Download Ensemble based Photonic Quantum Memories - GdR-IQFA

Optical Quantum Memories
Hugues de Riedmatten
ICFO-The Institute of Photonic Sciences
ICREA- Catalan Institute for Research and Advanced studies
GdR IQFA Colloqium, March 24th , Nice
Quantum memory for single photons
The goal of the quantum memory is to temporarily
store the quantum state  in of a photon:
A « quantum hard drive »
Quantum memory
Quantum Physical
system:
 in
WRITE
pWRITE
Must preserve the
quantum state of the
photon
Typically:
Coherent atoms
READ
pREAD
out
Quantum memory for single photons
The goal of the quantum memory is to temporarily
store the quantum state  in of a photon:
A « quantum hard drive »
Quantum memory
Quantum Physical
system:
 in
WRITE
pWRITE
Must preserve the
quantum state of the
photon
Typically:
Coherent atoms
READ
pREAD
out
Quantum memory for single photons
The goal of the quantum memory is to temporarily
store the quantum state  in of a photon:
A « quantum hard drive »
Quantum memory
Quantum Physical
system:
 in
WRITE
Must preserve the
quantum state of the
photon
pWRITE
READ
pREAD
out
Typically:
Coherent atoms
Three important properties:
- Efficiency
p
WRITE
pREAD
- Conditional fidelity Fcond   in out  in
- Storage time
F=1 means an output photon with the same
state as the input photon
cond
F=2/3 Classical threshold
Two types of QM
Absorptive Quantum memory
+quantum light source
(e.g. Entanglement source)
Emissive quantum memory
QM
 Wavelength flexibility.
Possibility to create entanglement between
photon at telecom wavelength and QM
Photon
 Source and memory in one system
 No wavelength flexibility
Emission not at telecom wavelengths
Photonic Quantum memories in Quantum
Information Science
• Interface between photons used for quantum communication and matter
used for quantum processing
• Needed in all complex protocols involving several probabilistic processes
(photon creation, transmission, processing, etc)
• Synchronize independent and probabilistic quantum channels in a
scalable fashion
• Examples
–
–
–
–
–
Photonic quantum computing
Deterministic single photon source
Complex Quantum light state engineering
Quantum Networks
Quantum Repeaters
Photonic Quantum memories in Quantum
Information Science
• Interface between photons used for quantum communication and matter
used for quantum processing
• Needed in all complex protocols involving several probabilistic processes
(photon creation, transmission, processing, etc)
• Synchronize independent and probabilistic quantum channels in a
scalable fashion
• Examples
–
–
–
–
–
Photonic quantum computing
Deterministic single photon source
Complex Quantum light state engineering
Quantum Networks
Quantum Repeaters
Quantum memories are required for scalable
quantum information technology
Quantum light matter interface
• Single quantum
systems
Cavity QED
• Atomic ensembles
 Easy to absorb light
 Collective enhancement
e
Ideal system, but
complicated to implement !
Optical
transition
g
Haroche, Kimble, Rempe, Chapman
g1...g j ...g N
1

N
 g ...e ...g
1
j
N
j
 Quantum Info multiplexing
Ensemble based quantum memories
Strong atom light coupling without high finesse cavities
Atomic gases
Atomic ensemble in Solid State
Rare-earth ion doped crystals
Far-off
resonance
Raman
Photon echo based protocols
DLCZ
Electro-magnetically
induced Transparency
Outline
• Atomic gases
• Duan-Lukin-Cirac-Zoller protocol
• EIT and Raman
• Solid state atomic ensembles
• Rare-earth doped solids
• Photon echo based quantum memories
• Quantum storage of photonic entanglement in a crystal
• Single atoms and ions quantum memories
Ensemble based quantum memories
The DLCZ protocol
Nature 414, 413 (2001).
Quantum repeater protocol using creation, storage and transfer
back to light of single collective spin excitations in atomic gases
N
1 A   g1....s j ...g N
j 1
Can be efficiently transferred to single photon fields
in a well defined direction and at well defined time
Strong atom light coupling without high finesse cavities
Single collective spin excitations
N
1
A
 e
  
i ( kw kS ) x j
j 1
g1....s j ...g N
Write
Read
N
e
  
i ( kw kS ) x j
j 1
e
 

i ( k r  k AS ) x ' j
g1....g N
Phase matching for collective interference
Atoms at rest:
Atoms moving
   
kw  kr  kS  k AS

  
kw  kS , kr  k AS
How to create entanglement between
remote quantum memories ?
Entanglement at a distance by measurement
A
B
Heralded Entangled
number
state of remote QM
Measurement-Induced Entanglement
for Excitation Stored in Remote Atomic Ensembles,
C.W. Chou, H. de Riedmatten, D. Felinto, S.V. Polyakov, S.van Enk, & H.J. Kimble, Nature 438, 828 (2005)
Conditions for entanglement :
-single excitation regime (p<<1)
-coherent superposition
A
Entangled !
B
1 quantum of excitation
shared in an entangled quantum state
between two atomic ensembles
located ~ 3 meters apart
DLCZ-based experiments: recent progress
Cavity enhanced : read out efficiency 84 %
Elementary quantum repeaters segments
Science 316 ,1319 (2007)
QMs based on
Electro-Magnetically Induced Transparency
Lvovsky et al, Nature Photonics 3, 706 (2009)
Nature 438, 833 (2005)
Nature 438, 837 (2005)
Nature 452, 67 (2008)
Raman memories
Bandwidth 1 GHz
Storage of 300 ps pulses
Heralded entanglement of absorptive QMs
Memory
Memory
1 click
SPDC
source A
Pump
SPDC
source B
Initial state
Conditional state (one click!)
Heralded entangled state
of remote QM
C. Simon, H. de Riedmatten, M.Afzelius, N. Sangouard, H. Zbinden and N. Gisin, PRL 98, 190503 (2007)
Heralded entanglement of absorptive QMs
Memory
Memory
1 click
SPDC
source A
SPDC
source B
Pump
- Similar as DLCZ scheme
Initial state
Duan, Lukin, Cirac, Zoller, Nature 414, 413 (2001)
Conditional state (one click!)
- Wavelength optimization
-Temporal multiplexing
Heralded entangled state
of remote QM
C. Simon, H. de Riedmatten, M.Afzelius, N. Sangouard, H. Zbinden and N. Gisin, PRL 98, 190503 (2007)
Storage of continuous quantum variables
EIT
Off resonant interaction and Feedback
Nature 432, 482 (2004)
Some reviews
- Quantum interface between light and atomic ensembles
K. Hammerer, A.S. Sørensen and E. S. Polzik
Rev. Mod. Phys. 82, 1041 (2010)
- Optical Quantum Memories
A.I. Lvovsky, B.C. Sanders & W. Tittel
Nature Photonics 3, 706 - 714 (2009)
- Quantum repeaters based on atomic ensembles and
linear optics
N. Sangouard, C. Simon, H. de Riedmatten and N. Gisin
Rev. Mod. Phys. 83, 33–34 (2011)
Outline
• Atomic gases
• Duan-Lukin-Cirac-Zoller protocol
• EIT and Raman
• Solid state atomic ensembles
• Rare-earth doped solids
• Photon echo based quantum memories
• Quantum storage of photonic entanglement in a crystal
• Single atoms and ions quantum memories
Atomic ensembles in the solid-state
Rare-earth ions doped into inorganic crystals
- Large number of stationary atoms with optical and spin transitions.
No atomic diffusion (frozen gas). No trapping needed.
- Excellent coherence properties (T< 4K)
e
Optical
transition
- Temporal multiplexing capability (multi qubit Q memory)
g
Spin states
s
Atomic ensembles in the solid-state
Rare-earth ions doped into inorganic crystals
- Large number of stationary atoms with optical and spin transitions.
No atomic diffusion (frozen gas). No trapping needed.
- Excellent coherence properties (T< 4K)
e
Optical
transition
- Temporal multiplexing capability (multi qubit Q memory)
g
Spin states
s
Controlling atomic coherences
Quantum storage using photon echo
techniques
 Absorption
Inhomogeneous
ensemble
 Inhomogeneous dephasing
absorption
g1...g j ...g N
1

N
e je
ikr
i j t
j
 Controlled rephasing
 Collective enhancement
e
k
g
Millions of atoms emit a single photon
in a well defined spatio temporal mode
g1...e j ...g N
Conventional (Two-pulse) Photon Echo
Rephasing triggered by optical p pulse
ppulse
Natural inhomogenous broadening
w0
t
absorption
Signal
t
Free Induction
Decay (FID)
w
w
t
Photon echo
u
w
w0
w
p-pulse
v
wInhomogeneous
dephasing
w
Echo at t=2t
Rephasing
27
N.A. Kurnit, I.D. Abella, and S.R. Hartmann, Phys. Rev. Lett. 13, 567 (1964)
Conventional (Two-pulse) Photon Echo
Rephasing triggered by optical p pulse
ppulse
Natural inhomogenous broadening
t
t
w0
absorption
2 pulses photon echoes:
Signal
w
w
- Simple (2 level system, no state preparation) 
- Strong optical pulse in
quantum channel
t
Free Induction
Photon echo
(Population
in the excited state) 
Decay (FID)
u - Unavoidable fluorescence spoils the fidelity of the
p-pulse
wsingle
photon echo.  (Phys. Rev. A 79, 053851 (2009) )
0
w
w
v
Not a good QM for single photons 
w-
Inhomogeneous
dephasing
w
Echo at t=2t
Rephasing
28
N.A. Kurnit, I.D. Abella, and S.R. Hartmann, Phys. Rev. Lett. 13, 567 (1964)
Photon echo based quantum memories
Controlling collective atomic coherences without adding noise
-Controlled Reversible Inhomogeneous Broadening (CRIB)
-Atomic Frequency Combs (AFC)
Photon echoes by Controlled Reversible
Inhomogeneous Broadening (CRIB)
Absorption &
Inhomogeneous dephasing
w0
absorption
w
t
w
u
w
v
w0
w
1
N
Absorption

g1...e j ...g N
j
30
Moiseev and Kröll, PRL 87, 173601 (2001), B. Kraus et al., PRA 73, 020302 (2006), N. Sangouard, et al, PRA 75, 032327 (2007)
Photon echoes by Controlled Reversible
Inhomogeneous Broadening (CRIB)
  -
t
t
Absorption &
Inhomogeneous dephasing
Rephasing &
Light emission
w0
w
After time t :
Mirror inhomogeneous
broadening!
u
w
v
w0
absorption
absorption
w
w0
t
w
u
w  w
w  w
w0  w0
w
w
Rephasing
1
N
e je
i t  i j ( t t )
w
w0
w
v
g1...e j ...g N
j
31
Moiseev and Kröll, PRL 87, 173601 (2001), B. Kraus et al., PRA 73, 020302 (2006), N. Sangouard, et al, PRA 75, 032327 (2007)
Photon echoes by Controlled Reversible
Inhomogeneous Broadening (CRIB)
  -
t
t
Absorption &
Inhomogeneous dephasing
w0
w
After time t :
Mirror inhomogeneous
broadening!
u
w
v
w0
w0
t
absorption
absorption
w
Rephasing &
Light emission
w
u
w  w
w  w
w0  w0
w
1
N
Re-emission

w
w
w0
w
v
g1...e j ...g N
j
32
Moiseev and Kröll, PRL 87, 173601 (2001), B. Kraus et al., PRA 73, 020302 (2006), N. Sangouard, et al, PRA 75, 032327 (2007)
CRIB in rare-earth doped solids
Nilsson and Kroll, Opt.Comm., 247, 393 (2005)
STEP 1
Natural broadening
Absorption
Absorption
STEP 2 « Burn a hole »
w
STEP 3
Optical pumping
w
STEP 4
Controlled broadening
Light
Storage !
w
Absorption
Absorption
Trigger re-emission
w
Linear Stark shifts by
Mirror broadening by changing
EXTERNAL ELECTRIC FIELD the POLARITY of the E-field
33
CRIB in rare-earth doped solids
Nilsson and Kroll, Opt.Comm., 247, 393 (2005)
STEP 1
Natural broadening
Absorption
Absorption
STEP 2 « Burn a hole »
Eu3+:Y2SiO5 (580 nm)
A.L. Alexander et al., PRL 96, 043602 (2006)
Pr3+:Y2SiO5 (606 nm)
G. Hétet et al., PRL 100, 023601 (2008)
eff = 10-6
w
Er3+:Y2SiO5 (1536nm) Telecom wavelength
STEP B.
3 Lauritzen et al, PRL 104, 080502
STEP
(2010)
87Rb
Optical pumping
4
w
eff =~10-2
Trigger re-emission
W. Tittel, M. Afzelius, R. L. Cone, T. Chanelière, S. Kröll,
Light
S. A. Moiseev, M. Sellars, arXiv:0810.0172,
Storage
!
Laser and Photonic Reviews, 4,244
(2010)
Absorption
Absorption
Review paper:
Controlled
broadening
eff = 0.13
gas (D1 line)
w
w
G.
Hétet
et
al.,
Opt.Lett.
33,
2323(2008),
Hosseini
et
al,
Nature
461,
241
(2009)
Linear Stark shifts by
Mirror broadening by changing
Raman-type interaction, CRIB on spin transition !!
EXTERNAL ELECTRIC FIELD
the POLARITY of the E-field
34
High efficiency CRIB quantum memory
Nature 465, 1052 (2010)
Pr3+:Y2SiO5
@606 nm
 = 69 %
Most efficient
quantum memory so far
35
Atomic Frequency Comb (AFC) Quantum Memory
Ensemble of inhomogeneously broadened atoms
e
State after absorption
N
c
k 1
g1 g 2 ...ek ...g N
Dephasing
N
Atomic density
i k t
c
e
g1 g 2 ...ek ...g N
k
k 1
 k  mk 

g
Atomic detuning 
Intensity
k
Output
mode
Input
mode
2p / 
Time
Periodic structure =>
Rephasing after a time
2p
te 

Collective emission in
the forward mode.
Photon echo like
emission
36
M. Afzelius, C. Simon, H. de Riedmatten and N. Gisin, Phys Rev A 79, 052329 (2009)
Atomic Frequency Comb (AFC) Quantum Memory
Ensemble of inhomogeneously broadened atoms
e
State after absorption
N
c
k 1
g1 g 2 ...ek ...g N
Dephasing
N
Atomic density
i k t
c
e
g1 g 2 ...ek ...g N
k
k 1
s

 k  mk 
Storage state
g
Periodic structure =>
Rephasing after a time
Atomic detuning 
Intensity
k
Input
mode
2p /   T0
Control fields
Ts
Output
mode
T0
Time
2p
te 

Collective emission in
the forward mode.
Photon echo like
emission
37
M. Afzelius, C. Simon, H. de Riedmatten and N. Gisin, Phys Rev A 79, 052329 (2009)
CRIB vs AFC
AFC
Absorption
Absorption
CRIB
w
w
CRIB vs AFC
AFC
Absorption
Absorption
Absorption
CRIB
APPLY
w
w
BROADENING
More atoms for the same bandwidth
using an AFC
 Efficiency constant with
bandwidth
w
Many atoms are lost in the
preparation step
 Efficiency decreases with
bandwidth
Truly Multimode memory
Ts 2p
2p
N 

N p  N p
t


Time multiplexing (multi-mode)
d  N2
 EIT based memory (stopped light)
J. Nunn et al, Phys. Rev. Lett. 101, 260502 (2008)
 Controlled Reversible Inhomogeneous Broadening
(CRIB) based memory
d  30  N
C. Simon et al, PRL 98, 190503 (2007), J. Nunn et al, Phys. Rev. Lett. 101, 260502 (2008)
 AFC based memory
N independent of d
10000
Optical depth d
EIT
CRIB
1000
100
New protocol AFC
0
5
10
15
20
25
30
35
Number of temporal modes
40
Counts [/200s]
Atomic Frequency Combs: recent progress
1000
Nature 456, 773 (2008)
800
600
400
200Detector noise
Nd3+:YVO
4 @879 nm
Pr3+:Y2SiO5@606nm
Phys.Rev. A, 81,033803(2010)
17 % efficiency, Tm: YAG@793nm
0
-2
0
2
4
6
Phase [rad]
8
Multi-mode storage in Nd3+:Y2SiO5
Mapping 64 input modes onto one crystal
n < 1 per mode
4F
(a)
3/2
3.0
Optical depth
2.5
n()
883 nm
Normalized counts
4I
9/2
2.0
1.5
1.0
-50

Input modes
1.0
T 1 
0.5
-25
0
25
50
Optical Detuning
Output[MHz]
modes x50
0.8
 1.3s
=1%
0.6
0.4
0.2
0.0
normalized counts
0.0
1.0
0.4
0.8
1.2
1.6
2.0
2.4
Time (s)
Input mode
Output mode x50
0.8
0.6
0.4
0.2
0.0
0.0
0.5
1.0
time [s]
1.5
2.0
2.5
Multi-mode storage in Nd3+:Y2SiO5
Mapping 64 input modes onto one crystal
n < 1 per mode
4F
(a)
3/2
3.0
Optical depth
2.5
n()
883 nm
2.0
1.5
1.0
Normalized counts
4I
0.5 used to code 32 time-bin qubits!
9/2 modes can be
64 time
-50
-25
0
25
50

Input modes
1.0
Optical Detuning
Output[MHz]
modes x50
I. Usmani, M. Afzelius, H de Riedmatten and N.Gisin,
arXiv:1002.3782
Nature Communications 1, 12 (2010)
0.8
0.6
0.4
T 1 
 1.3s
=1%
0.2
0.0
normalized counts
0.0
1.0
0.4
0.8
1.2
1.6
2.0
2.4
Time (s)
Input mode
Output mode x50
0.8
0.6
0.4
0.2
0.0
0.0
0.5
1.0
time [s]
1.5
2.0
2.5
In the lab
1060 temporal modes
Bandwidth ~1 GHz
But still storage
in excited state :
(quantum) delay only
AFC with spin wave storage in Pr3+:Y2SiO5
(collaboration with the group of Stefan Kröll, Lund University)
-On demand read-out
- Longer storage times
606 nm
(b)
Input
mode
Decay of coherence
due to inhomogeneous
spin dephasing.
1.0
Control
fields
Output
mode
Intensity (arb. units)
Intensity
Pr3+:Y2SiO5
0.8
0.6
Fitted spin distribution
Gaussian FWHM: 26 kHz
0.4
0.2
Ts
T 
Time 0.0
T
0
M. Afzelius et al, Phys. Rev. Lett. 104, 040503 (2010)
5
10
15
20
25
Duration of spin storage T (s)
30
AFC with spin wave storage in Pr3+:Y2SiO5
(collaboration with the group of Stefan Kröll, Lund University)
-On demand read-out
- Longer storage times
606 nm
(b)
Pr3+:Y2SiO5
1.0
Input
mode
Control
fields
Output
mode
Intensity (arb. units)
Intensity
Solution: Spin echo 0.8
 1 s spin
Decay of coherence
due to inhomogeneous
spin
coherence
! dephasing.
0.6
Fitted spin distribution
Gaussian FWHM: 26 kHz
0.4
0.2
Ts
T 
Time 0.0
T
0
M. Afzelius et al, Phys. Rev. Lett. 104, 040503 (2010)
5
10
15
20
25
Duration of spin storage T (s)
30
Outline
• Atomic gases
• Duan-Lukin-Cirac-Zoller protocol
• EIT and Raman
• Solid state atomic ensembles
• Rare-earth doped solids
• Photon echo based quantum memories
• Quantum storage of photonic entanglement in a crystal
C. Clausen, I.Usmani, et al, Nature 469, 508 (2011)
• Single atoms and ions quantum memories
Entanglement storage - Ingredients
1
‣ Quantum Light-Matter
interface
‣ Atomic Frequency
Comb in Nd3+:Y2SiO5
(Delay only)
2
‣ Entanglement Source
‣ SPDC in a PPKTP Waveguide
3
‣ Entanglement Measurement
‣ Franson type experiment
49
2 GHz
883nm
11 GHz
A narrowband SPDC source for interfacing
with the crystal memory
1 click
Requirements:
1 photon compatible with QM
1 photon at telecom wavelength
n=45 MHz
(SSPD)
C.Clausen et al, 2010
n=600 MHz
Absorption
~ 100 MHz
~ 6 GHz
Frequency
Storage and retrieval of
non classical light (heralded single photons)
Transmission
Echo
51
Storage and retrieval of
non classical light (heralded single photons)
Second order correlation vs storage time
Entanglement mapping
• Energy-time entanglement
– SPDC photons created in pairs (simultaneously)
– Time of creation uncertain within the coherence
time of the pump laser.
Entanglement mapping
• The Franson
Interferometer
- No single-photon interference
- Correlations visible in
coincidences
- Paths short-short and
long-long are indistinguishable
 interferences
i ( A B )
s
s

e
l AlB
Post-selected state
A B
Violation of Bell-inequality
possible for V > 0.71
Pair Source
long/long
short/short
long/short
short/long
Two-Photon interference with stored and
retrieved light
Violation of Bell-CHSH
inequality
S  E ( X 1 , Y1 )  E ( X 2 , Y1 )  E ( X 1 , Y2 )  E ( X 2 , Y2 )
S  2.64  0.23
C. Clausen, I.Usmani, F. Bussieres, M Afzelius, N. Sangouard, H. de Riedmatten and N. Gisin
Nature 469, 508 (2011)
Broadband waveguide quantum
memory for entangled photons
Group of Prof. Wolfgang Tittel
80 s
2.4 ms
Ti:Tm:LiNbO3 waveguides
 
1
 e,e  l,l )
2
E. Saglamyurek et al, Nature 469, 512 (2011)
Summary: atomic ensembles
• Atomic ensembles well suited for quantum light
storage, because of collective enhancement
• Cold atomic gases: one of the most advanced
quantum light matter interface
•Rare-earth doped solids: promising system
• First enabling steps towards multimode solid state
QM demonstrated
•Entanglement between a photon at telecomunication
wavelengths and a collective atomic excitation
Outline
• Atomic gases
• Duan-Lukin-Cirac-Zoller protocol
• EIT and Raman
• Solid state atomic ensembles
• Controlled Reversible Inhomogeneous Broadening
• Atomic Frequency combs
• Quantum storage of photonic entanglement in a crystal
• Single atoms and ions quantum memories
Single atom in high finesse cavity
Cavity QED in optical regime
A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, Phys. Rev. Lett. 98, 193601 (2007)
A single atom Quantum Memory
H. P. Specht, C. Nölleke, A. Reiserer, M. Uphoff, E. Figueroa, S. Ritter and G. Rempe, arXiv1103.1528
Heralded entanglement between two remote ions
S  2.22  0.07  2
F =0.81
Entanglement rate =1.5/ min (P heralding =5*10-8)
D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk, and C. Monroe, Phys. Rev. Lett. 100, 150404 (2008)
D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, C. Monroe, Nature 449, 68 (2007)
Summary
• Quantum memory: important device for QIS
Ensemble based QMs
Single atom QMs
-Strong coupling without cavities
-Collective enhancement
-Multiplexing
-QM for arbitrary quantum states
-Conceptually simple
-Challenging to implement
-Heralded absorption
-Quantum gates between 2 QMs !
Combine storage and
processing capabilities