teleportation of quantum dot exciton qubits via superradiance
DESCRIPTION
Aug. 5, 2005 Center for Theoretical Sciences NCKU. Teleportation of Quantum Dot Exciton Qubits via Superradiance. Yueh-Nan Chen ( 陳岳男 ) and Che-Ming Li Group leader : Prof. Der-San Chuu Dep. of Electrophysics, NCTU, Taiwan Collaborator : Prof. Tobias Brandes ( Univ. of Manchester ). - PowerPoint PPT PresentationTRANSCRIPT
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Teleportation of Quantum Dot Exciton Qubits
via Superradiance
Aug. 5, 2005
Center for Theoretical Sciences
NCKU
Yueh-Nan Chen ( 陳岳男 ) and Che-Ming Li
Group leader : Prof. Der-San Chuu
Dep. of Electrophysics, NCTU, Taiwan
Collaborator : Prof. Tobias Brandes (Univ. of Manchester)
2
感謝
1. 國科會特約博士後研究計畫： 介觀物理系統在光子晶體中的量子散粒雜訊 NSC 94-2112-M-009-019 計畫主持人：陳岳男 共同主持人：鄭舜仁
2. 國科會奈米計劃： 奈米結構的空腔量子電動力學及量子傳 NSC 94-2120-M-009-002 計畫主持人：褚德三 共同主持人：許世英，林俊源，朱仲夏，趙天生 計畫參與人員：林高進、邱裕煌、李哲明、廖英彥、 簡賸瑞、唐英瓚
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Outline
1. Brief review of quantum teleportation
2. Brief review of superradiance (collective decay)
3. Teleportation of charge qubits via superradiance
in purely quantum optic system
4. Extension to quantum dot systems
5. Summary
4
Teleportation: Science fiction or science?
From Prof. Beenakker’s web-page
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In 1993 an international group of six scientists, including IBM fellow Charles H. Bennett, confirmed the intuitions of the majority of science fiction writers by showing that perfect teleportation is indeed possible in principle, but only if the original is destroyed.
Quantum Teleportation
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QUANTUM TELEPORTATION OF A PERSON (impossible in practice but a good example to aid the imagination) would begin with the person inside a measurement chamber (left) alongside an equal mass of auxiliary material (green).The auxiliary matter has previously been quantum-entangled with its counterpart, which is at the faraway receiving station (right).
PREPARING FOR QUANTUM TELEPORTATION . . .Scientific American, April 2000; by Zeilinger
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... TRANSMISSION OF RANDOM DATA ...
MEASUREMENT DATA must be sent to the distant receiving station by conventional means.This process is limited by the speed of light, making it impossible to teleport the person faster than the speed of light.
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... RECONSTRUCTION OF THE TRAVELER
RECEIVER RE-CREATES THE TRAVELER, exact down to the quantum state of every atom and molecule, by adjusting the counterpart matter’s state according to the random measurement data sent from the scanning station.
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R. Ursin et al. describe the high-fidelity teleportation of photons over adistance of 600 metes across the River Danube in Vienna.
Nature 430, 849 (2004)
Quantum teleportation across the Danube
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Teleportation with real atoms:
1. Deterministic quantum teleportation with atoms
M. RIEBE et al., Nature 429, 734 (17 June 2004)
With calcium ions
2. Deterministic quantum teleportation of atomic qubits
M. D. BARRETT et al., Nature 429, 737(17 June 2004)
With atomic (9Be+) ions
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Proposal for teleportation in solid state system
Phys. Rev. Foucs, 6 February 2004
“Beam Up an Electron!” C. W. J. Beenakker and M. Kindermann, Phys. Rev. Lett. 92, 056801(2004)
12
Creation of an entangled
electron-hole pair. An electron meets a hole.
teleportation
13
Local Unitary Operations
UNOTATION
Qubit is denoted by horizontal lineSingle-qubit unitary transformation U :
H
PATICULAR UNITARY OPERATIONS
Hadamard transform
11
11
2
1H
Unilateral Pauli rotations
01
10x
0
0
i
iy
10
01x
14
Collective Unitary Operations
controlled-NOT(XOR) transformation
a
b
a
baaddition modulo 2
0100
1000
0010
0001
2
1CNOT
TCTC0000 CNOT
TCTC1101 CNOT
15
H
00
0)10(2
1
1)10(2
1
Maximally Entanglement Generation
)1100(2
1 0)10(2
1
01 1)10(2
1
10
11
16
H
H
U
)]1100(2
1)[10(
)]111100011000(2
1 )(
2
100
)(2
111
)(2
101
)(2
110
)]01()01(
)10()10([2
1
M
M
0
0
)]01(11)01(01
)10(10)10(00[2
1
H
Entanglement Source Party I : ALICE
Party II : BOB
y11
z10
x01
00
σ11
σ10
σ01
I00
M U
Party I : ALICE
One qbit Quantum channel
One bit Classical channel
Quantum Network for Teleportation
17
2. Brief review of superradiance
18
Interaction between a two-level atom and the photon reservoir:
In the interaction picture, the state vector :
, where
atomofoperatorcreatingcoperatorphotonb
cHecbDH
q
xqiq
::
..
q tftft
1;)(0;)()( 0
q1;
0;
: an atom initially in the excited state
: a photon of q in the radiation field
• Spontaneous emission of a single two-level atom
19
Results :Results :
,)(0ttietf where is the decay rate
represents the Lamb Shift
, where
0 is the energy spacing
q
q
qc
D
qcD
0
2
0
2),(
20
• Spontaneous emission from two atoms
The The interactioninteraction :
:
:
..2,1
j
j
xqijq
j
c
x
cHecbDH j
position of the j th atomraising operator of the j th atom
One can define the so-called Dicke states :One can define the so-called Dicke states :
1
0
0
1
2
1
2
12
1
2
1
T
S
T
T
21
Decay scheme for two-atom system :Decay scheme for two-atom system :
Limiting Limiting case :case :
<< wavelength of the photon
+=2, - =0
22
• Measurements of superradiance in previous works
Experiment in real atoms:
[R. G. DeVoe and R. G. Brewer, P. R. L. 76, 2049 (1996)]
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3. Teleportation of charge qubits via superradiance
in purely quantum optic system
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1 1 2
Collective decay
Cavity photon
teleportation 2 + 2
entangled
trap
detectordetector
leakage
Teleportation of charge qubit to cavity photon state
25
The scheme:
The interaction between the atom and single-mode cavity:
With the appropriate preparation of the initial state of atom-1 and the control of its passing time through the cavity, the singlet entangled state is created between atom-1 and the cavity photon.
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superradiant detector
subradiant detector
How to distinguish between super- and sub-radiance?
Our proposal:
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The advantages:
It’s a “one-pass” process!
i.e. the Hadamard and CNOT transformations are
omitted and the joint measurements are performed
naturally by collective decay.
The disadvantages:
The maximum successful chance is 50%.
(can be modified to teleportation with insurance by
“redundant encoding”)[S. J. van Enk et al., Phys. Rev. Lett. 78, 4293 (1997)]
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4. Extension to solid-state systems
QD excitons
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Recent experiment on QD excitons (I)
1. The QD exciton states are constructed from electron (e) and heavy hole (h) single-particle basis states with spin projections along the QD growth axis (z) of
2. However, the and eigenstates are often mixed in dots with reduced symmetry, forming two linearly polarized eigenstates separated by the anisotropic e–h exchange splitting of a few times 10 eV.
30
Optically programmable electron spin memory using semiconductor quantum dots
Miro Kroutvar et al., Nature, 432, 81 (2004).
To enable optical selection of pure spin states, magnetic field (B=4T) is applied to the QDs, such that
Zeeman splitting > anisotropic e–h exchange splitting
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Teleportation of QD exciton qubit to photonic qubit
32[Z. Yuan et al., Science 295, 102 (2002).]
It is now possible to generate single-photon electrically!
Recent experiment on QD excitons (II)
33
Energy-band diagram of the p-i-n junction:
Typical InAs QD exciton decay time: 1.3ns.
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1. Current through dot-1.
2. Superradiance between dot-1 and dot-2 excitons.
are the super-radiant and sub-radiant decay rate
D (U ): coupling constant between D (U) state and hole (electron) reservoir
Current detection of superradianceCurrent detection of superradiance
35
Double-dot embedded inside a rectangular microcavity with length
z
d
),)(2(
)1(
220
2
,
z
diqqqz
qc
eDdq z
zxy
36
Expectation value of the entangled state <nT> and <nS> in a rectangular microcavity
Solid line
Dashed line
[Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003)]
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p-GaAs
n-GaAs
insulator insulator
Vg1 Vg3
metal contact
InAs QDs1 2 3
collective decay
entangled
Teleportation with semiconductor QD excitons
I. Subradiance-induced singlet entangled state is generated between QD 1 and 2.
II. The bandgap of the exciton in QD 3 (1) is tuned to be (non)-resonant with that in QD 2.
III. A joint measurement is done naturally by collective decay of QD 2 and3.
Steps:
[Y. N. Chen et al., cond-mat/0502412]
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Some remarks about the fidelity of the entangled state:
When one starts to tune the energy band gap of QD 1, the excitons in QD 1 and 2 will no longer decay collectively but are described by the following interactions,
The fidelity of the singlet entangled state after the tuning time t is
( The initial condition is )
39
Existing experimental parameters:
1. The lifetime of QD excitons in a microcavity is shown to be greatly inhibited (≥10ns) by tuning the level-spacing 4 meV away from the resonant mode.
[M. Bayer et al., Phys. Rev. Lett. 86, 3168 (2001)]
2. The tuning pulse from the gate voltage is a step-like function with raising time 40ps.
[Y. Nakamura et al., Nature 398, 786 (1999)]
The fidelity of the entangled state can be as high as 0.98.
40
Detection scheme in QDs:
Angle resolved measurement. (x)Time resolved measurement is required!
But, it’s a statistical average, there must be errors!
The steps:
1. Setting the border line of time to distinguish between
super- and subradiance.
2. Estimating the success probability P.
- For the ration (super/sub) of (1+0.7)/(1-0.7),
P is about 0.47.
41
Another proposal for QD excitons (II)
GaAs 45°
Au
CdTe quantum dots
n+-ZnSe
V
45°
Vi
ZnTe
Experimental setup for entanglement generation Experimental setup for entanglement generation
42
1. We have proposed a teleportation
scheme based on superradiance.
2. This scheme can be applied to both
purely quantum optic and solid state
QD systems.
Summary
Y. N. Chen et al. cond-mat/0502412 (2005).
To appear in “New Journal of Physics” (2004 impact factor: 3.1)
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superradiant detector
subradiant detector
44
45
Current detection of superradianceCurrent detection of superradiance1. Current through dot-1.
2. Superradiance between dot-1 and dot-2 excitons.
are the super-radiant and sub-radiant decay rate
D (U ): coupling constant between D (U) state and hole (electron) reservoir
46
Some remarks about the fidelity of the entangled state:
When one starts to tune the energy band gap of QD 1, the excitons in QD 1 and 2 will no longer decay collectively but are described by the following interactions,
The fidelity of the singlet entangled state after the tuning time t is
( The initial condition is )
47
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Existing experimental parameters:
1. The lifetime of QD excitons in a microcavity is shown to be greatly inhibited (≥10ns) by tuning the level-spacing 4 meV away from the resonant mode.
[M. Bayer et al., Phys. Rev. Lett. 86, 3168 (2001)]
2. The tuning pulse from the gate voltage is a step-like function with raising time 40ps.
[Y. Nakamura et al., Nature 398, 786 (1999)]
The fidelity can be as high as 0.98.
49
In plotting the figure we have assumed :
D =1 , U =0.2 , and =1/(1.3[ns]) (in free space).
1. As the inter-dot distance is close enough, the current is inhibited.
2. The current shows oscillatory behavior as a function of inter-dot distance — superradiant effect!
• Current through the double-dot
, where is the decay
rate of the quantum
dot exciton
50
t
Decay rate
1/1.3(ns)
1/10(ns)
t
Constant speed
51
Double-dot embedded inside a rectangular microcavity with length
z
d
),)(2(
)1(
220
2
,
z
diqqqz
qc
eDdq z
zxy
52
• Entanglemant of double quantum dot excitons
[Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003)]
, where
By calculating the expectation value of the entangled state
<nT> and <nS>, we can know
the degrees of the entanglement.
Solid line
Dashed line
53
Double-dot embedded inside a rectangular microcavity with length
z
d
),)(2(
)1(
220
2
,
z
diqqqz
qc
eDdq z
zxy
54
In plotting the figure we have assumed :
D =1 , U =0.2 , and =1/(1.3[ns]) (in free space).
1. As the inter-dot distance is close enough, the current is inhibited.
2. The current shows oscillatory behavior as a function of inter-dot distance — superradiant effect!
• Current through the double-dot
, where is the decay
rate of the quantum
dot exciton
55
Energy-band diagram of the p-i-n junction:
Typical InAs QD exciton decay time: 1.3ns.