Novel HTS QUBIT based on anomalous current phase relation S.A. Charlebois a, T. Lindström a, A.Ya....
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Transcript of Novel HTS QUBIT based on anomalous current phase relation S.A. Charlebois a, T. Lindström a, A.Ya....
Novel HTS QUBIT based on
anomalous current phase relationS.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 -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
• In ideal cases– The current-phase relation
(CPR) is -periodic
– Tunneling thru both + and – lobes lifts the degeneracy of the ±k Andreev levels
• In real cases– The GB is facetted and wiggling
– The 2-periodic component is not completely cancelled
200
nm
2sinsin)( III III
The presence of second harmonic in the CPR of a SQUID
1211
12111
2sin2sin
sinsin,IIc
IIc
Ic
Ic
II
III
• the phase difference in junction i• • 1 and 2 represent the junction number• I and II represent the 1st and 2nd harmonics
i21
The CPR of a SQUID is given by the sum of the CPR of each junction including a 2nd harmonic
o 2
For small inductance, the effective washboard potential is the cross section where the applied magnetic flux
If symmetric: silent QUBIT
– The external field does not lift the state degeneracy (σx coupling)
– Unusable for quantum computing
IIc
IIc
Ic
Ic IIII 2121 ,
Functional QUBIT for a particular asymmetry
– The external field “gently” lifts the degeneracy (coupling σz·Φ3)
– All single QUBIT operations realized by applying magnetic field
Ic
IIc
Ic
IIcI
cIc I
II
III2
2
1
121 ,
First steps towards realisation
• 0°-45° YBCO grain boundary junctions
– 250nm thick films
• 2µm size jonctions– Ic ~ 25-60µA
– Rn ~ 3Ω
– Non hysteretic
• Submicron jonctions– Width 0.3-0.6µm
– Ic ~ 0.5-3µA
– Rn ~ 50-300Ω
– Hysteretic
5µm
• The “QUBIT” is connected to perform various SQUID measurements
Excellent correspondence
0.8
1
1.2
1.4
-1.4
-1.2
-1
-0.8
Cri
tical
Cur
rent
(ar
b. u
nits
)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-3
-2
-1
0
1
2
3
x/
0
Vol
tage
(ar
b.un
its.)
35
40
45
-20 -15 -10 -5 0 5 10 15 20-45
-40
-35
Applied Magnetic Field (T)
Cri
tical
Cur
rent
( A
)
Theory Experiment
Critical current:The theoretical
curve (red in the right figure) fits the measurement very
well
SQUID response:
The theoretical curve (left) fits the
measurements (left) show good qualitative agreement
0.8
1
1.2
1.4
-1.4
-1.2
-1
-0.8
Cri
tical
Cur
rent
(ar
b. u
nits
)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-3
-2
-1
0
1
2
3
x/
0
Vol
tage
(ar
b.un
its.)
2µm
junctions
µA7.22
µA7.3
µA3.0
µA9
2
1
2
1
IIc
IIc
Ic
Ic
I
I
I
I
-6 -4 -2 0 2 4 6
-60
-40
-20
0
20
40
60
Applied Magnetic Field (mT)
Cri
tical
Cur
rent
(A
)
Junction modulation in high field
• Absolute maxima not at B=0– Characteristic of 0°-45° grain
boundaries
– Due to 0 and facets
• Lack of ±B symmetry– Due to inductance (in large
junction limit)
– Due to 2nd harmonic (in small junction limit)
Different behavior in submicron junctions
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.
• 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:– approx. 0.1Φo
-0.5 0 0.5 1 1.50
1
0
/
Main max.Sec. max.
0
1
2
Main min.Sec. min.Cusp
Symmetric SQUID:
• Complex secondary maxima develop at (n+1) for >½
– for >½, the potential is double well like
• No shift between + and – current bias• Modulation is not complete even though
the junctions are identical
-2 -1 0 1 20
2
Ic
/o
=00
2
Ic
=0.250
2
Ic
=0.50
2
Ic
=0.750
2
4
Ic
=1
IIc
IIc
Ic
Ic IIII 2121 ,
Ic
IIc II 11 /
I c(
) fo
r va
rious
val
ues
of
Position of the minima and maxima of Ic()
-2 -1 0 1 20
2
Ic
/o
=0
0
2
Ic
=0.1
0
2
Ic
=0.25
0
2
Ic
=0.5
0
2
4
Ic
=1
-0.5 0 0.5 1 1.50
1
0
/
Main max.Sec. max.
0
1
2
Main min.Sec. min.
Asymmetric SQUID:
• Secondary maxima develop for >½– 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
I c(
) fo
r va
rious
val
ues
of
Position of the minima and maxima of Ic()
0 , 221 IIc
Ic
Ic III
Ic
IIc II 11 /
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 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