Invited talk at 26th Kansai Quantum Information Student Chapter

1. Prospects for
Ion-Electron-Circuit Hybrid Quantum Systems
Alto Osada
Noguchi lab., Komaba Institute of Science (KIS)
The University of Tokyo
1st July, 2019 Quantum-Information Student Chapter @ Osaka Univ.
1
Sqei

2. 2
Footprints
2017-2019
QD + photonic crystal cavity
@ Arakawa-Iwamoto lab., IIS, UTokyo
2011-2014
Two-species atomic BEC
@ Inouye lab., UTokyo
2014-2017
Cavity optomagnonics
@ Nakamura-Usami lab., RCAST, UTokyo

3. 3
Current status
2019- Hybrid quantum systems
@ Noguchi lab., Komaba Institute for Science, UTokyo
（先進科学研究機構）
Since Jan. 2019 Since Jun. 2018
Trapped electron
-
Trapped ion
+
Superconducting qubit
Novel quantum devices
based on hybrid quantum systems

4. 4
Current status
2019- Hybrid quantum systems
@ Noguchi lab., Komaba Institute for Science, UTokyo
（先進科学研究機構）
Since Jan. 2019 Since Jun. 2018
Trapped electron
-
Trapped ion
+
Superconducting qubit
Novel quantum devices
based on hybrid quantum systems

5. 5
Outline
• Introduction
• Hybrid quantum systems
• Trapped electrons
• Quantum interface
- From superconductor to optical fiber
• Toward ultracold electrons
- Resistive cooling and beyond

6. 6
Outline
• Introduction
• Hybrid quantum systems
• Trapped electrons
• Quantum interface
- From superconductor to optical fiber
• Toward ultracold electrons
- Resistive cooling and beyond

7. 7
Quantum systems
Atom
Superconducting circuit

8. 8
Josephson junction = nonlinear inductor
Normal Normal

9. 9
Josephson junction = nonlinear inductor
Super, 𝜑1 Super, 𝜑2

10. 10
Josephson junction = nonlinear inductor
Super, 𝜑1 Super, 𝜑2
𝐼 = 𝐼0 cos 𝜑
𝑉 =
ℏ
2𝑒
d𝜑
d𝑡
(𝜑 = 𝜑2 − 𝜑1)
Thin insulator
cf.
R. P. Feynman Vol. 3

11. 12
Superconducting qubit = nonlinear cavity
|𝑔⟩
|𝑒⟩
|𝑓⟩
𝐻 = ℏ𝜔𝑠 𝑎†
𝑎 +
𝛼
2
𝑎†
𝑎 𝑎†
𝑎
L (nonlinear)
C

12. 13
Superconducting qubit = nonlinear cavity
|𝑔⟩
|𝑒⟩
|𝑓⟩
𝐻 = ℏ𝜔𝑠 𝑎†
𝑎 +
𝛼
2
𝑎†
𝑎 𝑎†
𝑎
L (nonlinear)
C
Excellent review!

13. ~ tens of controllable ions
14
Paul trap
+-
|0⟩
|1⟩
|2⟩
~MHz
|3⟩
=
In courtesy of A. Noguchi

14. 15
Quantum systems
Atom
Superconducting circuit
Optical photon
Microwave photon
10 GHz ~ 0.5 K
300THz ~ 10000 K
|𝑔⟩
|𝑒⟩

15. 16
Quantum systems
Atom
Superconducting circuit
Optical photon
Microwave photon
10 mK
300 K
10 GHz ~ 0.5 K
300THz ~ 10000 K
|𝑔⟩
|𝑒⟩

16. 17
Quantum systems
Atom
Superconducting circuit
Optical photon
Microwave photon
10 mK
300 K
10 GHz ~ 0.5 K
300THz ~ 10000 K
|𝑔⟩
|𝑒⟩

17. 18
Quantum systems
Atom
Superconducting circuit
Solid-state spins
Optical photon
Microwave photon
10 mK
300 K
Opto/electromechanics (opto-)magnonics
10 GHz ~ 0.5 K
300THz ~ 10000 K
MHz-GHz

18. 19
Quantum systems
Atom
Superconducting circuit
Optical photon
Microwave photon
10 mK
300 K
10 GHz ~ 0.5 K
300THz ~ 10000 K
40 Hz
[ J.Verdu et al., PRL 103, 043603 (2009) ]

19. 20
Quantum systems
ion
Superconducting circuit
Optical photon
Microwave photon
10 mK
300 K
10 GHz ~ 0.5 K
300THz ~ 10000 K
10 kHz
[ S. Kotler et al., PRA 95, 022327 (2017) ]
+

20. electron
-
21
Quantum systems
Superconducting circuit
Microwave photon
10 mK
10 GHz ~ 0.5 K
1 MHz
[ S. Kotler et al., PRA 95, 022327 (2017) ]
~ GHz

21. 22
Trapped electrons
D. Wineland, P. Ekstrom, and H. Dehmelt, PRL 31, 1279 (1973)
D. Segal and M. Shapiro, Nano Lett. 6, 1622 (2008)
I. Marzoli et al., J. Phys. B 42, 154010 (2009)
S. Kotler et al., PRA 95, 022327 (2017)
HP of Hommelhoff’s group,
J. Hammer et al., PRL 114, 254801
(2015)
G. Koolstra et al., arXiv:1902.04190
T. K. Langin et al.,
Science 363, 61 (2019)

22. 23
Trapped electrons
D. Wineland, P. Ekstrom, and H. Dehmelt, PRL 31, 1279 (1973)
D. Segal and M. Shapiro, Nano Lett. 6, 1622 (2008)
I. Marzoli et al., J. Phys. B 42, 154010 (2009)
S. Kotler et al., PRA 95, 022327 (2017)
HP of Hommelhoff’s group,
J. Hammer et al., PRL 114, 254801
(2015)
G. Koolstra et al., arXiv:1902.04190
T. K. Langin et al.,
Science 363, 61 (2019)
• Quantum scanning electron microscopy
• Electron-on-helium “quantum dot”
• Ultracold neutral plasma
What else?
Quantum interface “Emergent solid”?

23. 24
Trapped electrons
✓ me ~ 10-5 x mCa
✓ Secular frequency ~ 1 GHz
✓ Depth of trapping potential ~ 0.5 eV
• Still “dark”

24. 25
Outline
• Introduction
• Hybrid quantum systems
• Trapped electrons
• Quantum interface
- From superconductor to optical fiber
• Toward ultracold electrons
- Resistive cooling and beyond

25. 26
Quantum interface
Superconducting circuit
Trapped electron
- Trapped ion
+
Electric dipole
Phonon-phonon
Electric dipole
Optical mode

26. Electric dipole
27
Superconducting circuit
Trapped electron
-
SC circuit-electron
Electrodes
~ GHz
~ GHz
1-10 MHz

27. 29
Electron-ion
Trapped electron
- Trapped ion
+Phonon-phonon
~ GHz
~ MHz
10 MHz

28. 31
Ion-cavity
Trapped ion
+
Optical mode
(cavity)
Electric dipole
H. Takahashi et al., arXiv:1808.04031
M. Steiner et al., Phys. Rev. Lett. 110, 043003 (2013).
250 µm
beam diam. 10 µm
10 MHz

29. 32
Quantum interface
Superconducting circuit
Trapped electron
- Trapped ion
+10 MHz
1-10 MHz
10 MHz
Optical mode
(cavity)

30. 33
Conversion efficiency
𝐻 = ℏ𝜔𝑠 𝜎𝑠
𝑧
+ ℏ𝜔 𝑒 𝑎 𝑒
†
𝑎 𝑒 + ℏ𝜔𝑖 𝑎𝑖
†
𝑎𝑖 + ℏ𝜔𝑐 𝑎 𝑐
†
𝑎 𝑐
+ℏ𝑔𝑠𝑒 𝜎𝑠
+ 𝑎 𝑒 + 𝜎𝑠
− 𝑎 𝑒
†
+ ℏ ෤𝑔 𝑒𝑖 𝑎 𝑒
†
𝑎𝑖 + 𝑎 𝑒 𝑎𝑖
†
+ ℏ ෤𝑔𝑖𝑐 𝑎𝑖
†
𝑎 𝑐 + 𝑎𝑖 𝑎 𝑐
†

31. 34
Conversion efficiency
𝐻 = ℏ𝜔𝑠 𝜎𝑠
𝑧
+ ℏ𝜔 𝑒 𝑎 𝑒
†
𝑎 𝑒 + ℏ𝜔𝑖 𝑎𝑖
†
𝑎𝑖 + ℏ𝜔𝑐 𝑎 𝑐
†
𝑎 𝑐
+ℏ𝑔𝑠𝑒 𝜎𝑠
+ 𝑎 𝑒 + 𝜎𝑠
− 𝑎 𝑒
†
+ ℏ ෤𝑔 𝑒𝑖 𝑎 𝑒
†
𝑎𝑖 + 𝑎 𝑒 𝑎𝑖
†
+ ℏ ෤𝑔𝑖𝑐 𝑎𝑖
†
𝑎 𝑐 + 𝑎𝑖 𝑎 𝑐
†

32. 35
Conversion efficiency
𝐻 = ℏ𝜔𝑠 𝜎𝑠
𝑧
+ ℏ𝜔 𝑒 𝑎 𝑒
†
𝑎 𝑒 + ℏ𝜔𝑖 𝑎𝑖
†
𝑎𝑖 + ℏ𝜔𝑐 𝑎 𝑐
†
𝑎 𝑐
+ℏ𝑔𝑠𝑒 𝜎𝑠
+ 𝑎 𝑒 + 𝜎𝑠
− 𝑎 𝑒
†
+ ℏ ෤𝑔 𝑒𝑖 𝑎 𝑒
†
𝑎𝑖 + 𝑎 𝑒 𝑎𝑖
†
+ ℏ ෤𝑔𝑖𝑐 𝑎𝑖
†
𝑎 𝑐 + 𝑎𝑖 𝑎 𝑐
†
~ 17 %

33. 36

34. 37
Outline
• Introduction
• Hybrid quantum systems
• Trapped electrons
• Quantum interface
- From superconductor to optical fiber
• Toward ultracold electrons
- Resistive cooling and beyond

35. 38
Concerns
Lasers in a fridge?
- 1eV = 10000K vs. 10mK
Simultaneous trapping of e- and ions?
- +/- charged,
- state-of-the-art electrode designs
Cooling electrons?
- “dark” - no internal structure
- me = mCa/105

36. Lasers in a fridge?
- 1eV = 10000K vs. 10mK
Simultaneous trapping of e- and ions?
- +/- charged,
- state-of-the-art electrode designs
39
Concerns
Separate trap chips?
Ions as a trapping “electrode”?
Cryogenic surface trap?
Ion/electron shuttling?
Cooling electrons?
- “dark” - no internal structure
- me = mCa/105

37. Separate trap chips?
Ions as a trapping “electrode”?
Ion/electron shuttling?
Lasers in a fridge?
- 1eV = 10000K vs. 10mK
Simultaneous trapping of e- and ions?
- +/- charged,
- state-of-the-art electrode designs
40
Concerns
Cooling electrons?
- “dark” - no internal structure
- me = mCa/105

38. 41
Resistive cooling
Final temperature ~ 300 K = 30 meV
→ < 500 meV (trap depth)
Electron’s secular motion ~ 1 GHz = 3 µeV
→ Final occupation ~ 104 phonons
Alternating current → consumed by impedance

39. 42
Laser cooling of ions
“Doppler cooling”
Final temperature
𝑇 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 ∼
𝛤 𝑖
2𝑘B
∼ 100 µK
Final occupation ∼
𝛤 𝑖
2𝜔 𝑖𝑝
∼ 10 phonons!
<< 1 phonon, if “sideband cooling” is applied
|𝑔⟩
|𝑒⟩
Γi

40. 43
Laser cooling of electrons?
“Sympathetic cooling” ℏ𝑔 𝑒𝑖
BS
𝑎 𝑒
†
𝑎𝑖 𝑒 𝑖𝛿𝑡
+ 𝑎 𝑒 𝑎𝑖
†
𝑒−𝑖𝛿𝑡
Nonlinear term : ℏ𝑔 𝑒𝑖 𝑎 𝑒
†
𝑎 𝑒 𝑎𝑖 + 𝑎𝑖
†
→ ℏ𝑔 𝑒𝑖 𝛼 𝑒 𝑎 𝑒
†
𝑎𝑖 + 𝑎 𝑒 𝑎𝑖
†
|𝑛 𝑒, 𝑛𝑖⟩
|𝑛 𝑒, 𝑛 + 1𝑖⟩
|𝑛 + 1 𝑒, 𝑛𝑖⟩
𝑔 matrix

41. |0 𝑒, 0𝑖⟩
|0 𝑒, 1𝑖⟩
|0 𝑒, 2𝑖⟩
|1 𝑒, 0𝑖⟩
|1 𝑒, 1𝑖⟩
|1 𝑒, 2𝑖⟩
|2 𝑒, 0𝑖⟩
|2 𝑒, 1𝑖⟩
|2 𝑒, 2𝑖⟩
44
Laser cooling of electrons?

42. |0 𝑒, 0𝑖⟩
|0 𝑒, 1𝑖⟩
|0 𝑒, 2𝑖⟩
|1 𝑒, 0𝑖⟩
|1 𝑒, 1𝑖⟩
|1 𝑒, 2𝑖⟩
|2 𝑒, 0𝑖⟩
|2 𝑒, 1𝑖⟩
|2 𝑒, 2𝑖⟩
45
Laser cooling of electrons?
,
,

43. 46
Summary
➢Hybrid quantum systems are inevitable for connecting every
quantum system to light
➢Trapped electron may bridge the gap between SC circuits
and trapped ions, with larger bandwidth
➢Electron can be cooled resistively, and further by tailoring
nonlinear interaction
• Actual designs and experiments
– superhard!

44. 47
Lab.

45. 48
Lab.

46. 49
Lab.
6/14

47. 50
Lab.
6/15

48. 51
Lab.
6/29
275℃

49. 52
Join us!
東京大学大学院 総合文化研究科 先進科学研究機構
東京大学大学院 総合文化研究科 広域科学専攻 相関基礎科学系
東京大学教養学部 統合自然科学科
275℃

50. 53

51. 54

52. 55

53. 56
Quantum systems
http://iontrap.umd.edu/
https://www.top500.org/news/google-and-ibm-
battle-for-quantum-supremacy/
http://www.riken.jp/en/research/rikenresearch/h
ighlights/7813/
https://www.rochester.edu/newscenter/2-million-nsf-grant-to-
add-efficiency-to-integrated-quantum-photonics-175132/
Photon Atom(ic ion)s
Superconducting circuits Quantum dots

54. 88Sr+イオン
光ファイバ
+GaAs/AlAs DBR
GaAs/AlAs DBR
↑光量子ネットワークへ

55. 2S1/2
2P1/2
2D3/2
3[3/2]1/2
2P3/2
2D5/2
2F7/2
1[5/2]1/2
171Yb+ energy levels
Isotopes Abundance I
174Yb 32% 0
172Yb 22% 0
173Yb 16% 5/2
171Yb 14% 1/2
176Yb 13% 0
1S0
1P1
398.911 nm
(ionization)
935.186 nm
(repump)
369.524 nm
(cooling)
Γ = 10 MHz
Γ = 2-4 MHz?
329.031 nm
1650.29 nm
410.970 nm
638.6 nm
HF = 12.6 GHz
HF = 2.1 GHz
HF = 0.86 GHz
HF = 2.2 GHz

56. 171Yb+ in fiber cavity (M. Kohl’s group)
935 nm transition is weak
F = 1000 (κ=320MHz)
g0 = 6 MHz for L=230µm, w=7µm cavity
369 nm light is harmful for the cavity mirrors
F = 1000 → 200 (130 days)
g0 = 67 MHz for L=150µm, w=3µm cavity

57. 2S1/2
2P1/2
2D3/2
2P3/2
2D5/2
Sr+ energy levels
Isotopes Abundance I
84Sr 0.56% 0
86Sr 9.86% 0
87Sr 7.00% 9/2
88Sr 82.58% 0
421.6706 nm
(cooling)
Γ = 20 MHz
Γ = 1.5 MHz
407.886 nm
1003.94 nm
1S0
1P1
461 nm
405 nm
1D2
1091.79 nm
Linewidths of the transitions are
almost the same as the ones of Ca+