Manipulating and characterizing spin qubits based on donors in silicon with electromagnetic field

Size: px

Start display at page:

Download "Manipulating and characterizing spin qubits based on donors in silicon with electromagnetic field"

Erick Farmer
5 years ago
Views:

1 Network for Computational Nanotechnology (NCN) Purdue, Norfolk State, Northwestern, MIT, Molecular Foundry, UC Berkeley, Univ. of Illinois, UTEP Manipulating and characterizing spin qubits based on donors in silicon with electromagnetic field Network for Computational Nanotechnology Purdue University West Lafayette, IN 47906

2 Multiple qubits required for quantum computing Challenging problems for classical computing: Search in big data Quantum chemistry simulation Network optimization Large number factorization can be solved efficiently with quantum computing algorithms. Ø Requires multiple coupled quantum bits (qubits) e.g. 4 qubits to factorize a small number 143 Multiple coupled qubits are needed to perform quantum computing. 2

3 The next milestone is to realize two qubits One qubit Single spin operation driven by ac B-field Si P 0 1 Experiment highlights: coherence time: 0.5 s control fidelity: 99.6% J. Muhonen et al., Nature Nanotechnology 9, 986 (2014) 3

The next milestone is to realize two qubits One qubit Single spin operation driven by ac B-field Two qubits Couple two qubits with exchange (J) Si P 0 1

4 The next milestone is to realize two qubits One qubit Single spin operation driven by ac B-field Two qubits Couple two qubits with exchange (J) Si P 0 1 Experiment highlights: coherence time: 0.5 s control fidelity: 99.6% P P J. Muhonen et al., Nature Nanotechnology 9, 986 (2014) P P Kane, Nature 393, 133(1998) 4

5 The next milestone is to realize two qubits One qubit Two qubits Multiple qubits Single spin operation driven by ac B-field Couple two qubits with exchange (J) Si P 0 1 Experiment highlights: coherence time: 0.5 s control fidelity: 99.6% J. Muhonen et al., Nature Nanotechnology 9, 986 (2014) P P P P Kane, Nature 393, 133(1998) D.P. DiVincenzo et al., Nature 408, (2000) A long way to go 5

6 The next milestone is to realize two qubits One qubit Two qubits Multiple qubits Single spin rotation driven by ac B-field Couple two qubits with exchange (J) Si P 0 1 Experiment highlights: coherence time: 0.5 s control fidelity: 99.6% Readout fidelity: 97% J. Muhonen et al., Nature Nanotechnology 9, 986 (2014) P P P P Kane, Nature 393, 133(1998) D.P. DiVincenzo et al., Nature 408, (2000) Understand and design experimental two-qubit devices in silicon. 6

7 The objectives of this work A STM-patterned two-qubit device from our collaborator P donors Characterization - Number of donors - Donor locations - Number of electrons Feasibility Prove that two-qubit operations can be realized Si Images from B.Weber et al, unpublished. 7

8 Outline Characterization of donor-cluster qubits with electron spin resonance (ESR) technique» ESR of a donor-cluster in silicon» Determine the configuration of a donor cluster using ESR ü Donor number ü Donor locations ü Electron number Feasibility: manipulation of two donor-cluster qubits with ESR» Two-qubits SWAP gate can be realized with donor-clusters» Individual manipulation of two coupled qubits with ESR 8

9 Outline Characterization of donor-cluster qubits with electron spin resonance (ESR) technique» ESR of a donor-cluster in silicon» Determine the configuration of a donor cluster using ESR ü Donor number ü Donor locations ü Electron number Manipulation of two donor qubits with ESR» Two-qubits SWAP gate can be realized with donor-clusters» Individual manipulation of two coupled qubits with ESR 9

10 Configurations of the two qubits are unknown Q1 Q2 Images from B.Weber et al, unpublished. Zoom in Q1 : P atom Si atom [010] nm nm nm [100] Q1/Q2 could have various configurations. 10

Importance of a donor-cluster configuration Q1 or Q2: 0.384 nm 0.

384 nm [010] P atom Si atom [100] Q1 and Q2 are exchange coupled.

11 Importance of a donor-cluster configuration Q1 or Q2: nm nm nm [010] P atom Si atom [100] Q1 and Q2 are exchange coupled. 1P D1 D4 Exchange energy Q1 Q2 Images from B.Weber et al, unpublished. A characterization technique is needed to identify configuration. 11

, Nature Nanotechnology 9, 430 435 (2014) map out G1 D Donor-cluster

12 Drawback of existing method Binding energy (BE) of donor-clusters S G2 Binding energy (mev) Electron number B. Weber et al., Nature Nanotechnology 9, (2014) map out G1 D Donor-cluster configuration Quantum confinement Binding energy Compare measurement and theory 12

Drawback of existing method Binding energy (mev) Binding energy (BE) of donor-clusters 1 2 3 4 Electron number S G2 current G1 D No current BE is measurable. BE is hard to be measured. B. Weber et al.

13 Drawback of existing method Binding energy (mev) Binding energy (BE) of donor-clusters Electron number S G2 current G1 D No current BE is measurable. BE is hard to be measured. B. Weber et al., Nature Nanotechnology 9, (2014) Images from B.Weber et al, unpublished. Is there a more general metrology that can characterize the donor-cluster configuration? 13

A metrology based on ESR to characterize clusters Donor-cluster configuration Quantum confinement Hyperfine interaction A (A ψ( r 0 ) 2 ) Electron

14 A metrology based on ESR to characterize clusters Donor-cluster configuration Quantum confinement Hyperfine interaction A (A ψ( r 0 ) 2 ) Electron spin resonance(esr) spectrum measurable Compare measurement and theory A metrology based on ESR is proposed to characterize a donor-cluster qubit. 14

ESR: electron spin resonance Free electron in vacuum: Spin

E=E1 E0 =hγ E 0 Bound electron in a donor-cluster in Si: More

interaction with background nuclei a.c. B-field γ Intensity (a.u.) Example:Single P in silicon J.

15 ESR: electron spin resonance Free electron in vacuum: Spin manipulation with ESR technique e Apply a static external B-field E 1 E=E1 E0 =hγ E 0 Bound electron in a donor-cluster in Si: More complicated for donorclusters in Si Electronic structure Spin interaction with background nuclei a.c. B-field γ Intensity (a.u.) Example:Single P in silicon J. J. Pla et al., Nature 489, (2013) Why 2 ESR frequencies? 15

16 Outline Characterization of donor-cluster qubits with electron spin resonance (ESR) technique» ESR of a donor-cluster in silicon» Determine the configuration of a donor cluster using ESR ü Donor number ü Donor locations ü Electron number Manipulation of two donor qubits with ESR» Two-qubits SWAP gate can be realized with donor-clusters» Individual manipulation of two coupled qubits with ESR 16

17 Effective spin Hamiltonian: Zeeman effect Ø The effective spin Hamiltonian is H spin = H Zeeman + H hyperfine nuclear spin electron spin Involved spins in a P donor in Si ( / ) ( / ) J. J. Pla et al., Nature 489, (2013) H Zeeman External B-field polarizes the spins. γ ESR2 γ ESR1 Only with H Zeeman (without hyperfine interaction): γ ESR1 = γ ESR2 (a.c. B-field frequency) Can only detect 1 frequency. Why 2 in experiment? 17

, Nature 489, 541-545 (2013) γ ESR2 γ ESR1 γ ESR2 = γ ESR1 H hyperfine couples electron and nuclear spin, H

18 Effective spin Hamiltonian: hyperfine effect Ø The effective spin Hamiltonian is H spin = H Zeeman + H hyperfine Involved spins in a P donor in Si ( / ) ( / ) J. J. Pla et al., Nature 489, (2013) γ ESR2 γ ESR1 γ ESR2 = γ ESR1 H hyperfine couples electron and nuclear spin, H hyperfine depends on electron wavefunction ψ( r 0 ) 2. Different donor-clusters have different H hyperfine We need to calculate H hyperfine accurately. 18

Impurity model in atomistic TB Capture Fermi-contact hyperfine interaction (A) 1, anisotropic hyperfine interaction (D) 2 of P donors in

19 Hyperfine interaction from atomistic TB To obtain H hyperfine ( ψ( r 0 ) 2 ) accurately, a good solution to wavefunctions of P donors in silicon is needed. Impurity model in atomistic TB Capture Fermi-contact hyperfine interaction (A) 1, anisotropic hyperfine interaction (D) 2 of P donors in silicon to construct H hyperfine 1. Rahman et al., PRL 99, (2007) 2. Park et al., PRL 103, (2009) Atomistic TB provides good solutions to A and D of P donors in silicon to construct hyperfine Hamiltonian. H spin = H Zeeman + H hyperfine 19

hyperfine ü Generalized for few-spin system (m nuclei, n electrons) ü Analyze the ESR frequencies

20 General effective spin Hamiltonian γ ESR2 γ ESR1 A donor-cluster configuration (input) Atomistic TB ψ(r) A D Spin Hamiltonian constructor (this work) H spin and γ (output) H spin = H Zeeman + H hyperfine ü Generalized for few-spin system (m nuclei, n electrons) ü Analyze the ESR frequencies of donor-clusters What are the ESR frequencies of different donor-clusters solved from H spin? 20

21 Outline Characterization of donor-cluster qubits with electron spin resonance (ESR) technique» ESR of a donor-cluster in silicon» Determine the configuration of a donor cluster using ESR 1. Donor number 2. Donor locations 3. Electron number or or How many electrons??? 21

22 1.Detection of the donor number in a cluster Ψ(r) 2 for one electron Y (nm) 1P 2P 3P 4P X (nm) ESR frequencies γ ESR1 γ ESR2 γ ESR1 γ ESR2 The number of ESR frequencies goes up with the number of donor nuclei. 22

23 2. Detection of donor locations in 2P clusters 0.543nm Si atoms Y [010] D1 D3 D2 D4 Different two-donor configurations? Hyperfine interaction (A ψ( r 0 ) 2 ) X [100] ESR frequencies D1 D2 D3 D4 D1 D2 D3 D4 Hyperfine interaction and the separation between ESR frequencies decrease with the distance between two donors. 23

captures the D- binding energy, 2 nd e in 1P*) *Rahman et al.

24 3. Detection of electron number in a cluster ψ(r) 2 in log scale (A ψ( r 0 ) 2 ) 5.5 nm ESR frequencies 2P 3 rd e 5 nm 2P1e 2P3e Ø Multi-electron occupation: self-consistent field method (which captures the D- binding energy, 2 nd e in 1P*) *Rahman et al., PRB 84, (2011) Ø Hyperfine interaction decreases from MHz (1e) to 10.5 MHz (3e). (A ψ( r 0 ) 2 ) Hyperfine interaction and the separation between ESR frequencies decrease with the number of electrons. 24

25 The objectives of this work A STM-patterned two-qubit device from our collaborator P donors Si Images from B.Weber et al, unpublished. Characterization ü Number of donors ü Donor locations ü Number of electrons Feasibility Show that two-qubit operations can be realized 25

26 The objectives of this work A STM-patterned two-qubit device from our collaborator P donors Si Images from B.Weber et al, unpublished. Characterization Number of donors Donor locations Number of electrons Feasibility Prove that two-qubit operations can be realized 26

27 Outline Characterization of donor-cluster qubits with electron spin resonance (ESR) technique» ESR of a donor-cluster in silicon» Determine the configuration of a donor cluster using ESR ü Donor number ü Donor locations ü Electron number Manipulation of two donor qubits with ESR» Two-qubits SWAP gate can be realized with donor-clusters» Individual manipulation of two coupled qubits with ESR 27

28 Two-qubit operations with exchange One qubit Two qubits Multiple qubits Single spin rotation driven by ac B-field Couple two qubits with exchange (J) Si P 0 1 Experiment highlights: coherence time: 0.5 s control fidelity: 99.6% Readout fidelity: 97% J. Muhonen et al., Nature Nanotechnology 9, 986 (2014) P P P P Kane, Nature 393, 133(1998) D.P. DiVincenzo et al., Nature 408, (2000) Two qubits are coupled by exchange which can be controlled. 28

A MOS double QD device A two-qubit logical gate achieved in an analogous device *Veldhorst et al., arxiv:1411.

29 A MOS double QD device A two-qubit logical gate achieved in an analogous device *Veldhorst et al., arxiv: (2014) Two-qubit logic Yes Not yet Central 2 qubits 2 e-spins in DQD 2 e-spins in D1 & D2 Exchange-coupled? Yes Yes Exchange control With G1 & G2 With G1 & G2 ESR Yes No Two-qubit gates can be realized by controlling exchange and ESR. What if we have ESR? 29

30 Operation details: J off, ESR off Qubit 1 Qubit 2 Exchange-coupled Gate bias à exchange (J) No bias, J is off ESR à individual qubit No ESR Wavefunctions: e1 e2 Small overlap à small exchange à slow evolution 30

J is on ESR à individual qubit No ESR Wavefunctions:

31 Operation details: J on, ESR off Qubit 1 Qubit 2 Exchange-coupled Gate bias à exchange (J) with bias, J is on ESR à individual qubit No ESR Wavefunctions: e1 e2 Large overlap à large exchange à fast evolution 31

32 Operation details: J off, ESR on γ 1 Qubit 1 Qubit 2 Exchange-coupled Gate bias à exchange (J) No bias, J is off ESR à individual qubit γ 1 Qubit 2 shouldn t be affected. 32

33 Operation details: J off, ESR on γ 2 Qubit 1 Qubit 2 Exchange-coupled Gate bias à exchange (J) No bias, J is off ESR à individual qubit γ 2 Qubit 1 shouldn t be affected. 33

Two-qubit gates can be realized by controlling J:on/off and ESR: on/off Qubit 1 Qubit 2 Exchange-coupled J: on/off ESR: on/off Summary: Gate bias à exchange (J) No bias, J is off with bias, J is on

34 Two-qubit gates can be realized by controlling J:on/off and ESR: on/off Qubit 1 Qubit 2 Exchange-coupled J: on/off ESR: on/off Summary: Gate bias à exchange (J) No bias, J is off with bias, J is on No bias, J is off No bias, J is off ESR à individual qubit No ESR No ESR γ 1 γ 2 By timing and switching J and ESR accordingly, various two-qubit gates can be realized. Two-qubit gates can be realized by controlling exchange and ESR frequencies. 34

35 Challenges of MOSDQD qubits and opportunities of STM donor devices *Veldhorst et al., arxiv: (2014) ESR source implemented, ESR frequencies tunable with gates Actual metal gate size hard to control -- hard to control separation Confined at interface -- sensitive to interface traps, charge in oxide, gate noise Ref: R. Rahman et al., Phys. Rev. B 85, (2012) ESR source not yet implemented ESR frequencies not tunable With atomic precision -- accurate qubit placement Confined deep away from interface surfaces -- can work in low noise regime S. Shamim et al., Phys. Rev. B 83, (2011). Donor qubit devices with STM lithography technique is more promising to scale up. 35

36 Proposed two-qubit device schematics with donors Qubit1 G 1 G (2P) (1P) 2 readout Qubit2 Images from B.Weber et al, unpublished. Combine S SET ESR D i B.Weber et al.,science 335, 64 (2012); Coupled through e-e exchange: turned on and off by G1,G2 Individual qubit manipulation with ESR 36

J: on/off J Gate bias à exchange (J) No bias, J is off with bias, J is on on ESR à

37 Exchange control in 2P-1P Qubit 1 Qubit 2 Exchange-coupled By timing and switching J and ESR accordingly, various two-qubit gates can be realized. J: on/off J Gate bias à exchange (J) No bias, J is off with bias, J is on on ESR à individual qubit No ESR No ESR Ideal J-control off What kind of system provides good J-controllability? VG1/VG2 37

38 2P-1P provides large exchange tunability Qubit1 G 1 G (1P/2P) (1P) 2 E Qubit2 Asymmetric: large J-tunability J Symmetric: small J-tunability E Wang et al., unpublished. Exchange coupling can be switched on and off in asymmetric 2P-1P systems. 38

Effective spin Hamiltonian: H spin = H Zeeman + H hyperfine + H

logical SWAP gate IN OUT Basis: a b SWAP b a :0 :1 H spin = ( E

ab On ab ba a,b: (0) / (1) J: exchange coupling Two-qubit SWAP

39 Effective spin Hamiltonian: H spin = H Zeeman + H hyperfine + H exchange Logical functionality of exchange: SWAP Truth table of a logical SWAP gate IN OUT Basis: a b SWAP b a :0 :1 H spin = ( E &0@0& E & 0&0@J/ a: 0 / 1 b: 0 / 1 J (on/off) Input output Off ab ab On ab ba a,b: (0) / (1) J: exchange coupling Two-qubit SWAP gate can be realized with electron-electron exchange interaction. 39

40 Time evolution A SWAP gate in 2P-1P Ψ(t) = e i H spin t/ħ Ψ(0), ( H spin is projected on a given nuclear spin configuration) Qubit1 Qubit2 G 1 G (2P) (1P) 2 J (MHz) G1(-), G2(+) 1.6 (off) G1(+), G2(-) (on) SWAP gate realization J(off) J(on) J (on/off) Input output Off(<3ns) ab ab On(> 3ns) ab ba a,b: (0) / (1) / Two-qubit SWAP gate can be realized in a 2P-1P system. 40

Individual qubit control with ESR Qubit 1 Qubit 2 Exchange-coupled By timing and switching J and ESR accordingly, various two-qubit gates can be realized.

41 Individual qubit control with ESR Qubit 1 Qubit 2 Exchange-coupled By timing and switching J and ESR accordingly, various two-qubit gates can be realized. Gate bias à exchange (J) ESR à individual qubit No bias, J is off No ESR J: on/off with bias, J is on No ESR ESR: on/off No bias, J is off γ 1 No bias, J is off γ 2 γ 1 γ 2 should be large enough to be resolved. Is it true for 2P-1P? 41

Qubit1 Qubit2 Qubit1 Qubit2 (2P) (1P) Initial state (input): ESR transition i

42 Individual qubit manipulation with ESR Individual qubit manipulation can be realized in the 2P-1P system. Qubit1 Qubit2 Qubit1 Qubit2 (2P) (1P) Initial state (input): ESR transition i transition γ 1 =39.1 GHz γ 2 =39.3 GHz / / Benefit from using donor cluster (asymmetric system): manipulating one won t affect another. 42

43 The objectives of this work A STM-patterned two-qubit device from our collaborator P donors Si Images from B.Weber et al, unpublished. Characterization Number of donors Donor locations Number of electrons ü Feasibility - two-qubit operations can be realized by controlling exchange + ESR - Asymmetric systems are favorable 43

44 Conclusion Characterization of donor-cluster qubits with ESR» The configuration of a donor-cluster can be distinguished by its ESR spectrum: ü Donor number ü Donor locations ü Electron number Manipulation of two donor-qubits with ESR exchange + individual qubit operations: two-qubit gates» Two qubits with donor-cluster (asymmetric systems): better exchange tunability and distinct driven frequencies» Individual qubit of two coupled qubits can be manipulated with ESR 44

45 Acknowledgement Committee members: Professor Gerhard Klimeck, Dr. Rajib Rahman, Professor Supriyo Datta Professor Michelle Simmons, Professor Lloyd Hollenberg, Holger Buch, Bent Weber, Thomas Watson, Mathew House, Sam Hile Archana Tankasala, Pengyu Long, Zhengping Jiang, Yuling Hsueh, Harshad Sahasrabudhe, Rifat Ferdous, Yaohua Tan, Yuanchen Chu, Hesameddin Ilatikhameneh, Yu He, Xufeng Wang, Kai Miao, Chinyi Chen, Fan Chen, Kuang-chong Wang and all my colleagues Ms. Vicki Johnson, Ms. Leslie Schumacher, Ms. Ashley Byrne 45

46 Thank you! 46

Electron Spin Relaxation of Donors in Silicon Nanoelectronic Devices

Electron Spin Relaxation of Donors in Silicon Nanoelectronic Devices FINAL EXAMINATION Yu-Ling Hsueh Electrical and Computer Engineering Purdue University Outline Introduction to quantum computing and