Shiro Saito1, Xiaobo Zhu1, Robert Amsuss1, Yuichiro Matsuzaki1 , William J. Munro1, Kosuke Kakuyanagi1, Hayato Nakano1, Takaaki Shimooka2, Norikazu Mizuochi2 ,

Kae Nemoto3, and Kouichi Semba 1,3

1 : NTT Basic Research Laboratories, NTT Corporation, 2 : University of Osaka, Graduate school of Engineering Science,

3 : National Institute of Informatics

超伝導・ダイヤモンド複合系におけるメモリー動作

2012年8月16日FIRST夏期研修会 @ 宮古島

1

Outline

1. IntroductionSuperconducting qubitSuperconductor-diamond hybrid system

2. Experiment under zero in-plane magnetic fieldStrong coupling , coherent oscillations

3. Experiment under zero in-plane magnetic fieldlower NV densitycoherence time is improved

4. Summary2

1CJ <EE CJ1 EE<1CJ ≈EE

Type charge quantronium flux

Coherence time 0.5 µs 0.5 µs 23 µs

φ

Charge (NEC)

Quantronium (Saclay)

Flux (Delft)

phase

0.15 µs

transmon

25 µs(95 µs)

CJ1 EE<<

Transmon (Yale)

Phase (UCSB)

3

Superconducting qubits

99 00 01 02 03 04 05 06 07 08 09 10 11 12

10-9

10-8

10-7

10-6

10-5

10-4

10-3

Year

Decoherence tim

e (s)

Based on J.S.Tsai’s plot, NTT’s data and the newest data are added.

Coherence time of superconducting qubits

NEC Off-OB + EchoCharge

SaclayOB Quantronium MIT/NEC

OB+EchoFlux

NTT OB+EchoFlux

NEC / RIKEN OB+EchoFlux

NEC Off-OBCharge

Delft / NTT OB+EchoFlux

Delft / NEC OffOB+EchoFlux

Yale univ.Transmon

in 3D cavity

IBMTransmon

in 3D cavity

Best data

T1 : 70 µs

T2Ramsey: 95 µs

∆ : 4.2 GHz

EchoRamsey

Energy spectrum

Optimal Bias (OB)

4

Quantum bit :

Processor + memory（superconducting device）

CPU: processor（semiconductor device）

Conventional computer

RAM: memory

（semiconductor device）

Quantum computer using superconductor

？

Components of Computers

5

① Long T2 at RT: 1.8 ms→ suitable for a memory

② B=0 Ground state splitting : 2.88 GHz → idealistic to couple to a superconducting qubit

③ coexistence of GHz (2.88 GHz) and sub-PHz transitions : 638 nm (0.47 PHz)

→ microwave ⇔ optical freq region : Quantum Frequency Converter / Transducer

PL : 638 nm

Microwave Compatible with superconducting qubit

Telecomunicationwavelength （QKD）

● coexistence of GHz and sub-PHz transitions

NV- center

~ ms coherence time at RT

G. Balasubramanian, et al., Nature material, 8, 383 (2009)

6

MW-resonator ⇔NV-diamondFlux-qubit ⇔NV-diamond

Superconducting circuits and spin ensembles

Transmon-qubit ⇔ MW-resonator ⇔NV-diamond

γκ ,singleens >>= Ngg MHz 22ens =g

Hz 22sigle =g1210=NY. Kubo, et al., PRL 105, 140502 (2010)

D. I. Schuster et al., PRL 105, 140501 (2010)

R. Amsuss et al., PRL 107, 060502 (2011)

Y. Kubo, et al., PRL 107, 220501 (2011)

X. Zhu, S. S. et al., Nature 478, 221 (2011)

D. Marcos, et al., PRL 105, 210501 (2010)

Proposal

Experiment (This work)

MHz 70ens =g

kHz 8.8single =g

7106×=N

7

|↓>

|↓>

Mooij et al. Science 285, 1036 (1999)

B

1γ 2γJECE

JECE

JEα

qubit

dc-SQUIDJosephson junctions

Superconducting flux qubits

( ) ( )tAH ZXZ MWMWqb

qb ωσσσε

cos22

+∆

+Φ

=

|↑> |↑>

E 0

(1)

1.5101.5051.5001.4951.490

Φqubit

/ Φ0

MW

∆

1

0

Φqb / Φ0

( )1

5.1

=

Φ−Φ=

0qbPIε

8

JE

JEJEα

|↓>

Qubit

Dc-SQUID

Josephsonjunctions

|R> |L>qbΦ

1.5041.5021.5001.4981.496 1.5041.5021.5001.4981.496

L R

R L

RL +

Flux through the qubit Φqb （Φ0） Flux through the qubit Φqb =Φex + Φα /2（Φ0）

Ener

gy le

vels

Ener

gy le

vels

exΦ αΦJE

JEJ2

Eα

J2E

α

Qubit

Dc-SQUID

∆ is tunable by Φα

∆ ：fixed ∆

Optimal point

RL −

5 µm

Gap tunable flux qubits

( )XZH σσ

ε22

∆+

Φ= qb

qb

F. G. Paauw, et al., PRL(2009), X. Zhu, SS et al., APL(2010)

( ) ( )XZH σσ

ε α

22

Φ∆+

Φ= qb

qb

9

Gap tunable flux qubits

X. Zhu, SS, et al., Appl. Phys. Lett. 97, 102503 (2010)

T2* ~ 350 ns

10

Preparation of diamond samples

HPHT diamond crystal(P1 (N) center ≲ 100 ppm)

12 C ++ ion implantation @ 0.7 MeV ( dose : 3 x 1013 /cm2 ) 900℃ for 3h

under vacuum

Annealing

~ 1 µm

~ 1 µm

Photoluminescence measured by Prof. Mizuochi and Mr. Simooka 11

Inte

nsi

ty (

arb

. u

nits

)

292029002880286028402820

Frequency (MHz)

Evaluation of diamond samples

Type

① HTHP Ib

② HTHP Ib

③ HTHP Ib

NV- density(cm-3)

1.1 x 1018

4.7 x 1017

6.8 x 1016

④ CVD IIa 3.0 x 1016

1-100

1-100

1-100

1-10

N conc.(ppm)

③

ODMR measurements

①

②

③

④

12

qubit NV ITotal Hamiltonian

Qubit Hamiltonian

NV Hamiltonian

Interaction Hamiltonian

Total Hamiltonian

13

This behaves like a harmonic oscillator !

After using rotating wave approximation, we obtain the following JC type model

Collective coupling strength

when an inhomogeneous broadening is negligible

Interaction Hamiltonian

14

HPHT Diamond (NV: 1.1 x 1018cm-3)

NV center concentration: 1.1 x 1018 cm-3 , N2 concentration : 1-100 ppm

70 MHz splitting shows strong coupling between NV centers and a flux qubit

Diamond crystal

Sapphire substrate

Gap tunableflux qubit

● Diamond mounted flux qubit Without diamond crystal

With diamond crystal

X. Zhu, SS, et al., Nature 478, 221 (2011) 15

Without a diamond chipT1_qb = 300 ns @ 2.88GHzT2* _qb= 280 ns

With a diamond chipT1_qb = 150 ns @ 3.12 GHzT2*_qb = 140 ns

T1_NV >> 10usT2*_NV = ?

Coherent oscillations between qubit and NV spin ensemble

HPHT Diamond (NV: 1.1 x 1018cm-3)

Single energy quantum is exchanged between a macroscopic superconducting flux qubit and macroscopic number of NV- spins

X. Zhu, SS, et al., Nature 478, 221 (2011)

16

17

μ0 = 4 ×10−7 N · A−2

R: the distance between a flux-qubitand

a single NV− center.

Biot-Savart lawB = μ0 Ip / (2R)

R =

Ip = 300 nA

×300 larger than ( ~28 Hz : NV-spin & MW-TL resonator)

Coupling strength of a flux qubit to a single spin

MHz, ens 70=g 7106×=NNgg singleens =18

19

Problems

The qubit coherence is good, ∆ ~ 3 GHzT1 ~ 150 nsT2

* ~ 140 ns

But the decay time of vacuum Rabi is short,Tdecay ~ 20 ns

T2 of NV- itself seems to be very short !

2.92

2.90

2.88

2.86

2.84

Tra

nsiti

on f

requ

ency

of

NV

(G

Hz)

3.02.52.01.51.00.50.0In-plane magnetic field (mT)

Possible reasons

Dense P1 center (spin ½)≲100 ppm

NV- density is also high~ 1.1 x 1018 cm-3

: P1 center : NV- center

10 ss −=→= mm

10 ss +=→= mm

Degeneracy of |ms=±１>Splitting due to strain

Reduce a spin density Apply in-plane magnetic field

B// ∝ (100)

20

Inte

nsi

ty (

arb

. u

nits

)

292029002880286028402820

Frequency (MHz)

Diamond samples

Type

① HTHP Ib

② HTHP Ib

③ HTHP Ib

NV- density(cm-3)

1.1 x 1018

4.7 x 1017

6.8 x 1016

④ CVD IIa 3.0 x 1016

1-100

1-100

1-100

1-10

N conc.(ppm)

③

ODMR measurements

①

②

③

④

21

α=4.76V

No signal from NV centers

Diamond crystal

Sapphire substrate

Gap tunable flux qubit (type I)

CVD Diamond (NV: 3 x 1016cm-3)

α=4.86V

NV center concentration: 3 x 1016 cm-3 , N2 concentration : 1-10 ppm

Magnet current (A)

Freq

uenc

y (H

z)

● Diamond mounted flux qubit

22

Inte

nsi

ty (

arb

. u

nits

)

292029002880286028402820

Frequency (MHz)

Diamond samples

Type

① HTHP Ib

② HTHP Ib

③ HTHP Ib

NV- density(cm-3)

1.1 x 1018

4.7 x 1017

6.8 x 1016

④ CVD IIa 3.0 x 1016

1-100

1-100

1-100

1-10

N conc.(ppm)

③

ODMR measurements

①

②

③

④

23

Diamond crystal

Intrinsic siliconeGap tunable flux qubit

HPHT Diamond (NV: 4.7 x 1017cm-3)

NV center concentration: 4.7 x 1017 cm-3 , N2 concentration : 1-100 ppm

35 MHz splitting shows strong coupling between NV centers and a flux qubit

● Diamond mounted flux qubit

35 MHz

Shift pulse height (arb. units)

Freq

uenc

y (G

Hz)

24

Time (ns)

Shift

pul

se h

eigh

t (ar

b. u

nits

)

T (ns)

Swit

chin

g pr

obab

ility

Vshift = -0.0115 V

Coherent oscillations between qubit and NV spin ensemble

HPHT Diamond (NV: 4.7 x 1017cm-3)

Without a diamond chipT1_qb = 900 ns @ 2.88GHzT2* _qb= 280 ns

With a diamond chipT1_qb = 270 ns @ 2.78 GHzT2*_qb = 100 ns

T1_NV >> 10usT2*_NV = ?

25

T (ns)

Swit

chin

g pr

obab

ility

Vshift = -0.0115 V

Coherent oscillations between qubit and NV spin ensemble

HPHT Diamond (NV: 4.7 x 1017cm-3)

Without a diamond chipT1_qb = 900 ns @ 2.88GHzT2* _qb= 280 ns

With a diamond chipT1_qb = 270 ns @ 2.78 GHzT2*_qb = 100 ns

T1_NV >> 10usT2*_NV = ?

26

Change the direction of the in-plane magnetic field

To improve coherence time of the NV ensemble

VN

x

y

z(001)

(001) substrate, B// ∝ (100)

x

y

B//

B//x

y

z

(110) x

y

B//

(110) substrate, B// ∝ (111)

B//

Improve the quality of diamond

Reduce P1 center (N impurity) from 100 ppm to 25 ppmIncrease the qubit persistent current from 300 nA to 600 nA

Same coupling strength of 30 MHz can be expected 27

Fabricate a flux qubit directly on a diamond substrate

To increase the coupling strength

A qubit persistent current x 10The distance between the qubit and the NV ensemble x 1/10

We can reduce the number of NVs by 1/10000N=1x107 -> N=1x103

28

Summary

・ Flux qubit – spin ensemble hybrid system

・ High NV density, zero in-plane magnetic field- Strong coupling and coherent oscillation- Decay time of the oscillation is about 20 ns

・ Middle NV density, zero in-plane magnetic field- Strong coupling and coherent oscillation- Decay time of the oscillation is about 40 ns

29