J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Quantum Computing and Electron Spins in
Semiconductors
John S. Colton
Brigham Young University
Acknowledgements:
• Some of this research was done at the Naval Research Laboratory
and University of Wisconsin-La Crosse.
• Thanks to Allan Bracker and Barry Jonker at NRL for providing
samples
Current Undergrad Students:
Steve Brown
Benjamin Heaton
Michael Johnson
Mitch Jones
Major Funding:
National Science Foundation
Talk for Physics Department Colloquium at UVU, Mar 25, 2009
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
•
•
•
•
Magnets
Lasers
Optics: polarizers, retarders, lenses, mirrors
Optical detectors: diodes, spectrometer,
photomultiplier tube, photon counter
•
•
Microwave & rf: sources, amplifiers
Electronics: Pulse pattern
generator, voltage detectors
Computers
•
rf amplifier (on stack, just off screen)
40 fs pulsed laser, 1 W, 800 nm
computer
microwave generator
microwave amplifier
computer
1.2 T electromagnet (1-2 tons)
boxcar integrator
computer
pulse pattern generator
lockin amplifier
Pause for video
photomultiplier tube
5W green laser
spectrometer
8T superconducting
magnet with cryostat
…and windows!
balanced
diode
detector
1W tunable laser, 700-1000 nm
Colton Lab at BYU, 23 Mar 2009
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spins in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What is a computer?
 Takes a number, does a
calculation
So you want to buy a computer…
• CPU
– Does the work
• Memory (0’s and 1’s)
– RAM (calculations)
– Hard disk (storage)
• Output (read-out)
– Monitor
– Printer
• Input
– keyboard
– mouse
• Communication
– Network adapter
– Modem
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What is a quantum computer?
A quantum computer is:
• a computer (eg. calculating device)
• uses quantum states for bits
 uses physics (laws/interactions) to
manipulate states (i.e. do the calculations)
The quantum states called qubits
Any quantum states are potential qubits
(but some are more likely to be useful than others)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
A Little Bit of Quantum Mechanics
• Electron Energy Levels in atoms
– light absorbed
– light emitted
• When observation is made, you
see electron in one of these
states
E.g. “Wavefunction is in n = 1 state”
photon emitted when
electron hops down
From Fishbane et al.,
Physics for Scientists and Engineers
• In between observations, electron
may be in combination of states
– Superposition Principle
E.g. “Wavefunction is split
between n = 1 and n = 2 states”
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Quantum Mechanics, cont.
Superposition state (notation: “ 1 ” = “state 1”)
  C1 1  C2 2
C1 and C2 represent the contributions of the 1 and 2
states to the overall combined state.
With a neighboring, interacting particle:
  C1 11  C2 12  C3 21  C4 22
represents combined state with particle 1 in state 1
and particle 2 also in state 1
With three interacting particles: 8 terms in the combined state
With N interacting particles: 2N terms in the combined state
 an incredibly large number for even moderate N
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What good is a quantum computer?
Faster Calculations!
(For certain applications)
Application 1: Modeling other quantum systems
Storing information about quantum state difficult!
33 particle state: 233  8 billion (1 gigabyte)
“Simulating physics with computers,” R. Feynman, 1982
“… if a computer simulates [a description of
an isolated part of nature with N variables]
by actually computing or storing this
function, then doubling the size of nature
(N2N) would require an exponentially
explosive growth in the size of the
simulating computer.”
“I therefore believe it’s true
that with a suitable class of
quantum machines you
could imitate any quantum
system, including the
physical world.”
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Application 2: Cryptography
Send Messages
Encrypted
public key
encode
Classical
Me
private key
decode
Read Messages
• RSA Protocol, 1977
– Can only deduce private key
by factoring large numbers,
not from public key
• Peter Shor, 1994: Factoring with
Quantum Computer
– Time exponentially faster!
Quantum
From http://www.themilkyway.com/quantum/FinalReport/
FactorisationOfNumbers.html
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What is a quantum computer? (revisited)
Quantum states used to represent computer bits
Regular Computer
•
•
•
•
•
CPU
Memory
Output
Input
Communication
• Error correction
Quantum Computers
The Five “DiVincenzo Criteria”
• Scalable physical system with
well-defined qubits
• Preparable in ground state
• Able to do many operations
(~10,000) before decoherence
• Universal set of operations
• Accurate single qubit
measurements
(Quantum communication)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spins in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What is spin?
• Fundamental property of particles
 Like charge, mass, etc.
• Related to angular momentum
• Can point in any direction, but has fixed
magnitude
 Electron spin = ½
(in the usual units)
B=0
B0
From Haliday & Resnick,
Fundamentals of Physics
“Stern-Gerlach experiment”
Image credit: wikipedia
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
How do you study spin?
Zeeman Effect
• Energy levels split when
E
magnetic field applied
“spin up” +½
Microwave photons: • A very natural two level
DE = g mB B
system
magnetic resonance
• Electrons in
h f = g mB B
“spin down” –½
semiconductors have spin
– Potentially scalable!
B
• Potentially “long”
coherence times
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
How do you study spin? (cont.)
Spins interact with other spins
• Think of spin as bar magnet
• Produces magnetic fields
• Is affected by other magnetic
fields
→ Spins can cause other spins to
change in ways you don’t want
http://www.bruker-biospin.com/brukerepr/
continuouswavetheory.html
Magnets precess in
applied (transverse) fields
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Spin directions & lifetimes
• asd
B-field
z:   0
z :   1
1
0 1

2
1
y :   ?? 0  ei 45 1
2
x:  

“Bloch Sphere”
Image credit: Wikipedia

Transverse spins fundamentally different
Spin lifetimes : how long does spin stay in state
• T1 – from z to –z: “spin flip time”; change in energy
• T2 – transverse: “spin decoherence time”
• T2* – inhomogeneous (transverse) dephasing time
In general: T2* ≤ T2 ≤ T1
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spins in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
What is a semiconductor?
Conductors (metals)
• elements (silver,
gold, etc.)
• alloys (brass,
steel, etc.)
Insulators
• crystalline (salt,
quartz, etc.)
• non-crystalline
(glass, rubber, wood,
plastic etc.)
Semiconductors
• elements (silicon,
germanium)
• alloys (gallium
arsenide, etc.)
 crystalline
 electrons not very
free to move
 regular structure—
 you can affect
they are crystals
 electrons free to
move
conduction and other
properties via (controlled) impurities: “doping”
 electrons not free to
move
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
How do you make semiconductors?
• “Bulk” growth of substrate
– Dip “seed crystal” into
molten silicon and slowly
remove
– Slice into “wafers”
A silicon boule
Image credit: wikipedia
• High purity layers
– “epitaxial” growth,
layer by layer
A typical MBE machine
Image credit: wikipedia
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Semiconductor Nanostructures
• Confinement
– Quantum wells – confined in 1D
– Quantum wires – confined in 2D
– Quantum dots – confined in 3D
7.5 nm InGaAs
http://lmn.web.psi.ch/shine/sigec.htm
Image: Carbon Nanotube, wikipedia
http://www.fkf.mpg.de/mbe/research.html
http://www.lpn.cnrs.fr/en/ELPHYSE/FaitsMarquants/
FM_ELPHYSE_Absorbsat.php
http://pages.unibas.ch/phys-meso/Pictures/
pictures.html
http://pages.unibas.ch/phys-meso/Pictures/
pictures.html
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
A Semiconductor Quantum Computer?
Quantum-dot array proposal
http://www.research.ibm.com/ss_computing/
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Time Line
Quantum Computers: Where are we now?
•
•
•
•
•
•
1985 Deutsch: algorithm for even vs. balanced
functions
1994 Shor: algorithm for factoring
1996 Grover: algorithm for database search
1998 Spins in semiconductors proposals
(electron/nuclear)
2001 Computer built! Vandersypen et al.
2009 – State of the art semiconductor: 2 qubits
15 = 3  5
Nuclear spins in molecule:
7 qubits to factor 15
Nature 414, 883 (2001)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Lightly-doped n-GaAs (impurities add extra electrons)
Electrons confined to donors—spin similarities with QDs
3E14 cm-3 “bulk” sample
3E10 cm-2 quantum well, 14 nm
(other narrower wells on top)
AlGaAs barrier
1 mm n-type GaAs
AlGaAs barrier
14 nm GaAs (mod.doped)
AlGaAs barrier
AlGaAs barrier
GaAs substrate
GaAs substrate
exciton
(higher energy)
negative trion
Free exciton
(higher energy)
Donor-bound exciton
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
T1 measurements: 3 data points for bulk
Hanle effect measurements
•
•
•
3E15 cm-3 sample (Colton et al., 2004)
– T1 up to 1.4 ms (1.5K, 5T)
1E15 cm-3 sample (Colton et al., 2007)
– T1 up to 19 ms (1.5K, 3-7T)
5E13 cm-3 sample (Fu et al., 2006)
– T1 up to 3 ms (1.5K, 2-4T)
T2: thought to be T1
•
Microseconds in QDs
– Gated GaAs (Harvard, Delft)
– Self-assembled InGaAs (Dortmund)
Why is T2* shorter? Random nuclear spins
Dzhioev et al., Phys Rev B (2002)
 
H  AI  S
T2* spin lifetimes of ~ 1-200 ns
(inhomogeneous dephasing)
(Agrees with time-resolved Faraday/Kerr,
magnetic resonance, etc.)
Beff
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
DiVincenzo Criteria, Revisited
•
•
•
•
•
Scalable physical system with well-defined qubits
Preparable in |000...> state
Able to do many operations (~104) before decoherence
Universal set of gate operations
Accurate single qubit measurements
Where do I fit in?
•
•
•
•
Electron spins in semiconductors (GaAs)
Investigating coherence (dephasing times)
Manipulating spin via magnetic resonance
Optical polarization and detection
More about optics…
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spins in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
How to study spin: Optics!
• In many semiconductors, optical polarization connects
to spin polarization
– Light: polarization = how the electric field oscillates
– Spin: polarization = what fraction of the electrons’ spins point
in a particular direction
Linear Polarization
Circular Polarization
image credits: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Using Optics: III-V Semiconductors
• Spin Orbit Coupling:
J=L+S
Atomic
• Optical selection rules
for circular polarized
light
Spin Polarization ↔ Optical Polarization
(Yu and Cardona)
CB
J = 1/2
L=0
S = 1/2
-1/2
+1/2
s+
hh
lh
so
J = 3/2
J = 1/2
L=1
S = 1/2
-3/2 -1/2 +1/2 +3/2
-1/2
+1/2
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Optical Orientation of 1E15 Sample
Photoluminescence
Look at the “glow”
that is produced by
shining a laser at the
material (aka
fluorescence)
• Right-Circular Polarized Laser
• For each power density
– Top curve is right circular detection
– Bottom curve is left circular detection
– Degree of polarization = (RCP-LCP)/total
• More power  More polarization
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Classic Faraday/Kerr Rotation Experiments
• Linearly-polarized light = superposition of RCP and LCP
• Aligned spins affect RCP/LCP light differently
→ Causes rotation of linear beam being transmitted/reflected
mm)
J. Kikkawa and D. Awschalom,
Phys Rev B 80, 4313 (1998)
Nature 397, 139 (1999)
Doped electrons in GaAs extend spin lifetime to 100+ ns (“long”!!)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spin in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Optically Detected Magnetic Resonance
Recall Zeeman effect slide
E
Why optical?
• Directly interacts with
electron spin
– Initialization
– Readout
• High sensitivity, can
probe small structures
“spin up”
“spin down”
+½
–½
Microwave photons:
magnetic resonance
h f = g mB B
B
Why magnetic resonance?
• Can measure spin lifetimes
– Including T2
• Information about hyperfine
interaction (electron-nuclei)
• Microwaves directly affect spin
– Coherent manipulations
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Hyperfine Interaction with Nuclei
H = A S•I, effective magnetic field
Effect on electrons
• “Overhauser Effect”
– Electrons polarize nuclei
– Polarized nuclei produce
effective magnetic field
Effect on nuclei
• “Knight Shift”
– Polarized electrons
shift nuclear
resonance
Effect on both
• Inhomogeneous line
broadening
Our solution: Prevent the nuclei from becoming polarized
• If circularly polarized laser, alternate RCP/LCP
• Use linearly polarized probe laser sometimes
• Use pulsed laser sometimes
• Resonate nuclear frequencies
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Low Field (<0.1 T) Magnetic Resonance
laser
photoelastic
modulator
PMT
lens
VHF & rf
PL
polarization
analyzer
spectrometer
B
0
liquid He
cryostat sample
Polarize – Depolarize – Detect
•
•
•
•
Polarize with RCP light (alternating with LCP)
Depolarize with resonant VHF circuit
Detect with optical PL polarization
rf coils to deal with nuclei
B0
Brf
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Low-field ODMR Results
(curves shifted vertically for clarity)
J.S. Colton et al, Solid State Comm 132, 613 (2004)
J.S. Colton et al, Phys Rev B 67, 165315 (2003)
• Position  g-factor
– -0.42, -0.41, -0.42
• Width  lifetime
– 47 ns, 35 ns, 5 ns
• 1.2 mT very sharp!
• 5 ns lifetime for 3E14
sample
– Matches theoretical
prediction for fully
localized case
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Electron-Nuclear Coupling
0.3
Electron polarization changes
Nuclear polarization changes
Effective field changes
0.25
44
0.2
43
0.15
42
0.1
41
0.05
goes to 0
40
0.01
0.1
0
1
Peak amplitude ( D P/P)
Electron resonance reached
45
Peak position/width (mT)
If No Nuclear Resonance
10
rf power (W)
Electrons go off-resonance
• Vary sweep coverage
– Deduce NMR peaks broadened
to 50-100 kHz
• Vary rate of sweep
– Deduce nuclei take ~2s to
polarize
Peak unobservable without
simultaneous nuclear resonance!
rf freq.
71Ga
69Ga
t
As
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spin in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
T1: Time Resolved PL Polarization
(detector)
(excitation)
(detector)
• Pulse sequence generator turns cw laser on/off
• Long/short pulse sequences can be done: “pump/probe”
– No need for pulsed laser
– Pump/probe beams in same line
• No delay line
– Can easily probe long times
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Single Light Pulses…
CW light
Pulsed light
(3E15 sample)
•
•
•
•
CW results: shown earlier in talk
Similarity between CW and pulsed light
Pulse results: sets conditions for pump & probe lengths
– Pump: Re-orients electrons
– Probe: Allows polarization to be detected without much re-orientation
Photoelectrons replacing doped electrons in n-type samples
– Number of injected electrons must be comparable to doped electrons
to get appreciable polarization
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Data: n = 110-15 cm-3 sample
• T1 vs B for the 4 temps
• Some raw data
>20
ms (1.5K,in7T)
zoomed
Beautiful exponential decays!
3.3
3.0
25000
1750
22500
1500
20000
1E15 sample
2.8
1.5K: S = 2134 ns
2.5
1E15 sample: all data
1E15 sample: all data
5K
5K: 369 ns
2.0
1.8
8K: 180 ns
1.5
1.3
12K: 116 ns
16K: 88 ns
1.0
0
500
1000
1500
2000
1.5 K
1.5 K
1250
17500
2.3
(ns)
T1 (ns)
PL Polarization (%)
2000
1 T raw data
15000
1000
8K
12500
750
10000
500
7500
5K
12 K
8K
5000
250
2500
3000
Pump-probe delay (ns)
3500
4000
2500
0
0
0
0
1
1
2
2
3
3
4
4
5
5
6
6
12 K
7
7
Magnetic
Magnetic Field
Field (T)
(T)
Theory: T1 decrease with B expected for QDs
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Quantum-dot-like behavior?
My data
Rashba spin relaxation
Bulaev and Loss, PRB 71 205324 (2005)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spin in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
A Microwave Resonant Cavity
• Magnetic resonance (esp. pulsed resonance):
– Need strong ESR microwave (AC) B-field
– Previously: VHF used resonant LCR circuit—low fields only
– Now: resonant cavity
“I want louder!”
“That’s great!”
(if you happen
to match the
bell frequency)
“Bell” = Metal
cylindrical shell
Image credits: wikipedia
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Cylindrical TE011 Resonant Cavity
Maxwell Equations predict
standing AC waves
• “011” specifies Bz
– 0: no f dependence
– 1: one antinode across center
– 1: one antinode top to bottom
• Strong B field in center by sample
• Weak E field in center near
sample
– Avoids sample heating & cavity
losses
• Surface currents allow for holes
– Optical access!
Simulations: CST Microwave Studio
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Cavity with Dielectric Resonators
• Dielectric to increase the “optical
path length”
– 10 GHz with just 1 inch diameter
• Optical access
– Two stacked dielectrics
– Hole in metal shell
• Held in place by Teflon (later:
Rexolite)
• NMR: string a wire down the
middle (later: outside)
• Coupling loop to “ring” the cavity in
correct mode
• Spring to hold things tight (later:
two springs)
• Later: interchangeable
dielectrics
Colton & Wienkes, RSI 2009
1”
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
8.5 – 12 GHz Microwave Resonant Cavity
Different “dielectric resonators”:
•
•
5 possible resonant frequencies
Q-factors (without sample): 2000-5000
Goals:
• Use microwaves to measure and
manipulate spin
• Develop techniques for seeing
coherent oscillations (Rabi) and,
e.g., measuring T2
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Outline
• Quantum computers
– What is a quantum computer?
– What good is a quantum computer?
• Spins in semiconductors
– What is spin? How do you study spin? Spin lifetimes
– What are semiconductors? Semiconductor nanostructures?
– Optics for studying spin in semiconductors
• (Some of) My experiments
– Low field (~40 mT) spin resonance
– Time-resolved photoluminescence polarization
– Design/testing of microwave resonant cavity
– High field (~2T) magnetic resonance
• Conclusion
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Kerr rotation optical detection
Linearly
polarized
probe
laser
Balanced
detector
vert
horiz
Polarizing
beam
splitter
Computer
Lockin amplifier
data
Difference signal
 proportional to polarization angle
 proportional to spin polarization
reference
Resonant
cavity
Sample in cryostat
control
control
Pulse sequence
generator
PIN diode Microwave source/amplifier
switch
• Polarize via thermal effects (Boltzmann factor)
• Depolarize with resonant microwaves
• Detect with Kerr rotation of linear polarized laser
Typical ODMR peak
• QW sample
• width: T2*  10-15 ns
Various optical powers
KR signal (arb units)
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
uwave: 11 dBm, 50% duty, 7 kHz rep rate
laser: 0.1 mW
field sweep 1T/min
1.55 1.60 1.65
1.70 1.75 1.80 1.85 1.90
Magnetic Field (T)
“Probe” is affecting system
microwave power 15 dBm
KR Signal (arb units)
0.01
light power
6.011 mW
1E-3
3.005
1.507
0.751
1E-4
0.376
0.185
1E-5
30 Jan 2009, files 9-18
0.0927
0.049 mW
1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82
(External) Magnetic Field (T)
What’s going on?
• Linear polarized probe laser
→ unpolarizes electrons
• Electron spins polarize the nuclei
(when taken out of equilibrium)
• Nuclear spins produce Beff, etc.
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Microwave pulses needed to (hopefully) control spins
Problems:
KR signal (arb units)
1 us pulses (30 dBm)
40 us pulses (17 dBm)
(1) Lockin response limited to 100 kHz (10 ms)
(2) Need to use as little laser power
as possible
70 us pulses (11 dBm)
(50% duty cycle)
1.70
1.75
1.80
1.85
1.90
Magnetic Field (T)
microwave
boxcar 1 gate
(microwave response)
Pulses
Solutions:
• use boxcar integrators
 gated signal detection
via analog electronics
• use pulsed light in addition
to pulsed microwaves
mwave
boxcar1
laser
boxcar2
repeat after
a long time
Signal =
BC1 – BC2
laser
boxcar 2 gate (reference)
Time
Later: BC2 not always needed
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
KR Signal (arb units)
Pulsed Microwaves, cw light
26 dBm, 5 us pulses
10 kHz rep rate
laser: 0.3 mW
Boxcar can be as good as lockin
 possibly better
lockin
Still see ODMR peaks
down to 10 ns gates!
boxcar, 5 us gate
1.70
1.72
1.74
1.76
1.78
1.80
1.82
Magnetic Field (T)
files 11-16
26 dBm
10 kHz rep rate
0.3 mW
26 dBm
boxcars
10 kHz filter
5 us pulses
1 us pulses
Allows for
very short
pulse
lengths, little
loss of S/N
2 us pulses
500 ns pulses
200 ns pulses
1.72
1.74
1.76
1.78
1.80
Magetic Field (T)
1.82
500 ns gate
KR Signal (arb units)
KR Signal (arb units)
20 Feb 2009
26 dBm
500 ns pulses
20 kHz rep rate
200 ns gate
va
ga
26
box
ove
ligh
100 ns gate
p
50 ns gate
10 ns gate
100 ns pulses
1.72
1.74
1.76
1.78
1.80
Magnetic Field (T)
1.82
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Pulsed Light (pulsed microwaves at same time)
26 dBm, 1 us
10 kHz rep rate
0.3 mW
1.72
1.74
1.76
KR Signal (arb units)
KR Signal (arb units)
19 feb 2009
file 17
1.78
1.80
1.82
Magnetic Field (T)
32 dBm, 500 ns
1 kHz rep rate
overall rep rate 1 kHz
laser: 5.5% duty cycle
(55 us)
1 mW
0.5 mW
0.25 mW
1.70
1.72
1.74
1.76
1.78
1.80
1.82
Magnetic Field (T)
• Why the difficulty?
– Our current idea: the vast difference in signal between light
on/light off is “leaking through” the boxcar somehow
– Limited success came only when light pulses long enough that
we could filter out that component of the signal and leave
behind the faster response to microwaves
• Requiring that long of light pulses ruins the major benefit
• Giving up nice idea…for now
20 Feb 200
files 28-32
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Spin LED
25% polarized
PL signal (arb units)
Black: 0T
Red: 2T
0.20
0.15
0.10
0.05
0.00
780
•
800
820
840
Wavelength (nm)
Iron spin contact
– Spin polarized electrons into 10 nm QW
•
•
•
•
0.30
0.25
-0.05
0% polarized
Image from Jonker, Proc IEEE 2003
0.35
Substantial optical/spin polarization when B  2 T
Eliminates probe beam altogether!
Also: doesn’t rely on low T to initialize spin
Experiments planned for immediate future
860
-0.10
880
PL Polarization (dashed)
0.40
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
It’s not a bug, it’s a feature…
Nuclear spin has a relaxation time of 2.3 minutes
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Nuclear Polarization
vs. Resonating field
of our Helmholtz coil
As with laser, if
microwaves too
strongly affect
electron spins, they
polarize nuclei
→ Must resonate
the nuclear spins
more strongly
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Spin Oscillations?
Quantum Well Sample
Bulk Sample
Microwaves turn on
Microwaves turn on
boxcar
gate
Long T1≈ 50 μs
Short T1≈ 200ns
• Oscillations gone (different) when not on microwave resonance
• Oscillations present at 1.5K, but not at 5K
• Source of spin oscillations?
– Wrong dependence on field to be coherent precession
– Wrong dependence on microwave power to be Rabi oscillations
J.S. Colton, Quantum Computing and Electron Spins in Semiconductors
Conclusion: the “take home” message
•
•
•
•
•
•
Quantum computing is cool
Semiconductor nanostructures are cool
Spins are cool
Lasers are cool
Microwaves are cool
Interesting/important physics
–
–
–
–
Interplay between electron and nuclear spins
Measuring “long” spin lifetimes
Spin relaxation mechanisms
Coherent oscillations
• Future plans: other materials, nanostructures
→ We’re always looking for a few good graduate students at BYU!
http://www.physics.byu.edu