1. Alexey Bolgar alexgood@list.ru
Superconducting quantum bit coupled to a surface acoustic phonon mode of periodic structure
Alexey Bolgar 1

2. Our Team Alexey Bolgar Rais Shaikhaidarov Head of the Lab:
Oleg Astafiev
Julia Zotova 2
Daniil Kirichenko 2

3. Report structure 1 . Short introduction to surface acoustic waves
1.1 Basic properties
1.2 Prospects for quantum acoustics
1.3 Previous achievements of other groups
2. Our Sample structure
3. Fabrication technology
4. Results:
4.1 Observation of coupling between a transmon and vacuum acoustic mode of periodic structure
4.2 Two-port SAW resonator coupled to a transmon 3 3

4. SAW. Basic introduction
What is it?
Propagation layer thickness about 1 λ only.
wave speed for ST-Quartz 3,1 km/sec. λ
𝑉 𝑆𝐴𝑊 =3,1 km/sec
How to emit or receive?
On piezoelectric wafer an interdigital transducer can be used.
The frequency of efficient SAW generation depends on IDT periodicity:
𝑓 0 = 2𝑝 𝑣 𝑆𝐴𝑊 4 4

5. Previous results of other groups
«Propagating phonons coupled to an artificial atom»
Martin V. Gustafsson and Per Delsing1, Chalmers University of Technology† (2014)
«Surface acoustic wave resonators in the quantum regime»
R. Manenti and P. J. Leek∗ University of Oxford, (2015)
f0 up to 4,5 GHz
Qi up to at single phonon regime 5 5

6. Our structure design b, mm c, mm d, mcm a, nm p, nm w, mcm
Josephson junctions size, nm x nm 10 5
320
250
1000 15
100 x 100 c p a
Np=200
ɛ=4
Ct= 100 fF
fac = 3.1 GHz
Ec= 𝑒 2 2 𝐶 𝑡 = 0.8 mceV d b
Rn=12 kOhm, Ej= ℏ 𝐼 𝑐 2𝑒 = 48 mceV
Ej /Ec ≈ 60 6 6

7. IDT Fabrication: Aluminum-hat
1. Preparing mask +
E-beam lithography
2. Resist developing
3. Aluminum evaporation +80deg
4. Aluminum evaporation -80deg
6. Lift-off process
7. Etching titanium sublayer
8. Structure is ready 7 7

8. Josephson junction fabrication
Quartz
MMA
ARP Al
EBeam
We used double layer mask with the following parameters:
bottom layer: MMA 9%, 760 нм
top layer: ARP , 120 нм
We used standard double angle evaporation technique with
the following parameters:
first Al layer: 25 nm,
static oxidation for 10 min at 5 mBar.
second Al layer: 45 nm
Final SEM photo: 8

9. Results. Overall scan 3.1 Ghz the frequency of interest
Frequency at maximum: expected 3, 8 GHz, measured 4,5. Most probably, due to not well controlled junctions size.
Expected effect: broadening of reflection peak at the frequency of effective SAW emission due to opening additional channel of relaxation… 9

10. Results. Anti-crossing at acoustic frequency
… However, we found an anti-crossing there! Looks like our qubit is coupled to resonator…
The coupling value: g = 67 MHz
Power = -15dB
Power = -25dB
Power = -35dB
2g=66 MHz 10

11. Explanation of the observed effect
Ordinary single-port SAW resonator with Bragg-grating mirror
Long single-electrode IDT as
a resonator rs Г Г N N
Reflection from a single stripe is similar for the both cases:
|rs|= 0,0154
Reflection from a grating: 11
David Morgan. «Surface Acoustic Wave Filters. With applications to electronic communications and signaal processing» , 2013 11

12. Characterization of IDT as a resonator
P=1mcm
Reflection measurements
T=300 K
T=12 mK
T=300 K
Np=200
Q= 1388
Np=200
Q= 3573
P=1mcm
No resonance
Np=350
Q= 2121 12 12

13. Coupling strength estimation (first approach)
𝑎, mcm
𝑏, mcm
𝜌, kg m 3
𝐸 𝑗 , mceV
𝐸 𝑐 , mceV
𝑒 𝑝𝑧 𝜖 , V m
200 12
320 48
0.8
2∙ 10 9
«Circuit quantum acoustodynamics with surface acoustic waves»
R. Manenti1 and P. J. Leek, March 14, 2017 b a
= 51 MHz
In experiment 33 MHz ! 13 13

14. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator 14 14

15. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
Transmon 15 15

16. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
acoustic resonator
Transmon 16 16

17. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
electroacoustic admittance Ym(ω)
acoustic resonator
Transmon 17 17

18. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
electroacoustic admittance Ym(ω)
Equivalent circuit
acoustic resonator
Transmon 18 18

19. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
electroacoustic admittance Ym(ω)
Equivalent circuit
acoustic resonator
Transmon 19 19

20. Coupling strength estimation (second approach)
«Prospects for quantum acoustics with phononic crystal devices»
Patricio Arrangoiz-Arriola and Amir H. Safavi-Naeini, July 4, 2016
general recipe for a coupling calculation between a transmon and any acoustic resonator
electroacoustic admittance Ym(ω) g
Equivalent circuit
acoustic resonator
Transmon 20 20

21. Coupling strength estimation (second approach)21

22. Coupling strength estimation (second approach)22

23. Coupling strength estimation (second approach)

24. Coupling strength estimation (second approach)

25. Coupling strength estimation (second approach)25

26. Coupling strength estimation (second approach)26

27. Coupling strength estimation (second approach)

28. Coupling strength estimation (second approach)

29. Coupling strength estimation (second approach)

30. Coupling strength estimation (second approach)

31. Coupling strength estimation (second approach)31

32. Coupling strength estimation (second approach)
C = Сj
СIDT 32

33. Equivalent circuit parameters extraction
Reflection amplitude
Reflection complex value
Extracted admittance
Fit function:
|𝑟(𝑓)|= 𝑟 0 +𝐴 Г 2 (𝑓− 𝑓 0 ) Г 2 2
𝑟 𝑓 = 1−𝐴 Г 2 −𝑖 𝑓− 𝑓 Г 𝑓− 𝑓 ∗𝐵 𝑓 +𝐶
C = Сj
СIDT

34. Equivalent circuit parameters extraction
Reflection amplitude
Reflection complex value
Extracted admittance
Fit function:
|𝑟(𝑓)|= 𝑟 0 +𝐴 Г 2 (𝑓− 𝑓 0 ) Г 2 2
𝑟 𝑓 = 1−𝐴 Г 2 −𝑖 𝑓− 𝑓 Г 𝑓− 𝑓 ∗𝐵 𝑓 +𝐶
Im 𝑌 ω =Im 𝑖ω 𝑅 1 +𝑖 ω 𝐿 1 − 1 ω 𝐶 𝑅 1 +𝑖ω 𝐿 1 𝐶 1 + 𝐶 0 𝐶 1 𝐶 0 − 𝑖 ω 𝐶 1 𝐶 0
C = Сj
СIDT

35. Equivalent circuit parameters extraction
Reflection amplitude
Reflection complex value
Extracted admittance
Fit function:
|𝑟(𝑓)|= 𝑟 0 +𝐴 Г 2 (𝑓− 𝑓 0 ) Г 2 2
𝑟 𝑓 = 1−𝐴 Г 2 −𝑖 𝑓− 𝑓 Г 𝑓− 𝑓 ∗𝐵 𝑓 +𝐶
Im 𝑌 ω =Im 𝑖ω 𝑅 1 +𝑖 ω 𝐿 1 − 1 ω 𝐶 𝑅 1 +𝑖ω 𝐿 1 𝐶 1 + 𝐶 0 𝐶 1 𝐶 0 − 𝑖 ω 𝐶 1 𝐶 0
Parameters fitting result:
𝐶 0 = 𝐶 IDT =120 fF, 𝐶 1 =0.202 nF, 𝐿 1 =12.9 pH
C = Сj
СIDT

36. Equivalent circuit parameters extraction
Reflection amplitude
Reflection complex value
Extracted admittance
Fit function:
|𝑟(𝑓)|= 𝑟 0 +𝐴 Г 2 (𝑓− 𝑓 0 ) Г 2 2
𝑟 𝑓 = 1−𝐴 Г 2 −𝑖 𝑓− 𝑓 Г 𝑓− 𝑓 ∗𝐵 𝑓 +𝐶
Im 𝑌 ω =Im 𝑖ω 𝑅 1 +𝑖 ω 𝐿 1 − 1 ω 𝐶 𝑅 1 +𝑖ω 𝐿 1 𝐶 1 + 𝐶 0 𝐶 1 𝐶 0 − 𝑖 ω 𝐶 1 𝐶 0
Parameters fitting result:
𝐶 0 = 𝐶 IDT =120 fF, 𝐶 1 =0.202 nF, 𝐿 1 =12.9 pH
C = Сj
СIDT
calculated coupling result: 𝑔=38,3 MHz
Not bad agreement with the experiment (33 MHz) !

37. Conclusion
1. We have experimentally demonstrated the interaction between a transmon and a fundamental surface acoustic mode of its own periodic structure. The coupling strength is 33 MGz.
2. It has also been shown in additional experiment, that such structure work like a resonator with a quality factors of a few thousand. Using new obtained resonator characteristics we have calculated the coupling strength close to experimental result.
3. The results may be useful to research quantum acoustic in further experiments and to build new compact devices for quantum informatics. 37 37

38. Thank you for your attention!38 38

39. Measurement procedure
Sample holder mounted on the bottom level of dilution cryostat
Scheme of measuring setup: S 39 39

40. Measured characteristic for Measured characteristic for
S-parameters
Measured characteristic for
1-port resonator
Measured characteristic for
2-port resonator
Reflection Transmission 40
Riccardo Manenti. Surface Acoustic Wave Resonators for Quantum Information// Thesis, 2013 40

41. Quantum acoustic prospects
SAW resonator
Decreasing geometric size of systems at Ghz frequency range
Insensibility to electromagnetic noise
Qubit manipulation «in-flight»
λ 𝑎𝑐𝑜𝑢𝑠𝑡𝑖𝑐 ≈𝑚𝑖𝑐𝑟𝑜𝑛𝑠, λ 𝑒𝑚 ≈𝑐𝑚
Electromagnetic resonator 41 41

42. S-parameters Mirror reflection coefficient Δ𝑓=2 𝑓 𝑟𝑒𝑠 𝑟 𝑠 π
Band width
Δ𝑓=2 𝑓 𝑟𝑒𝑠 𝑟 𝑠 π
is reflection coefficient
per single electrode
𝑟 𝑠
Width and numbers mirror electrodes
determine the band width center
Δ 𝑓 𝑛 = 𝑓 𝑟𝑒𝑠 𝑟 𝑠 2𝑑∗ 𝑟 𝑠 +λ 𝑑
is a resonator distance 42
Riccardo Manenti. Surface Acoustic Wave Resonators for Quantum Information// Thesis, 2013 42

43. Fabrication: ARP-Titanium-ARP
1.Preparing mask
2. E-beam lithography
3. Top resist developing
4. Developing result
5. Titanium layer etching
6. Bottom resist etching
7. Etching result 43 43

44. Fabrication: ARP-Titanium-ARP
9. Evaporation result + liftoff
10. Structure is ready
8. Metal evaporating
SEM photo mask ARP-Ti-ARP
Profile view
Optic photo of structure.
Top view 44 44

45. Measured characteristics
ARP-Ti-ARP
𝑓=1.5ГГц
𝑤=500нм
𝑄≈7⋅ 10 4 45 45

46. Fabrication: Aluminum-etching
Top: Optic IDT photo (increasing)
Right: SEM photo of resonator
on 3.1 Ghz
Diagonaly: Optic photo of resonator with capacitance (same as IDT) of transmon 46 46

47. Measured characteristics
Aluminium-etching
𝑓=3.1ГГц
𝑄≈6⋅ 10 3
𝑤=250нм
𝑇≈20𝑚𝐾 47 47

48. A Qubit in an acoustic resonator
Transmon placement into an acoustic resonator
Scheme Optic photo 48 48

49. Coupling transmon to acoustic resonator 49 49

50. Coupling transmon to acoustic resonator 50 50

51. Coupling transmon to acoustic resonator 51 51

52. Coupling transmon to acoustic resonator
Coupling acoustic resonator to superconducting qubit (transmon):
Measuring qubits with small coherence time
Qubit driving
𝑘 2 ℎω 𝑁 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛 𝑁 = 𝑞 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛 𝐶 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛
𝑘 2 = 𝐸 𝑐 𝐸 𝑚𝑒𝑐ℎ
𝐸 𝑐 = 4 𝑒 2 2 𝐶 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛
𝐶 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛 = 𝑁 𝑡 𝐶 𝑓𝑖𝑛𝑔𝑒𝑟
ℎ𝑔= 𝐸 𝑐 𝑞 𝑡𝑟𝑎𝑛𝑠𝑚𝑜𝑛 2 𝑒
𝑔= 𝐾 2 ω 𝐶 𝑓𝑖𝑛𝑔𝑒𝑟 𝑅 𝑞 𝑁 52 52

53. Transmon qubit 53 53