Download Qubit Storage in Atomic Ensembles

Quantum Memory in
Atomic Ensembles
BY GEORG BRAUNBECK
Table of contents
1.
Motivation
2.
Quantum memory
3.
Implementations in general
4.
Implementation based on EIT in detail
QUBIT STORAGE IN ATOMIC ENSEMBLES
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Table of contents
1.
Motivation
2.
Quantum memory
3.
Implementations in general
4.
Implementation based on EIT in detail
QUBIT STORAGE IN ATOMIC ENSEMBLES
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Quantum Information Processing
E
 Idea: Use Quantum Mechanical properties/effects to gain new possibilities:
 Quantum Computing
Shor-Algorithm
 Quantum Communication
Cryptography
A
B
 Quantum memory to synchronize different operations
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Bit vs. Qubit
 Classical bit: Stores binary information ‚0‘ or ‚1‘
1
 Which quantum mechanical properties set a qubit apart from a classical bit?
 superposition: 𝑎0 0 + 𝑎1 𝑒 𝑖𝜙 1
 entanglement: no classical pendant
e.g.: 0 𝐴 1 𝐵 − 1 𝐴 0
A
𝐵
QUBIT STORAGE IN ATOMIC ENSEMBLES
0
B
1
A
1
B
0
A
0
B
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Table of contents
1.
Motivation
2.
Quantum memory
3.
Implementations in general
4.
Implementation based on EIT in detail
QUBIT STORAGE IN ATOMIC ENSEMBLES
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Quantum Memory
stationary qubit
i.e. quantum memory
(e.g. atom)
flying qubit
(e.g. photon)
storage
classical:
1
0
flying qubit
(e.g. photon)
read-out
𝑎𝐿 𝐿 + 𝑎𝑅 𝑒 𝑖𝜙 𝑅
𝑎𝐿 0 + 𝑎𝑅 𝑒 𝑖𝜙 1
𝑎𝐿 𝐿 + 𝑎𝑅 𝑒 𝑖𝜙 𝑅
current
magnetization
current
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
 Many more (bandwidth, wavelength, scalability…)
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
 Many more (bandwidth, wavelength, scalability…)
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Fidelity
How ‚well‘ do we store?
𝜓 ,𝜌 = 𝜓 𝜓
coherent
decoherent
Quantum
memory
𝜓 ′ , 𝜌′ =?
(pure state)
𝐹 = 𝜓 𝜌′ 𝜓
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
 Many more (bandwidth, wavelength, scalability…)
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Performance Criteria
 Fidelity
 Efficiency =
𝑬𝒏𝒆𝒓𝒈𝒚 𝒂𝒇𝒕𝒆𝒓 𝒓𝒆𝒂𝒅−𝒐𝒖𝒕
𝑬𝒏𝒆𝒓𝒈𝒚 𝒃𝒆𝒇𝒐𝒓𝒆 𝒔𝒕𝒐𝒓𝒂𝒈𝒆
=𝜼
 Storage time
 Many more (bandwidth, wavelength, scalability…)
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
 Many more (bandwidth, wavelength, scalability…)
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
𝑭 𝒕 , time evolution of fidelity
𝜼 𝒕 , time evolution of efficiency
 Many more (bandwidth, wavelength, scalability…)
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Performance Criteria
 Fidelity
 Efficiency
 Storage time
 Many more (bandwidth, wavelength, scalability…)
QUBIT STORAGE IN ATOMIC ENSEMBLES
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Table of contents
1.
Motivation
2.
Quantum memory
3.
Implementations in general
4.
Implementation based on EIT in detail
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Single Quantum Emitter
Internal states of:
 Atoms
 Ions
 NV-center
 storage
cavity needed
 read-out
 Quantum dots
Purcell-effect
(also needs a cavity)
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Ensembles
 Ion-doped solids
 storage?
 Gases at roomtemperature
 Cold/ultracold gases
 read-out?
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Ensembles
 Ion-doped solids
 storage?
 Gases at roomtemperature
 Cold/ultracold gases
 read-out?
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Ensembles - Storage
≈
Cavity can be replaced by a
huge number of particles
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Ensembles
 Ion-doped solids
 storage?
 Gases at room temperature
 Cold/ultracold gases
 read-out
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Ensembles – Read-Out
storage
read-out
𝑘𝑝ℎ𝑜𝑡𝑜𝑛
𝑘𝑠𝑝𝑖𝑛 𝑤𝑎𝑣𝑒
𝑘𝑝ℎ𝑜𝑡𝑜𝑛
electromagnetic
wave
spin wave
electromagnetic
wave
𝑘
photon
storage
j
𝑘
read-out
𝑘
photon
𝑗
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Ensembles
 Ion-doped solids
 Gases at room temperature
 Cold/ultracold gases
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Rare-earth ions in solids
 Ions doped into solids function as stationary qubits
 High coherence times: optical transition ~ 1µs – 1ms
 Easy to reproduce, scalable
 But: inhomogenous broadening (causing dephasing) needs to be controlled
 Low Temperatures needed (1-4 K)
[1]
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Rare-earth ions in solids
 Fidelity: up to 95%
 Efficiency:
45% - maximum reached so far
 Storage time: 𝑂(10µs) – reached so far
[1]
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Ensembles
 Ion-doped solids
 Gases at room temperature
 Cold/ultracold gases
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Alkali gases
 roomtemperatured atomic gas of alkali atoms → cheap
 spin wave in medium serves as stationary qubit
 But: coherence time limited by atomic motion → cooling
[1]
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Alkali gases
 Fidelity: > 90% possible
 Efficiency: up to 87%
 Storage time: up to 4 ms
[1]
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Ensembles
 Ion-doped solids
 Gases at roomtemperature
 Cold/ultracold gases
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EIT – Quick review
Ωp
Γ
Ω𝑐
Light
𝑎0 = 𝐴 1 − 𝐵 2
no contribution of 3
[2]
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EIT - Slow light
0 =𝑐
𝑣𝑔𝑟
m ∝ Ω
c ≫ 𝑣𝑔𝑟
𝑐
2
[3,4]
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EIT - Stored Light
control beam
Ω𝑐
probe photon
Ωp
(superposition of
electromagnetic
and spin wave)
storage
polariton state:
store: switched off
read-out: switched back on
EIT Medium
1
Ω𝑐 2 +𝐴2
Ω𝑐 1 1
𝑝ℎ
photonic
part
QUBIT STORAGE IN ATOMIC ENSEMBLES
𝑚 ∝ Ω
𝑣𝑔𝑟
𝑐
2
read-out
−𝐴 2 0
𝑝ℎ )
atomic
part
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EIT – Qubit storage
3−
3+
probe photon
probe photon
Ω𝑐
𝐿
Ω𝑐
𝑅
2−
2+
1
𝑎𝐿 𝐿 + 𝑎𝑅 𝑒 𝑖𝜙 |𝑅⟩
𝑎𝐿 2− + 𝑎𝑅 𝑒 𝑖𝜙 |2+ ⟩
QUBIT STORAGE IN ATOMIC ENSEMBLES
𝑎𝐿 𝐿 + 𝑎𝑅 𝑒 𝑖𝜙 |𝑅⟩
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Experimental Results
Input L,H,D
⇒
BEC
⇒
QUBIT STORAGE IN ATOMIC ENSEMBLES
Polarization Detection
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Entaglement - Setup
polarization
detection
control beam
(2)
probe photon
(1)
BEC
beam splitter
QUBIT STORAGE IN ATOMIC ENSEMBLES
polarization
detection
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Entanglement
𝜓𝑝ℎ⊗𝑝ℎ =
𝑅 𝐿 − |𝐿⟩|𝑅⟩)/ 2
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entaglement fidelity
Results
[5]
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Summary
 Qubit: 𝑎0 0 + 𝑎1 𝑒 𝑖𝜙 1
 Stationary vs flying qubit
 Fidelity, Efficiency, Storage time …
 Single quantum emitter vs ensemble
 Qubit Storage via EIT
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Thank you, Simon!
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Sources
(1) C. Simon et al.: Quantum memories. In: THE EUROPEAN PHYSICAL JOURNAL D 58. (2010)
(2) A. Neuzner: Light Storage and Pulse Shaping using Electromagnetically Induced Transparency.
Max-Planck-Institut für Quantenoptik. (2010)
(3) M. Lettner: Ein Bose-Einstein-Kondensat als Quantenspeicher für Zwei-Teilchen-Verschränkung.
Max-Planck-Institut für Quantenoptik. (2011)
(4) S. Baur: Speicherung der Polarisation von Licht in einem Bose-Einstein-Kondensat. Max-PlanckInstitut für Quantenoptik. (2010)
(5) M. Lettner et al.: Remote Entanglement between a Single Atom and a Bose-Einstein Condensate.
In: PHYSICAL REVIEW LETTERS 106. (No. 21, 2011, May)
(6) A. Lvovsky et al.: Optical quantum memory. In: NATURE PHOTONICS 3 (No. 12, 2009)
(7) M. Fleischhauer et al.: Eletromagnetically induced transparency: Optics in Coherent Media. In:
REVIEWS OF MODERN PHYSICS 77 (No. 2, 2005)
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