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 2
Table of contents 1. Motivation 2. Quantum memory 3. Implementations in general 4. Implementation based on EIT in detail QUBIT STORAGE IN ATOMIC ENSEMBLES 3
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 QUBIT STORAGE IN ATOMIC ENSEMBLES 4
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: a 0 0 + a 1 e iφ 1 entanglement: no classical pendant e.g.: 0 A 1 B 1 A 0 B A 1 A B 1 B 0 0 A 0 B QUBIT STORAGE IN ATOMIC ENSEMBLES 5
Table of contents 1. Motivation 2. Quantum memory 3. Implementations in general 4. Implementation based on EIT in detail QUBIT STORAGE IN ATOMIC ENSEMBLES 6
Quantum Memory flying qubit (e.g. photon) storage stationary qubit i.e. quantum memory (e.g. atom) flying qubit (e.g. photon) a L L + a R e iφ R a L 0 + a R e iφ 1 a L L + a R e iφ R classical: current magnetization current 1 0 read-out QUBIT STORAGE IN ATOMIC ENSEMBLES 7
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? coherent decoherent ψ, ρ = ψ ψ Quantum memory ψ, ρ =? (pure state) F = ψ ρ ψ QUBIT STORAGE IN ATOMIC ENSEMBLES 10
Performance Criteria Fidelity Efficiency Storage time Many more (bandwidth, wavelength, scalability ) QUBIT STORAGE IN ATOMIC ENSEMBLES 11
Performance Criteria Fidelity Efficiency = Storage time Energy after read out Energy before storage = η 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 F t, time evolution of fidelity Storage time η t, time evolution ofefficiency 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 QUBIT STORAGE IN ATOMIC ENSEMBLES 16
Single Quantum Emitter Internal states of: Atoms Ions NV-center Quantum dots storage read-out cavity needed Purcell-effect (also needs a cavity) QUBIT STORAGE IN ATOMIC ENSEMBLES 17
Ensembles Ion-doped solids Gases at roomtemperature Cold/ultracold gases storage? read-out? QUBIT STORAGE IN ATOMIC ENSEMBLES 18
Ensembles Ion-doped solids Gases at roomtemperature Cold/ultracold gases storage? read-out? QUBIT STORAGE IN ATOMIC ENSEMBLES 19
Ensembles - Storage Cavity can be replaced by a huge number of particles QUBIT STORAGE IN ATOMIC ENSEMBLES 20
Ensembles Ion-doped solids Gases at room temperature Cold/ultracold gases storage? read-out QUBIT STORAGE IN ATOMIC ENSEMBLES 21
Ensembles Read-Out k photon electromagnetic wave storage k spin wave spin wave read-out k photon electromagnetic wave k storage read-out k photon j j k photon QUBIT STORAGE IN ATOMIC ENSEMBLES 22
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) [1] QUBIT STORAGE IN ATOMIC ENSEMBLES 24
Rare-earth ions in solids Fidelity: up to 95% Efficiency: 45% - maximum reached so far Storage time: O(10µs) reached so far [1] QUBIT STORAGE IN ATOMIC ENSEMBLES 25
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 [1] QUBIT STORAGE IN ATOMIC ENSEMBLES 27
Alkali gases Fidelity: > 90% possible Efficiency: up to 87% Storage time: up to 4 ms [1] QUBIT STORAGE IN ATOMIC ENSEMBLES 28
Ensembles Ion-doped solids Gases at roomtemperature Cold/ultracold gases QUBIT STORAGE IN ATOMIC ENSEMBLES 29
EIT Quick review Γ Ω c Ω p Light a 0 = A 1 B 2 no contribution of 3 [2] QUBIT STORAGE IN ATOMIC ENSEMBLES 30
EIT - Slow light v 0 gr = c c v m gr Ω 2 c [3,4] QUBIT STORAGE IN ATOMIC ENSEMBLES 31
EIT - Stored Light control beam Ω c store: switched off read-out: switched back on v gr m Ω c 2 probe photon Ω p storage EIT Medium read-out (superposition of electromagnetic and spin wave) polariton state: 1 Ω c 2 +A 2 Ω c 1 1 ph A 2 0 ph ) photonic part atomic part QUBIT STORAGE IN ATOMIC ENSEMBLES 32
EIT Qubit storage 3 3 + probe photon probe photon Ω c L R Ω c 2 2 + a L L + a R e iφ R a L 2 + a R e iφ 2 + 1 a L L + a R e iφ R QUBIT STORAGE IN ATOMIC ENSEMBLES 33
Experimental Results Input L,H,D BEC Polarization Detection QUBIT STORAGE IN ATOMIC ENSEMBLES 34
Entaglement - Setup (2) polarization detection control beam probe photon (1) BEC beam splitter polarization detection QUBIT STORAGE IN ATOMIC ENSEMBLES 35
Entanglement ψ ph ph = R L L R )/ 2 QUBIT STORAGE IN ATOMIC ENSEMBLES 36
entaglement fidelity Results [5] QUBIT STORAGE IN ATOMIC ENSEMBLES 38
Summary Qubit: a 0 0 + a 1 e iφ 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) QUBIT STORAGE IN ATOMIC ENSEMBLES 41