Electron spin qubits in P donors in Silicon

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Tobias Martin
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1 Electron spin qubits in P donors in Silicon IDEA League lectures on Quantum Information Processing 7 September 2015 Lieven Vandersypen

2 Slides with black background courtesy of Andrea Morello (UNSW Sydney) with minor modifications

3 Kane proposal: phosphorus in silicon Encode quantum information in single P donors spin B. Kane, Nature 393, 133 (1998)

4 P in Si = H in vacuum P vs Si: one more proton Loosely bound 15 th electron of P Bohr radius ~ 2.5 nm Electron spin 1/2 Nuclear spin 1/2 Coulomb binding potential

5 Placing phosphorus in silicon Single-ion implantation Same technology as used in ordinary microchips Challenge: positioning D. Jamieson et al., APL 86, (2005)

The scanning tunnelling microscope can manipulate individual devices to each individual dopant.

logic circuits has been hampered single phosphorus atom between highly phosphorusy the covalent nature of its bonds.

2012 s transistors with extremely short gate lengths4, spin-based a b uantum computers5 8 and solitary dopant optoelectronic Ejected D

Here, we use a combiation of scanning tunnelling microscopy and hydrogen-resist thography to demonstrate a single-atom transistor in which

9 G2 ally placed within an epitaxial silicon device architecture S with a spatial accuracy of one lattice site.

21 tes at liquid helium temperatures, and millikelvin electron [100] ransport measurements confirm the presence of discrete Experiment c

We find a charging energy that is close to the bulk I II III IV 300 only observed by optical spectroscopy10.

dopant atoms within a device will 100 47 ± 3 mev ISD (A) etermine its characteristics11, and the variability in device performg (µs) P 0 0

the physical limits 10 7 Lee et al, Nanotechnology 2014 13 are reached.

6 The scanning tunnelling microscope can manipulate individual devices to each individual dopant. toms2 and molecules on surfaces, but the manipulation of Figure 1 shows the approach we used to determinis ilicon to make atomic-scale logic circuits has been hampered single phosphorus atom between highly phosphorusy the covalent nature of its bonds. Resist-based strategies and drain leads in a planar, gated, single-crystal silic ave allowed the formation of atomic-scale structures on device. This involved the use of hydrogen-resist lithog ilicon surfaces3, but the fabrication of working devices such Fuechsle et al, Nature Nano 2012 s transistors with extremely short gate lengths4, spin-based a b uantum computers5 8 and solitary dopant optoelectronic Ejected D evices9 requires the ability to position individual atoms in Si G1 silicon crystal with atomic precision. Here, we use a combiation of scanning tunnelling microscopy and hydrogen-resist thography to demonstrate a single-atom transistor in which m n individual phosphorus dopant atom has been deterministi2n. 9 G2 ally placed within an epitaxial silicon device architecture S with a spatial accuracy of one lattice site. The transistor opers NATURE NANOTECHNOLOGY DOI: /NNANO tes at liquid helium temperatures, and millikelvin electron [100] ransport measurements confirm the presence of discrete Experiment c uantum levels in the energy spectrum of the phosphorus Saturation dosing Dissociation a 400 b 50 tom. We find a charging energy that is close to the bulk I II III IV 300 only observed by optical spectroscopy10. alue, previously Silicon technology is now approaching a scale at which both the PH3 EC = PH2 H umber and location of individual dopant atoms within a device will ± 3 mev ISD (A) etermine its characteristics11, and the variability in device performg (µs) P 0 0 D0 D D nce caused by the statistical nature of dopant placement is D0 D D+ 100 PH PH3 xpected to impose a limit on scaling before the physical limits 10 7 Lee et al, Nanotechnology are reached. 1 ssociated with 200lithography and quantum effects Controlling the 300precise position of dopants within a device and 10 9 RT T = C nderstanding how this affects device behaviour have therefore Devices on deterministic ecome essential based 0 the placement 1 VG (V) candidates for solid-state f single dopants in silicon are also leading (V) Figure 1 Single-atomVGtransistor based on deterministic posi uantum computing architectures, because the dopants can Theory have phosphorus atom in epitaxial silicon. a, Perspective STM ima 0] [01 VG 0.82 V D D0 VG 0.45 V D+ D0 VSD (mv) VSD (mv) LETTERS nm nm STM lithography for P positioning

7 Reading quantum information H = gµ B B 0 S z γ n B 0 I z + A I S E Empty states Energy-selective tunneling into an electron reservoir gµ B B 0 E F ~ 4 kt Requires gµ B B 0 >> kt N(E) Occupied states = Electron Spin = 31 P Nuclear Spin J. Elzerman et al., Nature 430, 431 (2004)

8 Si MOS Single Electron Transistor Single-electron transistor à modified Si MOSFET SiO 2 Al 2 O 3 island 2DEG gate source Al Si n + n + drain tunable tunnel barriers S. Angus et al., Nano Lett. 7, 2051 (2007); APL 92, (2008)

9 Energy landscape donor reservoir & SET island drain E F plunger gate potential top gate potential E c V top gate V plunger

10 100% contrast charge sensing donor I SET N-1 N N+1 Zero current : neutral donor Finite current: ionized donor V top gate I SET V top gate V plunger

Single-shot spin readout load read empty 1 2 I SET (na) I SET (na) 0 0

4 1 0 0 Time (µs) 500-2 -200 0 200 400 600 Time (µs) 0 + electrical

11 Single-shot spin readout load read empty 1 2 I SET (na) I SET (na) Read Level (mv) Time (µs) Time (µs) 0 + electrical spin-down initialization A. Morello et al., Nature 467, 687 (2010) Single-shot readout of a P donor electron spin

12 Writing quantum information H = gµ B B 0 S z γ n B 0 I z + A I S hν e1 gµ B B 0 A/2 ν n1 ESR ν e1 ν e2 hν e2 gµ B B 0 + A/2 ν n2 hν n1 A/2 γ n B 0 NMR = Electron Spin = 31 P Nuclear Spin hν n2 A/2 + γ n B 0

13 Electron spin resonance B 0 = 1.78 T ν n1 Electron spin-up fraction, f mt ν ESR (GHz) c ν e1 e e -, 31 P 0 31 P + ν n2 n2 ν n1 n1 ν e2 e2 ν e1 purified Hyperfine-split, 28 Si epilayer (with residual Stark-shifted 29 Si concentration of 800 purified 28 ESR lines of P donor Si epilayer (with a ppm) on top of a natural residual 29 Si wafer. Si c, concentration Energy level of 800 diagram the supplementary section A. ν n0 n0 FIG. FIG Device Device structure structure and and electron/nuclear electron/nuclear spin spin qubits. a, Scanning electron micrograph image of device qubits. a, Scanning electron micrograph image of a device similar to Device A, highlighting the position of the donor, similar to Device A, highlighting the position of the P donor, the microwave (MW) antenna, and the SET for spin readout. the microwave (MW) antenna, and the SET for spin readout. b, Schematic of the Si substrate, consisting of an isotopically b, Schematic of the Si substrate, consisting of an isotopically ppm) on top of a natural of the coupled 31 0 Si wafer. c, Energy level diagram system (left) and the ionized 31 of the coupled e 31 P 0 system (left) and the ionized 31 P + + nucleus (right). Arbitrary quantum states are encoded on the nucleus (right). Arbitrary quantum states are encoded on the qubits by applying pulses of oscillating magnetic field 1 at qubits by applying pulses of oscillating magnetic field B the frequencies corresponding to the electron spin resonance 1 at the frequencies corresponding to the electron spin resonance (ESR), e1,2 e B 0 ± A/2, and nuclear magnetic resonance ν n2 ν e2 measured electron coherence times T 2e H 1 ms in both devices (Fig. 2c), only a factor 5 longer than in nat Si [22]. However, using the CPMG dynamical decoupling technique we extended the e spin coherence of the order of 1 second, T 2e DD 31 2e DD =0.56 s in Device B (Fig. 4a). For the 31 P qubit we report coherence measurements in the neutral ( P 0 ) and the ionized ( P + ) case (Fig. 2c,d). The P 0 shows a similar dephasing time to e, T 2n0 2n0 500 µs. The Hahn echo decay was found to be very di erent between Devices A and B, with values 1.5 ms and 20 ms, respectively. As observed before in both single-atom [20] and bulk experiments [8], the nuclear spin coherence = Electron improves dramatically Spin by removing the electron from the P atom. The P + Ramsesey decay times reached the the value T 2n+ = Nuclear =0.6 De- 2n+ =0.6 s Devicvice B, B, which which would would correspond correspond to to an an NMR NMRSpin linewidth linewidth fwhm 0.5 Hz. The simple Hahn echo sequence fwhm 0.5 Hz. The simple Hahn echo sequence preserves preserves the the qubit qubit coherence coherence beyond beyond 1 second, second, T 2n+ 2n+ H = s, s, and and the the CPMG dynamical decoupling extends it beyond 30 s, 2n+ DD CPMG dynamical decoupling extends it beyond 30 s, T 35.6 in Device (Fig. 4a). This 2n+ DD = 35.6 s in Device B (Fig. 4a). This currently currently represents represents the the record record coherence coherence for for any any single single qubit qubit in in solid solid state. state. summary of the coherence benchmarks for 31 A summary and 31 of the coherence benchmarks for e, 31 P 0 and 31 P + in in both both devices devices is is shown shown in in the supplementary section A. The qubit measurement fidelities were extracted The qubit measurement fidelities F from the data in Fig. 3, using method m were extracted developed in from the data in Fig. 3, using a method developed in earlier work [20, 22]. For the qubit, is limited earlier work [20, 22]. For the e qubit, F by the interplay of measurement bandwidth m is limited and electron 2

14 Electron spin resonance B 0 = 1.78 T ν n1 Electron spin-up fraction, f mt ν ESR (GHz) ν e1 ν e2 ν n2 = Electron Spin = Nuclear Spin Hyperfine-split, Stark-shifted ESR lines of P donor

$12 mt Electron spin-up fraction, f 0.4 0.3 0.$

15 Electron spin Rabi oscillations P ESR = 10 dbm f rabi (MHz) 2 1 B 1 = 0.12 mt Electron spin-up fraction, f P ESR = 7 dbm P ESR = 4 dbm P ESR 1/2 (mw 1/2 ) t π/2 = dbm π-pulse fidelity = 10 dbm t p (µs) P ESR = 1 dbm Measurement fidelity = 82% (electrical) 77% (elec. + thermal effects) J. Pla et al., Nature 489, 541 (2012)

16 High-fidelity electron Rabi in 28 Si Spin-up fraction Rabi pulse length (µs)

17 Single-shot nuclear spin readout f ν e1 ν n1 ν e2 Spin-up fraction f ν n2 Δf Δf Time (mins) We can observe nuclear spin quantum jumps

18 Nuclear Rabi electron OFF empty load read read read read ν n0 ν e2 ν e2 ν e2 ν e2 ν RF t p 1.0 Nuclear spin flip prob t p (µs) P = 6 dbm P = 0 dbm P = -6 dbm f rabi (khz) Power 1/2 (mw 1/2 ) Visibility > 97% π - pulse fidelity 98 % J. Pla et al., Nature 496, 334 (2013)

19 Summary electron and nuclear spin coherence timescales in 28Si Muhonen et al, Nature Nano 2014 e Device A 31 P Device B 31 P e 31 P 31 P Ramsey (T 2* ) Hahn-Echo (T 2 ) CPMG (T 2 DD ) 270 µs 570 µs 250 ms 160 µs 430 µs 600 ms 0.95 ms 1.5 ms 580 ms 1.1 ms 20 ms 1.8 s 220 ms 2.7 ms 1.1 s 550 ms 20 ms > 30 s

same technology as normal microchips Reading quantum information: Energy-dependent

20 Summary: single-atom spin qubits A single phosphorus atoms contains 2 qubits: Electron spin and nuclear spin P can be introduced and manipulated in Si using the same technology as normal microchips Reading quantum information: Energy-dependent tunneling of the donor-bound electron Writing quantum information: Magnetic resonance

Quantum Information Processing with Semiconductor Quantum Dots

Quantum Information Processing with Semiconductor Quantum Dots slides courtesy of Lieven Vandersypen, TU Delft Can we access the quantum world at the level of single-particles? in a solid state environment?