Transcript Novel HTS qubit based on anomalous current phase relation

Novel HTS QUBIT
based on
anomalous current phase relation
S.A. Charleboisa, T. Lindströma, A.Ya. Tzalenchukb,
Z. Ivanova, T. Claesona
aDep.
of Microtechnology and Nanoscience - Quantum Device Physics Laboratory,
Chalmers University of Technology, SE-412 96 Göteborg, Sweden
bNational Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK
D-Wave Systems Inc.
THE QUANTUM COMPUTING COMPANYTM
Outline
• On QUBITs
– In LTS and with p-SQUIDs
– Novel design in HTS with 0/45° grain boundary jonctions
• First steps towards realisation
– Observation of a strong second harmonic component
• Coming work
– Spectroscopy of the Josephson potential
Transport through a 0°-45° grain
boundary in d-wave HTS
– The current-phase relation
(CPR) is p-periodic
– Tunneling thru both + and –
lobes lifts the degeneracy of
the ±k Andreev levels
• In real cases
– The GB is facetted and wiggling
– The 2p-periodic component is
not completely cancelled
I ( )  I I sin   I II sin 2
200nm
• In ideal cases
The presence of second harmonic
in the CPR of a SQUID
The CPR of a SQUID is given by the sum
of the CPR of each junction including a
2nd harmonic
I  1 ,    I cI1 sin 1   I cI2 sin 1   
 I cII1 sin2 1   I cII2 sin2 1   
•  i the phase difference in junction i
•   1   2
• 1 and 2 represent the junction number
• I and II represent the 1st and 2nd
harmonics
For small inductance, the effective washboard
potential is the cross section   2p   o
where  the applied magnetic flux
Eigenstates of the washboard potential
with second harmonic
If symmetric: silent QUBIT
I cI1  I cI2 , I cII1  I cII2
– The external field does not lift the state degeneracy (σx coupling)
– Unusable for quantum computing
Functional QUBIT for a particular asymmetry
I cI1

I cI2 ,
I cII1
I cI1

I cII2
I cI2
– The external field “gently” lifts the degeneracy (coupling σz·Φ3)
– All single QUBIT operations realized by applying magnetic field
First steps towards realisation
• 0°-45° YBCO grain boundary
junctions
– 250nm thick films
5µm
• 2µm size jonctions
– Ic ~ 25-60µA
– Rn ~ 3Ω
– Non hysteretic
• Submicron jonctions
• The “QUBIT” is connected to
perform various SQUID
measurements
–
–
–
–
Width 0.3-0.6µm
Ic ~ 0.5-3µA
Rn ~ 50-300Ω
Hysteretic
Excellent correspondence
Experiment
45
1.4
1.2
1.4
1
Critical current:
1.2
0.8
The theoretical
curve (red in the
right figure) fits the
measurement very
well
1
-0.8
0.8
-1
-0.8
-1.2
Critical Current (A)
Voltage
Voltage
(arb.units.)
(arb.units.)
Critical
Critical
Current
Current
(arb. units)
(arb. units)
Theory
40
I cI2  0.3µA
I cII1  3.7µA
-35
I cII2  22.7µA
-40
-45
-20
-1
-1.4
I cI1  9µA
35
-15
-10
-5
0
5
10
Applied Magnetic Field (T)
-1.2
3
-1.4
2
3
1
2
0
1
-1
0
-2
-1
-3
-2-2
-1.5
-1
-0.5
-3
-2
-1.5
-1
-0.5
SQUID
response:
0
0.5
1
1.5
2
0
0.5
1
1.5
2
x/0
x/0
The theoretical
curve (left) fits the
measurements (left)
show good
qualitative
agreement
15
20
Junction modulation in high field
• Absolute maxima
not at B=0
Critical Current (A)
60
– Characteristic of 0°-45° grain
boundaries
– Due to 0 and p facets
40
20
• Lack of ±B symmetry
0
– Due to inductance (in large
junction limit)
– Due to 2nd harmonic (in small
junction limit)
-20
-40
-60
-6
-4
-2
0
2
4
Applied Magnetic Field (mT)
6
Different behavior
in submicron junctions
• The SQUIDs with
submicron junctions
do not show doubling
of the Ic() curves
• A small shift between
the positive and
negative current bias is
observed:
The critical current vs. applied magnetic field for two SQUIDs with
the same loop size (15×15) µm2. SQUID A: 0.3/0.2 µm wide
junctions (values multiplied by 10 for clarity). SQUID B: 2/2 µm
junctions. All curves measured at 4 K.
– approx. 0.1Φo
Symmetric SQUID: I cI1  I cI2 , I cII1  I cII2
Ic2
2

Main min.
Sec. min.
Cusp
0
1
 =0.75
Ic2
0
0
Main max.
Sec. max.
 =0.5
Ic2
1
0
 =0.25
Ic2
0
-0.5
0
 =0
Ic2
0
-2
Position of the minima and maxima of Ic()
 =1

Ic() for various values of 
4
-1
0
/o
  IcII1 / IcI1
1
•
2
0.5
/p
1
1.5
Complex secondary maxima develop
at (n+1)p for >½
–
•
•
0
for >½, the potential is double well like
No shift between + and – current bias
Modulation is not complete even though
the junctions are identical
Asymmetric SQUID: IcI1  IcI2 , IcII2  0
Position of the minima and maxima of Ic()
4
2
Main min.
Sec. min.
 =1
0

Ic() for various values of 
Ic 2
1
Ic 2
 =0.5
0
0
Main max.
Sec. max.

Ic 2
1
 =0.25
0
Ic 2
0
-0.5
 =0.1
0
•
Ic 2
0
-2
-1
0
/o
  IcII1 / IcI1
1
2
•
0.5
/p
1
1.5
Secondary maxima develop for >½
–
–
 =0
0
for >½, the potential is double well like
the position is parameter dependant
Shift between + and – current bias
–
Shift present for <½ where the potential is not double
well like
Conclusion
• 2nd harmonic in CPR has been observed
– In micron size junctions with direct measurement in SQUIDs
• Showed obvious unconventional CPR
• High field modulations indicate the presence of 0 and p facets
– In submicron size junctions:
• Presence of a small 2nd harmonic component is observed
• Measurements below 1K needed to confirm
• The observation of unconventional CPR in 0°-45°
bicrystal Josephson junctions
– Confirms the “good quality” of junctions
– Confirms that the fabrication process we use limits the damages to
the grain boundary
– Is a prerequisite to further work with the novel QUBIT design
Coming work
• Spectroscopy of the
Josephson potential
– Following work by Mooij
– Measuring the switching current of
an outer SQUID
– Inductive coupling between the
readout SQUID and the QUBIT
– HF tuned to the level spacing
modify the flux in the QUBIT
– The readout SQUID measures the
variation of the QUBIT flux
van der Wal, 2001
Tobias Lindström, Serge Charlebois,
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and J T Janssen
D-Wave Systems Inc.
THE QUANTUM COMPUTING COMPANYTM
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and Alexander Blais