Unconventional%20Josephson%20junction%20arrays%20for%20qubit%20devices.

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Unconventional Josephson junction arrays for
qubit devices.
Giacomo Rotoli
Superconductivity Group INFM Coherentia
Dipartimento di Energetica, Università di
LAquila ITALY
Collaborations F. Tafuri, Napoli II A.
Tagliacozzo, A. Naddeo, P. Lucignano, I.
Borriello, Napoli I
Jacksonville, October 5 2004
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Superconductivity GroupApplied Physics
DivisionDipartimento di EnergeticaLAquila
We are here
Gran Sasso range (2914 m/9000 ft) and LAquila
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1D open unconventional arrays
Building block the two-junction loop
conventional loop for small b (use g Eq)

• dia, g(0)0

g
p-loop for small b

• g para, g- dia, moreover there are
• spontaneous currents for f going to zero,
• i.e., g(0)1 and g-(0)-1

g-
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1D open unconventional arrays
Model 1D GB Long Josephson Junction with
presence of p-sections alternanting with
conventional sections. This is equivalent to
have localized p-loops in a 1D array
Quest what is the fundamental state in zero
field ?
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1D open unconventional arrays
Quest what is the effect of the magnetic field ?
screening current adds
Two solutions are no longer degenerate! Red ones
is paramagnetic and have a lower energy with
respect to Blue ones which is diamagnetic and
with higher energy
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Total energy
Total energy is the sum of Josephson and magnetic
energy
We can write
Moreover, using flux quantization, Magnetic
energy is written
Where b 2pI0L/F0 . With Djjjj-jj-12pnj we
obtain
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The winding number
The quantum number nj is typically zero for open
arrays because the variations of the phases are
small if b is not Large. On the other hand, in an
annular array the last loop nNn play the role of
winding number of the phase, i.e., the number of
flux quanta into the annulus.
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1D open unconventional arrays
Q How we find phases ji ? A Solving Discrete
Sine-Gordon equation (DSG)
With jN2j00, ii,i-i-1,fN1f00
We assume f constant, i.e., fif , moreover
(see E. Goldobin et al., Phys. Rev. B66, 100508,
2002 J. R. Kirtley et al., Phys. Rev. B56, 886,
1997)
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1D open unconventional arrays
G. Rotoli PRB68, 052505, 2003
hd

• 0-p junction (equal length)
• diamagnetic sol
• paramagnetic sol
• N63, b0.04

Mean magnetization for different
GBLJJs symmetric 0-p gt circles
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Previous work on 1D open unconventional arrays
G. Rotoli PRB68, 052505, 2003

• N255, b0.04
• with 15 p-loops
• 7 dia 8 para
• 5 dia 10 para
• 3 dia 12 para
• (b) and (c) corresponds to
• a pre-selection of paramagnetic
• solutions due to FC

FC can be introduced assuming that it flips
some SF from dia to para state
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Other papers in unconv. arrays and junctions
F. Tafuri and J. R. Kirtley, Phys. Rev. B62,
13934, 2000 Tilt-Twist 45 degree YBCO GB
junctions sample diamagnetic with ½ half flux
quanta pinned to defects and along GB,
paramagnetism only local F. Lombardi et al.,
Phys. Rev. Lett. in print, 2002 Tilt-Twist GB
junctions with angles betw 0 and 90 rich
structure of spontaneous currents for 0/90
GB Ilichev et al., to be subm. Phys. Rev. B,
2002 First paramagnetic signal recorded, very
flat GB form 45 deg asymmetric twist junctions,
no spontaneous currents have been
experimentally observed H. J. H. Smilde et al.,
Phys. Rev. Lett. 88, 057004, 2002 Artificial
zig-zag LTC-HTC arrays
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1D open unconventional arrays
Some estimate of demag field hd
Hd(a)7.6 mG Hd(b)36 mG Hd(c)80 mG
we use lLlc-axis equal to 5 mm Note that in (a)
fields are of the same order of magnitude cited
in Tafuri and Kirtley (lc-axis5.9 mm)
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0-p Annular JJ arrays

• Have properties similar to the Annular Josephson
  junction
• So can be thinked are related to fluxon qubit
  (A. Ustinov,
• Nature 425, 155, 2003)
• 2) Will have some protection from external
  perturbation
• In the limit of large N (Doucout et al., PRL90,
  107003, 2003)
• 3) Can be build using p-junctions as in
  Hilgenkamp et al.,
• Nature 50, 422, 2003

Merging together these three ideas we have
1 qubit
2 qubit
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Annular arraysA practical layout
N 8 array, with CF (control field) CB (control
barrier) CN (control loop N)
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0-p Annular JJA DSG
Q How we find phases ji ? A Solving Discrete
Sine-Gordon equation (DSG) for the ring
With jN1j12pn, n is the winding number
ii,i-i-1
A f constant do no longer apply, f have to be
not uniform to have effect on a 0-p AJJA
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Fundamental states in AJJA
Spin notation
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AJJA arrays (excited states)
N 2 4
N 6
n 0
n 1
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AJJA (excited states) (2)
K-AK states
large b
small b
Fractionalization phenomenon
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0 p Annular long junction
E. Goldobin et al. PRB66, 100508, 2002 E.
Goldobin et al. PRB67, 224515, 2003 E. Goldobin
et al. cond-mat/0404091 (ring)
Fund. state
k 0-p boundaries N/k sections
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LJJ case 0-p JJ
l/k2 (nor. length of sections)
l/k1
K 2,4 N32,64
k6 N96
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Annular arrays in magnetic field I
Single loop (Cn) frustation on an N16 array
Frustation over loops 10-16 On an N16 array
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Annular arrays in magnetic field II
Critical field for flip between fund. states
Frustation applied via CF is independent of N
and induce a flip between para-dia sol. at h2.1
Effect of frustation applied via a single loop,
say C1, decrease with N
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Magnetic behavior of annular 0-p LJJ
The effect of field in LJJ case is very similar
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Magnetic behavior for different spatial
configuration
Variation of fundamental state energy for
different values of b and Magnetic field In the
N16 and N64 AJJA Top magnetic field in a
single loop Bottom magnetic field over 7 loops
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Annular arrays flip dynamics
N256, k16 array via s-type control
N 16 array via C1
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The process (classical)
Classically it is possible to flip an half-flux
quantum adding it a full flux quantum (fluxon) E.
Goldobin et al. cond-mat/0404091
motion direction
Successive time plot of annihilation of a fluxon
on a 0-p boundary where a positive half-flux
quantum was localized. Annihilation ends in a
negative half flux quantum radiation
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The process (quantum)
Calculation for quantum process in collaboration
With A. Tagliacozzo, A. Naddeo and I . Borriello
(Napoli I) is in progress The flip process is
approximated summing up the analytical expression
for fluxon (kink) and a localized half-flux
quantum with kink velocity As free parameter to
be used in a variational approach. Next step is
the calculation of euclidean action for the flip,
its minimization will give the result.
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p-Junction realization
There are essentially three way to fabricate
p-junctions dId YBCO made have the best
performances in dissipation and recently show
also MQT effect (collaboration Napoli II, F.
Tafuri Chalmers, T. Cleason) dissipation are
good (100 W) control of currents and capacity
not so easy dIs used by Hilgenkamp et al. in
zigzag arrays, are YBCO-Nb ramp edge
junctions dissipation are intermediate (20 W),
control on other parameters is good SFS these
are Nb-(Ni-Cu)-Nb junctions which show a phase
shift depending on F barrier thickness dissipatio
n is high at moment, critical currents and
capacitance can be controlled in a fine manner
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Conclusion

• Annular unconventional arrays and their LJJ
  counterpart the annular 0-p junction are very
  interesting physical object condensing the
  properties of half-flux quantum arrays and
  annular junction together with some energy and
  topological protection properties
• It is conceivable to think to a protected qubit
  made of unconventional arrays, which will be the
  simplest topologically not trivial system showing
  the above properties and realizable with present
  tecnology (conventional ring array was realized
  for study
• breather solutions, see PRE 66, 016603, 2002)
• A quantum description of flip process between
  half-flux quantum is in progress

Part of results shown here will be submitted to
ASC04 conference, Jacksonville, FL USA 3-8
october 2004 session 3EI01
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Acknowledgements
We would like to thank F.Tafuri, A. Tagliacozzo,
I. Borriello, A. Naddeo for helpful discussions
and suggestions. This work was supported by
Italian MIUR under PRIN 2001 Reti di giunzioni
Josephson quantistiche aspetti teorici e loro
controparte sperimentale.
Contact e-mail gt rotoli_at_ing.univaq.it web
gt http//ing.univaq.it/energeti/research/Fisica/s
upgru.htm