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

Eigenstates of the washboard potentialwith second harmonic

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

Alexander Ya. Tzalenchuk, John Gallop and J T Janssen

Alexander Zagoskin, Mohammad Amin and Alexander Blais

Tobias Lindström, Serge Charlebois, Evgueni Stepantsov and Zdravko Ivanov

D-Wave Systems Inc.THE QUANTUM COMPUTING COMPANYTM