Download Manipulation and detection of electron charge/spin qubits

Meeting of FIRST QIP Project/Quantum Cybanetics
Kyoto, Dec. 15, 2011
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Manipulation and detection of
electron charge/spin qubits
Agenda
• 
• 
• 
• 
• 
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
Yasuhiro Tokura
NTT Basic Research Laboratories
FIRST Project, theory subtheme
Quantum Cybanetics, semiconductor nano-system
FIRST research theme
Theory of physical qubits
In collaboration with experimental groups
spin qubit system, quantum interface
• Entanglement of two spin qubits (Tarucha, U. Tokyo)
• Interference circuits to initialize and analyze flying spin
qubits (Aharony, Ben Gurion U.)
• Back-action of charge detector (Kubo, poster Thu-3)
• Coherent coupling of flux-qubit and NV ensemble
(Semba NTT, Nemoto NII)
• Quantum computing with coherent photon conversion
(Munro)
Build/predict long-term research directions through
own/integrated theoretical activities in collaboration
with experimental groups.
2005.8.18 那覇平和通り
Q cybanetics research theme
Control, detection, and transfer of quantum states in semiconductor
nanostructure
Spin manipulation, detection
S. Tarucha, U. Tokyo
T. Ota, NTT BRL
• Control of spin-orbit interaction in QD (Oiwa, Tarucha,
U. Tokyo)
• Transport in QD with g-tensor modulation (Ono, Riken)
• Improved spin detection scheme with field gradient
• Quantitative analysis of dynamical nuclear spin pumping (Nazarov, TUD, Ono, Amaha, Riken)
• Quantum capacitance of a few electrons in coupled QD
(Ota, NTT)
2005.8.18 那覇平和通り
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
Two qubits system with split micro-magnets
Dumping of the Rabi
oscillation is originating
from nuclear spin
fluctuations
Rabi frequency is order of
1MHz – need to be faster
R. Brunner et al., Phys. Rev. Lett. 107,
146801 (2011).
5
Manipulation of two spin states
J. Petta et al. Science (05)
cf T. Hatano et al. Science (05).
SWAP operation
One spin manipulation (Hadamard) + two spin SWAP operations
L-ESR 3π/2
|↑� + |↓�
√
|↑, ↑� →
⊗ |↑� →
2
Charge moves
�
(SWAP + L-ESR π2 )
(SWAP2 + L-ESR π2 )
→
→
1
2 {|↑, ↑�
|↑, ↑�
− |↓, ↓� −
√
2S0 }
No charge move
→ Distinguish this change by QPC charge detector
6
Demonstration of partial SWAP and entanglement
Solid lines: theory with being
averaged over the nuclear spin
random distribution
Estimation of concurrence: no effect of
nuclear spin fluctuation is taken into account.
7
Two-qubit Hamiltonian with Zeeman offset
H
=
1
1
J⊥ (σ̂1+ σ̂2− + σ̂1− σ̂2+ ) + Jz σ̂1z σ̂2z
2
4
1
1
+ EZ (σ̂1z + σ̂2z ) + δ(σ̂1z − σ̂2z ),
2
4
EZ
|↑, ↓�
ω
δ
≡
≡
1
(E1Z + E2Z ),
2
E1Z − E2Z
θ
Bloch vector obeys precession frequency
x
|↑, ↓� + i |↓, ↑�
√
2
y
|↑, ↓� + |↓, ↑�
√
2
1
ω≡
2�
�
2
δ 2 + J⊥
around the axis determined by
δ
2
δ 2 + J⊥
cos θ = �
|↓, ↑�
Bloch sphere spanned with two electron Sz=0 basis
8
SWAP cannot be accomplished by controlling J once
Two spin state dynamics is determined by the evolution operator: Û (t)
=




|↑, ↑�
i 1
( 2 Jz +EZ )t
−�
e
0
0
0
|↑, ↓�
0
cos ωt − i cos θ sin ωt
−i sin θ sin ωt
0
|↑, ↓�
θ
|↑, ↓� + i |↓, ↑�
√
2
ω
|↓, ↑�
0
−i sin θ sin ωt
cos ωt + i cos θ sin ωt
0
|↓, ↓�
i
1

0
0
0
e− � ( 2 Jz −EZ )t
|Ψ(t)� = Û (t)|Ψ(0)�
x
|↑, ↓� + |↓, ↑�
√
2
y
|↓, ↑�
9

.

SWAP by three π pulses
SWAP operation is realized with a combination of three π pulses
for a given fixed δ.
z
π/4
2θ1 − θ2 = π/2
π/4 < θ1 < π/2
θ2
π/2-θ2
θ1
θ1
TSW AP
=
=
=
2T1π + T2π
π
π
+
2
2ω1
2ω2
π�
δ
δ
�
{2 �
+
}
2
2
2
2
δ
δ + J⊥1
δ + J⊥2
This scheme cannot realize √SWAP.
x
π/4-θ2/2
10
SWAP by two exchanges and one zero-J pulses
Alternative SWAP operation realized with a combination of three pulses
for a given fixed δ, allowing a √SWAP.
We assume: J >
Time evolution operator:
Usw
U√sw
=
=
U (t, J )
≡
i
−�
Hex t
e
U (T, J ) · U (τ, J = 0) · U (T, J )
τ
τ
U ( , J = 0) · U (T, J ) · U ( , J = 0)
2
2
|↑, ↓�
Operation times are determined by
τ
T
=
=
δ
δ
2
(π − arcsin √
)
2
2
δ
√ J −δ
2
√
sin−1
δ2 + J 2
δ2 + J 2
√
2J
ω
θ
|↑, ↓� + i |↓, ↑�
√
2
y
|↓, ↑�
x
|↑, ↓� + |↓, ↑�
√
2
11
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
Spin-charge conversion/charge detection
N
N-1
N+1
J. M. Elzerman, et al.,
Nature 430, 431 (2004).
Spin-to-charge
conversion
Level separation EZ >> kBT
Destructive measurement
A high sensitive charge sensor is realized by a
quantum point contact, but how to detect spin ?`
Signal
Idot
IQPC
QPC
electrometer
Signal only discriminates spin singlet/triplet or just spin flip!
K. Ono, et al., Science 297, 1313 (2002).
New spin detection scheme
Non-destructive both spin readout with micro-magnet and microwave
Y. –S. Shin, et al., Phys. Rev. Lett. 104, 046802 (2010).
Backaction dephasing by a quantum dot detector
Environment
The quantum dot detector (QDD)
couples to the reservoir with a
large number of degrees of freedom.
Thermal noise,
Charge noise,
Current noise,…
Backaction by coupling with
an environment
• Capacitive coupling to neighboring QDs in multi-qubit systems
• Spin-charge conversion in spin qubits
Origin of backaction dephasing
γd1: Charge noise
γd2: Nonequilibrium current noise
related charge noise
Visibility of AB oscillations
in linear conductance
T. Kubo, Poster TODAY
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
SOI in a parabolic quantum dot
External uniform magnetic field
Rashba spin-orbit interaction (SOI) Hamiltonian HSOI
=
� × p� · �σ
λR E
Effective field is assumed to
normal to plane
• Self-organized InAs quantum dot on GaAs
contacted laterally
• Large (anisotropic) g-factor ~ 5
• Quasi-two dimensional anisotropic
confinement potential
S. Takahashi, et al., Phys. Rev. Lett. 104, 246801 (2010).
Control of SOI by a side gate
Anti-crossing of two two-electron levels
•  SOI and g-factor can be controlled with side gate
Y. Kanai, et al., Nature
Nanotechnology 6 511, (2011).
R. Deacon et al., Phys. Rev. B
84, 041302(R) (2011).
Fig. The strength of SOI, Δ,
controlled by a side gate. Inset shows
the InAs quantum dot (red)
sandwiched with electrodes.
Aharonov-Bohm-Casher interferometer
Controlled spin-orbit interaction and
magnetic flux in a diamond-like loop
- works as an emitter, rotator, and
detector of flying spin qubits Magnetic flux φ
Effective field from
Rashba spin-orbit
interaction, α
Coupled diamonds offer more
flexible, and ideal realization
of Datta-Das spin transistor
A. Aharony, Y. Tokura, Guy Z. Cohen, O. Entin-Wohlman,
and S. Katsumoto, Phys. Rev. B 84, 035323 (2011).
Perfect spin filter
β=.05π
β=.15π
β=.25π
β =.27π
β =.25π
β =.23π
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
Nuclear Spin Bath Problem
Contact interaction to nuclei:
69
Ga, 71Ga, 75As (I=3/2) in GaAs QD
Flip-flop
50 nm
2 ⎛ I + S − + I − S +
(
)
H HF = A ø x ⎜
⎝
e
Bext
N=105 to 106 nuclei
in GaAs QD
2
⎞
+ I Z S Z ⎟
⎠
Nuclear spins are dynamically polarized Btot
because of the long lifetime (~min.).
Bext
Overhauser shift (ΔEZeeman)
…Shift of ESR condition
µ
Inhomogeneous broadening of ESR condition
Phase fluctuation (or dephasing) in the
ensemble measurement
T2*=10 to 30 ns
Bnuc
Decoherence mechanism by electron spin mediated spin
diffusion T ~> 1µs L. Cywinski, et al., Phys. Rev. B 79, 245314 (2009).
2
W. A. Coish, et al., Phys. Rev. B 81, 165316 (2010).
Coherence time of spin qubits
•  Hyperfine coupling with the nuclear spins is the dominant factor
R. Brunner, et al., to be submitted.
Dynamical nuclear spin pumping: DNP
Instead of conventional Fermi’s golden rule, we calculate DNP rate
using new scheme by electron spin response and correlation function.
Danon and Nazarov, Phys. Rev. B 83, 245306 (2011). E-
Hysteresis loops of nuclear spin polarization :stable fixed point
Energy
ε
ε=2
ε=4
ε=6
<Kz>
EZ
ε=-6
ε=-4
ε=-2
-EZ
Magnetic field sweep
d<Kz>/dt
=
P±peak
�K z �
−
1 + [C± (K0± − �K z �)]2
τN
E+
<Kz>
d�K z �
dt
Spontaneous symmetry breaking
We found the condition when the difference of the nuclear spin
polarizations between the two QDs becomes finite.
Note:
• The physical origin of τN: diffusion
• Statistical fluctuation about the
average value
• Limit cycle around unstable fixed point
• Quantum entanglement, interaction
with the environment
Coherent control of spins
Measurement of spins
New gear : spin-orbit interaction
Unpleasant neighbors : nuclear spins
Topics
LETTER
doi:10.1038/nature10463
Efficient quantum computing using coherent photon
Nature 478, 360 (2011)
conversion
N. K. Langford1,2,3, S. Ramelow1,2, R. Prevedel1,4, W. J. Munro5,6, G. J. Milburn7,1 & A. Zeilinger1,2
Single photons
quantum information carriers: they
The
storyaresoexcellent
far ...
have suggested that they cannot in fact produce phase shifts large enough
were used in the earliest demonstrations of entanglement1 and in for NLOQC because of spectral correlations created between the interthe production of the highest-quality entanglement reported so acting fields20. Other work, however, shows that these difficulties can be
•  2,3. Efficient
linear
optics
Knill,processing
Laflamme
Milburn, Nature
409, 46 (2001)
However, current
schemes
for QC:
preparing,
and &circumvented
far
in the related case of strong, second-order nonlinear (x(2))
measuring them are inefficient. For example, down-conversion pro- interactions by carefully engineering the phase-matching conditions21.
linear
vides
randomly timed,QC:
single Nielsen,
photons4, and
•  heralded,
Opticalbutcluster-state
PRL
93, 040503
(2004)
Coherent
photon conversion is an alternative nonlinear approach
5
optics gates are inherently probabilistic . Here we introduce a deter- that uses coherent oscillations between different multi-excitation
•  …process—coherent photon conversion (CPC)—that pro- states. The underlying process is a nonlinear interaction between m
ministic
vides a new way to generate and process complex, multiquanta bosonic modes that coherently converts single excitations in some of
states for photonic quantum information applications. The tech- the modes (depending on the precise form of the interaction) into
nique uses classically pumped nonlinearities to induce coherent single excitations in the remaining modes. A key principle of CPC is
oscillations between orthogonal states of multiple quantum excita- that this basic nonlinearity can in turn be generated by pumping some
One example
of CPC,
on a pumped
four-wave-mixing
• tions.One
process
tobased
provide
a whole
toolbox ofmodes
components
fornonlinearity
QCMC
of a higher-order
with applications
strong classical fields. This
interaction, is shown to yield a single, versatile process that provides induces an effective coupling between the quantum modes that can be
e.g.
⇒ addresses
all DiVincenzo
Criteria
a full set
of photonic
quantum processing
tools. This set satisfies
the tuned and enhanced by the classical pumps, even to the point where
DiVincenzo criteria
for a scalable quantum
computing
architecture6, the effective
⇒ high-quality,
heralded
single-photon
sources
interaction is stronger than naturally occurring couplings
including deterministic multiqubit entanglement gates (based on a of the same form. A similar effect is achieved in photon-pair sources
Fock-state
filter high-quality heralded based on four-wave mixing in photonic crystal fibres. Such systems
novel form of⇒
photon–photon
interaction),
single- and multiphoton states free from higher-order imperfec- have produced some of the highest-brightness photon-pair sources
tions, and robust, high-efficiency detection. It can also be used to with very low pump powers7, and precise dispersion engineering
produce heralded multiphoton entanglement, create optically and fibre-structuring technologies have allowed optimization of these
switchable quantum circuits and implement an improved form of sources to produce ultrabright, high-purity, heralded single photons4.
down-conversion with reduced higher-order effects. Such tools are
To illustrate the potential of CPC, here we focus on a novel case that
valuable building blocks for many quantum-enabled technologies.
has very interesting properties for quantum optics applications and
Finally, using photonic crystal fibres we experimentally demonstrate
which is based on the following standard four-wave-mixing interquantum correlations arising from a four-colour nonlinear process
action involving four distinct frequency modes (a, b, c and d):
suitable for CPC and use these measurements to study the feasibility
4,7
of reaching the deterministic regime with current technology . Our
H~cab{ c{ dzc! a{ bcd{
ð1Þ
What we have now…
Parametric Processes
Standard Spontaneous Parametric Down-conversion (SPDC)
(non-depleted pump)
photon pairs
higher-order
terms
Stronger χ(2) nonlinearities via pumped χ(3) (4-wave mixing) processes
•  χ(3) nonlinearities < χ(2)
•  nonlinearity can be enhanced (and
tuned) by a pump laser
•  near-degenerate frequencies possible
(e.g., all in telecom band)
•  all materials possess χ(3) nonlinearity
Applications
Solving the DiVincenzo Criteria - scaleable photon QC with CPC
initialised multiphoton sources
high-efficiency measurement
Other Applications
• 
two-qubit entangling (CZ) gates
• 
• 
• 
• 
• 
• 
heralded entangled states
(Bell
pairs, GHZ states)
error correction protocols
single-photon sources
n-photon Fock filters
better down-conversion
switchable gates for QC circuits
…
Very early results
• 
• 
• 
ΓL ~ 10-4 for 1W 532nm
ΓL ~ π/2 for 100%
χ(3) (chalcogenide)
~ 103 χ(3) (silica)
⇒ 103 improvement
• Measured efficiency with
off-the-shelf
components shows we re within reach of
deterministic regime with PCFs (using
chalcogenides)
ΓL ~ 10-5
~ 29 ± 1 counts / sec
Future work
• experiment with chalcogenide PCFs
Future directions
Spin measurement
Non-demolition measurement and characterize the back-action
Amicable relationship to nuclei
Quantum nature of ensemble nuclear spins through DNP
Explore to suppress the fluctuation of nuclear spins
Small scale quantum circuits
Propose faster operation scheme and evaluate its fidelity
New directions
Explore possible quantum interfaces: local spin/flying qubits (Q-bus)