fundamental = exp(-2) ~ 2 10-3 (-54dB)
MO image
- sample with small L
- high sensitivity MO films
• Signal loss in optical system
FGF
FGF
FGF
FGF
superconductor
L
- optimize optics for
polarization contrast
• Mechanical noise
- reduce vibrations from cryosystem and other sources
NbSe2 field-cooled to 4.3 K
BFC = 0.3 mT
10 m
Supercond. Sci. Technol. 14, 729 (2001)
BFC = 0.7 mT
NbSe2
edge behavior
(crystal thickness 0.3 mm)
edge
T = 3.5 K
Effect of magnetic domain wall
Bloch wall
MS
edge
FGF
superconductor
vortices
the stray magnetic field
from the domain wall can
generate a vortex chain
even in Ba = 0
Initial state: FC to 3.5 K in B=0.5 mT
After one sweep of the BW
10 m
Bloch wall
Cleaving the crystal to 1/5 thickness
the vortex dynamics change significantly
vortex comb  vortex shovel
Tunable and movable nanomagnets can
serve as vortex manipulators.
Fluxtronics?
Appl. Phys. Lett. 82(1), 79-81 (2003)
Vortex guidance using antidots
YBaCuO film
Preparation: R.Wordenweber, Julich
Magneto-optics
Simulations
NATO Advanced Research Workshop
Magneto-Optical Imaging
28-30 August 2003
Øystese, Norway
Organized: Superconductivity Lab @ UiO
first ever conference
on Magneto-optical imaging
~ 100 participants
~ 400 page Proceedings
The qubit is the analogue of the ordinary computer’s 1 or 0, heads or tails bit.
Unlike such digital representations, a qubit remains in an indeterminate state until
it is observed, like a tossed coin that is still spinning.
Classical bit:
or
Quantum bit:
0 or 1
Qubit: Cooper pair box
Number of excess Cooper pairs
n=0
n=1
n=2
Effective Hamiltonian
Nakamura et. al. ,
Nature, 398, 786 (1999)
Noise
• Qubit is surrounded by fluctuators,
which behave as two-level systems
(i.e. charge traps near a gate)
.
Switching
• The fluctuators randomly switch
between their states due to
interaction with environment
• Distribution of the switching rates
is exponentially broad
Random fields
1/f noise
Decoherence
Assumptions:
1. Noise only in Bz
2. Off-degeneracy, i.e. Bz is the precession frequency
Pure dephasing
The dephasing from fluctuations in precession frequency
is described by the phase memory functional
Strong/Weak coupling
1. v << , weak and fast fluctuators - Gaussian
2. v ~ , strong and slow fluctuators - non-Gaussian
Re  (t)
v /2  0.7
v /2  5
Gaussian
Exact
Plateaus in Y(t)
We predict plateaus at v=2
Echo signal,
1
v/2 = 10
0.0
0.2
0.4
time, 
0.6
0.8
From Nakamura et al., PRL 2002
From the position and height of the plateau
we can determine the parameters of the fluctuating charge:
Coupling strength:
v = 285 MHz,
0.5 m
.
20 A
Switching rate
 = 27 MHz