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

2QUBIT STORAGE IN ATOMIC ENSEMBLES

Table of contents

1. Motivation

2. Quantum memory

3. Implementations in general

4. Implementation based on EIT in detail

3QUBIT STORAGE IN ATOMIC ENSEMBLES

Quantum Information Processing

Idea: Use Quantum Mechanical properties/effects to gain new possibilities: Quantum Computing Shor-Algorithm

Quantum Communication Cryptography

Quantum memory to synchronize different operations

QUBIT STORAGE IN ATOMIC ENSEMBLES 4

A B

E

Bit vs. Qubit

Classical bit: Stores binary information ‚0‘ or ‚1‘

Which quantum mechanical properties set a qubit apart from a classical bit?

superposition: 𝑎0 0 + 𝑎1𝑒𝑖𝜙 1

entanglement: no classical pendant

e.g.: 0 𝐴 1 𝐵 − 1 𝐴 0 𝐵

QUBIT STORAGE IN ATOMIC ENSEMBLES 5

0

1

1 A

0 A 0 B

1 B

A B

Table of contents

1. Motivation

2. Quantum memory

3. Implementations in general

4. Implementation based on EIT in detail

6QUBIT STORAGE IN ATOMIC ENSEMBLES

Quantum Memory

QUBIT STORAGE IN ATOMIC ENSEMBLES 7

flying qubit(e.g. photon)

flying qubit(e.g. photon)

stationary qubiti.e. quantum memory

(e.g. atom)

𝑎𝐿 𝐿 + 𝑎𝑅𝑒𝑖𝜙 𝑅 𝑎𝐿 0 + 𝑎𝑅𝑒

𝑖𝜙 1 𝑎𝐿 𝐿 + 𝑎𝑅𝑒𝑖𝜙 𝑅

classical: current magnetization current

storage read-out1

0

Performance Criteria

Fidelity

Efficiency

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 8

Performance Criteria

Fidelity

Efficiency

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 9

Fidelity

How ‚well‘ do we store?

QUBIT STORAGE IN ATOMIC ENSEMBLES 10

Quantum memory𝜓 , 𝜌 = 𝜓 𝜓 𝜓′ , 𝜌′ =?

(pure state)

𝐹 = 𝜓 𝜌′ 𝜓

coherent decoherent

Performance Criteria

Fidelity

Efficiency

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 11

Performance Criteria

Fidelity

Efficiency =𝑬𝒏𝒆𝒓𝒈𝒚 𝒂𝒇𝒕𝒆𝒓 𝒓𝒆𝒂𝒅−𝒐𝒖𝒕

𝑬𝒏𝒆𝒓𝒈𝒚 𝒃𝒆𝒇𝒐𝒓𝒆 𝒔𝒕𝒐𝒓𝒂𝒈𝒆= 𝜼

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 12

Performance Criteria

Fidelity

Efficiency

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 13

Performance Criteria

Fidelity

Efficiency

Storage time 𝑭 𝒕 , time evolution of fidelity

𝜼 𝒕 , time evolution of efficiency

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 14

Performance Criteria

Fidelity

Efficiency

Storage time

Many more (bandwidth, wavelength, scalability…)

QUBIT STORAGE IN ATOMIC ENSEMBLES 15

Table of contents

1. Motivation

2. Quantum memory

3. Implementations in general

4. Implementation based on EIT in detail

16QUBIT STORAGE IN ATOMIC ENSEMBLES

Single Quantum Emitter

Atoms

Ions

NV-center

Quantum dots

QUBIT STORAGE IN ATOMIC ENSEMBLES 17

storage

read-out

cavity needed

Purcell-effect(also needs a cavity)

Internal states of:

Ensembles

Ion-doped solids

Gases at roomtemperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 18

storage?

read-out?

Ensembles

Ion-doped solids

Gases at roomtemperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 19

storage?

read-out?

Ensembles - Storage

QUBIT STORAGE IN ATOMIC ENSEMBLES 20

≈ Cavity can be replaced by a huge number of particles

Ensembles

Ion-doped solids

Gases at room temperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 21

storage?

read-out

Ensembles – Read-Out

QUBIT STORAGE IN ATOMIC ENSEMBLES 22

storage𝑘 read-out 𝑘

𝑘𝑝ℎ𝑜𝑡𝑜𝑛

electromagneticwave

storage

𝑘𝑠𝑝𝑖𝑛 𝑤𝑎𝑣𝑒

read-out𝑘𝑝ℎ𝑜𝑡𝑜𝑛

electromagneticwave

spin wave

j𝑘

𝑗photon photon

Ensembles

Ion-doped solids

Gases at room temperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 23

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)

QUBIT STORAGE IN ATOMIC ENSEMBLES 24

[1]

Rare-earth ions in solids

Fidelity: up to 95%

Efficiency: 45% - maximum reached so far

Storage time: 𝑂(10µs) – reached so far

QUBIT STORAGE IN ATOMIC ENSEMBLES 25

[1]

Ensembles

Ion-doped solids

Gases at room temperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 26

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

QUBIT STORAGE IN ATOMIC ENSEMBLES 27

[1]

Alkali gases

Fidelity: > 90% possible

Efficiency: up to 87%

Storage time: up to 4 ms

QUBIT STORAGE IN ATOMIC ENSEMBLES 28

[1]

Ensembles

Ion-doped solids

Gases at roomtemperature

Cold/ultracold gases

QUBIT STORAGE IN ATOMIC ENSEMBLES 29

EIT – Quick review

QUBIT STORAGE IN ATOMIC ENSEMBLES 30

Light𝑎0 = 𝐴 1 − 𝐵 2

[2]

Γ Ω𝑐Ωpno contribution of 3

EIT - Slow light

QUBIT STORAGE IN ATOMIC ENSEMBLES 31

𝑣𝑔𝑟0 = 𝑐 c ≫ 𝑣𝑔𝑟

m ∝ Ω𝑐2

[3,4]

EIT - Stored Light

QUBIT STORAGE IN ATOMIC ENSEMBLES 32

EIT Medium

control beamΩ𝑐

probe photonΩp

polariton state: 1

Ω𝑐2+𝐴2

Ω𝑐 1 1 𝑝ℎ − 𝐴 2 0 𝑝ℎ)

read-outstorage

photonicpart

atomicpart

store: switched offread-out: switched back on

𝑣𝑔𝑟𝑚 ∝ Ω𝑐

2

(superposition ofelectromagneticand spin wave)

EIT – Qubit storage

QUBIT STORAGE IN ATOMIC ENSEMBLES 33

𝐿 𝑅Ω𝑐

1

2+

3+3−

2−

probe photon

𝑎𝐿 𝐿 + 𝑎𝑅𝑒𝑖𝜙|𝑅⟩ 𝑎𝐿 2− + 𝑎𝑅𝑒

𝑖𝜙|2+⟩

probe photon

𝑎𝐿 𝐿 + 𝑎𝑅𝑒𝑖𝜙|𝑅⟩

Ω𝑐

Experimental Results

Input L,H,D ⇒ ⇒ Polarization Detection

QUBIT STORAGE IN ATOMIC ENSEMBLES 34

BEC

Entaglement - Setup

QUBIT STORAGE IN ATOMIC ENSEMBLES 35

probe photon

beam splitter

BEC

control beam

polarizationdetection

(1)

(2)

polarizationdetection

Entanglement

QUBIT STORAGE IN ATOMIC ENSEMBLES 36

𝜓𝑝ℎ⊗𝑝ℎ = 𝑅 𝐿 − |𝐿⟩|𝑅⟩)/ 2

Results

QUBIT STORAGE IN ATOMIC ENSEMBLES 38

[5]

enta

glem

ent

fid

elit

y

Summary

Qubit: 𝑎0 0 + 𝑎1𝑒𝑖𝜙 1

Stationary vs flying qubit

Fidelity, Efficiency, Storage time …

Single quantum emitter vs ensemble

Qubit Storage via EIT

QUBIT STORAGE IN ATOMIC ENSEMBLES 39

Thank you, Simon!

QUBIT STORAGE IN ATOMIC ENSEMBLES 40

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-Planck-Institut 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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