M. L. W. Thewalt , A. Yang, M. Steger, T. Sekiguchi, K. Saeedi, Dept. of Physics, Simon Fraser University, Burnaby BC, Canada V5A 1S6
T. D. Ladd, E. L. Ginzton Laboratory, Stanford University, Stanford CA, USA (now HRL)
K. M. Itoh, Keio University, Yokohama, Japan
H. Riemann, N. V. Abrosimov, IKZ, Berlin, Germany
A. V. Gusev, A. D. Bulanov, ICHPS, Nizhny Novgorod, Russia
A. K. Kaliteevskii, O. N. Godisov, “Centrotech-ECP”, St Petersburg, Russia
P. Becker, PTB, Braunschweig, Germany
H. J. Pohl, VITCON Projectconsult GmbH, Jena, Germany
J. J. L. Morton, Oxford, UK
S. A. Lyon, Princeton, USA
Avogadro
Project
Highly Enriched 28Si – new frontiers in semiconductor spectroscopy
SILICON – 2010 Nizhny Novgorod
E
T0 R.T.
bare EG
actual EG
EG depends on M due to zero point
motion
ΔE
The renormalization goes as M -1/2
recent review:Cardona and ThewaltReviews of Modern Physics 77, 1173 (2005)
Natural Si: 92.2% 28Si + 4.7% 29Si + 3.1% 30Si I = 0 I = ½ I = 0
Why does the isotopic composition affect electronic and optical properties?
the electron-phonon interaction
Eg(0) increases by ~2 meV from 28Si to 30Si
~62 meV for natSi
9275.0 9280 9281
T=1.3 KB1NPa1
NP
28Si
natural Si
Pho
tolu
min
esce
nce
Inte
nsity
Photon Energy for natural Si (cm-1)
D. Karaiskaj et al., Phys. Rev. Lett. 86, 6010 (2001) [ FWHM < 0.005 cm-1 ]
P BE Boron BE
The spectroscopic challenge of highly enriched 28Si
( 8 cm-1 ~ 1 meV )
Boron BE
200 neV !
a
Improved shallow bound exciton linewidths – observation of the 31P ground state hyperfine splitting in the donor bound exciton transition.Phys. Rev. Lett. 97, 227401 (2006). Nuclear and electron spin readout…
31P prime Si qubit
candidate
can we use this to
polarize the spins?
Initialization problem
Almost zero equilibrium polarization
Hyperpolarizationusing optical pumping
Phys. Rev. Lett.102, 257401 (2009)
Resolved bound exciton hyperfine spectroscopy gives the populations of all four donor hyperfine levels in a single measurement
Nuclear polarization of 76% and electronic polarization of 90% are achieved simultaneously – in less than 1 second!
Higher polarization should be possible with reduced linewidths
New experiments: NMR on dilute 31P in 28Si using optical polarization and optical nuclear spin readout
CW NMR
55,846,700 55,846,750
FWHM = 24 Hz
RF power: -75dBm (40 µV)B = 844.77 G
PL
inte
nsity
RF frequency (Hz)
pump 8, probe 10
Why 845 Gauss?Schematic energy diagram
Magnetic field (nonlinear)
Max. 55.85 MHz
Min. 61.68 MHz
844.9G 34,043G
A = 117.53 MHz
Ener
gy (n
onlin
ear)
A
ge = 1.99850g31P = 2.26320e, 31P
Magnetic Field Dependence
55,846.65
55,846.70
55,846.75
61,677.15
61,677.20
61,677.25
Magnetic field (Gauss)
e: probe 4, pump 6RF: -75 dBm (40 µV)
f0=61,677.172 kHzB0=844.85 G
RF
frequ
ency
(kH
z)
e: probe 10, pump 8 RF: -75 dBm (40 µV)
840 845 850
f0=55,846.712 kHzB
0=844.89 G
transient NMR - Rabi Oscillations
0.0 0.5 1.0 1.5 2.0
PL
Inte
nsity
Time (ms)
pump 8, probe 10lasers always on
RF: CW 15 dBm (1.26V) at 55,846,714 Hz
First pulsed NMR -Ramsey Fringe Experiment
p/2
t
p/2
Lasers
on (polarizing)
measurement
off
RF pulseson
off
RF freq. = Resonance freq. +/– 1 kHz fringes of 1 kHz
signal
Ramsey FringesTemperature (Pressure) dependence
fRamsey
= 2,453.6 Hz, T2* = 21.0 ms
T=4.2K (P=1atm)
0 10 20 30
PL
inte
nsity
t (ms)
T=1.3K (P=1.0Torr)fRamsey
= 975.4 Hz, T2* = 16.4 ms
RF=55,847,712 HzPump 8(), Probe 10(), ; RF = 55,847,712 Hz;
probe
pump
RF
31P Donor Hyperfine Constant
me RF freq. (Hz)
Fringe freq. (Hz)
NMR freq. (Hz)
55,845,712.0 1,024.9
55,846,736.8(1)55,847,712.0 975.4
Σ = 2,000.3
61,676,172.0 1,027.2
61,677,199.1(1)61,678,172.0 972.9
Σ = 2,000.1
Hyperfine constant A = 117.523 935 9(2) MHz at T=1.3K
[existing value 117.53(2) MHz]
At 4.2 K and 1 atm, A is 3.116 kHz (26.5 ppm) lower! Why?
At T=1.3K (P=1.0Torr)
Pulsed NMR—Hahn echo method—
p/2
t
p/2
Lasers(Pump&Probe)
on
measurement
off
RF pulseson
off
fRF = fNMR
Signal decay with 2t measurement of T2
PL signal
rotation for optical readout
refocusing
(initialization)
t
p
0 500 1000
10
100
1000
ampl
itude
2 tau (ms)
Hahn echo result: 61,677,199 Hz, pump 6, probe 4, B = 845.3 G, T = 1.3 K (P = 1.0 Torr)
T2 = 250 ms
0 500 1000
10
100
1000
ampl
itude
2 tau (ms)
Hahn echo result: 61,677,199 Hz, pump 6, probe 4, B = 845.3 G, T = 1.3 K (P = 1.0 Torr)
T2 = 250 ms
T2 from Hahn Echo Method
probe
pump
RF
T2 = 250 ms
2t (ms)
PL
inte
nsity
Pump 6(), Probe 4(); RF = 61,677,199 Hz; B = 845.3 G, T = 1.3 K (P = 1.0 Torr)
Highly Enriched 28Si – new frontiers in semiconductor spectroscopy
Resolved donor bound exciton hyperfine structure:
- optical readout of 31P electron and nuclear spin - fast optical hyperpolarization of electron and nuclear spin - possibility of single donor readout - promising new approaches to silicon quantum computing - have begun NMR of 31P in 28Si combining optical readout and optical hyperpolarization
Studies which were thought to be limited to isolated single atoms and ions in vacuum are now becoming possible in semiconductors.