[email protected] [email protected] rufus l. cone department for physics montana state university...

[email protected]@ucalgary.ca

Rufus L. Cone

Department for PhysicsMontana State UniversityBozeman, Montana, USA

Photon-echo type storage of quantum information using rare-

earth-ion doped crystals

Wolfgang TittelInstitute for Quantum Information Science and Department of Physics & Astronomy

University of CalgaryCalgary, Alberta, Canada


Rare-Earth-Activated Optical MaterialsEfficient, High-Power, Long-Lived IR, Visible, & UV Lasers

– Nd3+:YAG and Yb3+:YAG lasers for high power

– Nd3+:YAG doubled for green pointers– Nd3+:YVO4 doubled for watts of

green– Ho3+, Er3+, Tm3+, … medical, dental,

and industrial devices, …

Phosphors, Displays, Hg-Free Lamps, Solid-State Lighting

– Red Eu3+:Y2O2S, a critical factor in success of color TV

– Blue Eu2+ phosphors– Green Tb3+:(Ln, Ce)PO4 phosphor– White light by phosphors & diodes– Electroluminescent semiconductors

with rare-earth ions

Scintillators, Digital X-Ray Imaging, CAT and PET Scans, Particle Physics, and Oil Exploration, …

– Lu3+ provides high density for efficient absorption

– Some of the fastest and most efficient scintillator materials such as CeF3, Ce3+:YAlO3, and Ce3+:Lu2SiO5

Spectral Hole Burning Devices– High bandwidth analog signal

processing– Lasers stabilized to 2 parts in 1013 – Stabilized lasers for local oscillator in

atomic clock– Optical data storage

Quantum Information Devices– Eu3+:Y2SiO5, Pr3+:Y2SiO5, Er3+:Y2SiO5,

Tm3+:YAG, Tm3+:LiNbO3, Er3+:LiNbO3

– Er-doped optical fiber


Photon-echo type storage of quantum information using rare-earth-ion

doped crystals

- QIP, quantum memory, dream and reality

- Two-pulse photon-echo-based storage of light

- Photon-echo quantum memory (CRIB & AFC)

- Spectroscopic investigations of RE crystals for quantum memory

- Quantum state storage in RE crystals

- Conclusion

WT, M. Afzelius, T. Chanelière, RLC, S. Kröll, S.A. Moiseev, and M. Sellars, Las. Phot. Rev. 2010


Quantum information processing

Encoding information in quantum states of light allows doing some tasks better (as compared to classical encoding)

-Quantum computing - promises solving certain computational tasks in polynomial time - classical computers require exponentially increasing resources

-Quantum Communication - promises information-theoretic secure encryption - provides strong forward security (that does not break down in

the event of a quantum computer)

- QIP requires generation, (transmission), processing and detection of quantum states


Quantum memory, a synchronization device for quantum

data

Lvovsky, Sanders, WT, Nature Photonics (2010); Simon et al., quant-ph (2010)

|>QM |>

|>

|>

01010

01000


Quantum memory: dream and reality

Property Desired performance

State-of-the-art (quantum & classical memory)

Efficiency ≈1 0.69

Fidelity ≈1 0.92*

Multi-mode storage capacity

high 64 modes(>1000)

Pulse duration ≤ ns 700 ps

Storage time > sec >2 sec

Complexity simple …

Hedges et al., Nature 2010; X.-M. Jin et al., arXiv (2010); Usmani et al., Nature Comm. (2010); Chanelière, ISOMQIS 2010; Tittel et al., ISOMQIS 2010; Longdell et al., PRL (2005)

Diff

ere

nt s

tora

ge m

edi

a an

d p

roto

cols

* post selected


Storage of light using two-pulse photon-echoes

Kopvil’em & Nagibarov, Fiz. Metall. Metalloved. (1963)Kurnit, Abella & Hartmann, Phys. Rev. Lett. (1964), Mossberg, Opt. Lett. (1982)

hom

frequency

abso

rptio

n

/2-pulse

t

elec

tric

fi e

ld a

mp

litu

de

pulse

u

v

dephasing

=0

>0

<0

-pulse

0<0

rephasing

echo-pulse

echo at t=2

u

v

w

allows data storage!


Photon storage using two-pulse photon-echoes

Massar & Popescu, PRL (1995); Ruggiero et al, PRA (2009); Sanguard, WT et al., PRA (in press)

u

v

w-Storage of a weak (single photon) input followed by pulse inverts the atomic medium

- spontaneous emission of photons in random states (polarization, time) adds noise

-> decreased fidelity of output with input state

Pecho = Pnoise

out = Fin+(1-F)in

F = tr(inout) = 2/3

= Fclassical(max)


Photon-echo quantum memory (CRIB)1. Preparation of an optically thick, single absorption line

2. Controlled reversible inhomogeneous broadening (CRIB)

3. Absorption of light in arbitrary quantum state -> fast dephasing

4. Reduction of broadening to zero

5. Phase matching: (z) = -2kz ; Ein eikz Eout e-ikz

6. Reestablishment of broadening, with reversed sign

frequency

abso

rptio

n

(interaction with external electric field)

-> Time reversed evolution of atomic system and reemission of light in backward direction with unity efficiency and fidelity

frequency

abso

rptio

n hom

frequency

opt.

dep

th

Moiseev et al., PRL (2001); Nilsson et al., Opt. Comm. (2005); Kraus, WT et al., PRA(2006); Alexander et al., PRL (2006); Hoseini et al., Nature 2009; Hedges et al., Nature (2010); WT, RLC, et al., Las. Phot. Revs. (2010).

i -> -i i

i = it


Photon-echo quantum memory (AFC)

1. Preparation of an atomic frequency comb

2. Absorption of light in arbitrary quantum state -> fast dephasing and repetitive rephasing at tn =1/comb with 2itn= n 2

3. Phase matching (z) = -2kz enables backwards recall

4. Reversible mapping of optical coherence onto spin coherence allows recall on demand

frequency

abso

rptio

n

-> Reemission of light with unity efficiency and fidelity, very good

multi-mode storage capacities

frequency

abso

rptio

n hom

Hesselink et al., PRL (1979); Afzelius et al., PRA (2009); De Riedmatten et al., Nature. (2008); Afzelius et al., PRL (2010); Usmani et al., Nature Com. (2010).

comb


Why solid state quantum memory?

- Compared to atomic vapors, optical centers in solids do not move

-> allows for longer storage times-> no laser cooling necessary

- Many possibilities (color centers in diamond, RE ions in crystals, quantum dots,..)

- More degrees of freedom to explore (and master) -> spectroscopy needed


What Makes Rare Earth-Doped Crystals Special?• Why Use Solid State Materials for Quantum Memory?

Compared to Atomic Vapors, Ions in Solids Do Not MoveAllows for longer storage timesNo laser cooling necessary

• Only the Transition Elements Form Stable Compounds with Partially Filled Electron Shells Needed for a Resonant Optical MaterialTransition metals (3dN, 4dN, or 5dN), Rare earths (4fN), Actinides (5fN)Localized electronic transitions & sharp linesWavelengths range from far-IR to vacuum-ultraviolet

• Rare-Earth Ions Set Apart from Others4f electrons remain highly localized within the ion Optical transitions maintain much of an atomic-like character even in a crystalline

solid Atomic-Like Behavior and Strong Localization of the 4f ElectronsMany Options for Ions & Crystal Hosts

• Sharp Contrast to Transition Metal d Electronsd electrons are involved in chemical bonding strongly affected by host lattice d electrons may show significant delocalization and mixing with electronic states of

other ions in the lattice• Actinide 5f Electrons Provide an Intermediate Case, Properties Vary

Depending on the Material


Lanthanide Contraction Mayer (1941)/Meggers (1947)

• Strong Coulomb potential draws 4f electrons nearer to nucleus due to imperfect shielding of one 4f by another

• Lowest-energy electrons are not the outermost electrons

• The 5s2 5p6 closed shells “shield” the 4fN electrons from the crystal environment

• 4fN electrons maintain most of free ion atom-like character in a crystal

• Also responsible for chemical similarity of rare-earth ions

Rare Earth 3+ Ions

r (arbitrary units)


Summary of Special Rare Earth Properties

4fN to 4fN Optical Transitions of Rare Earths in Solids CanBe long lived; optical T1 ~ 10 ms observed

Have high fluorescence quantum efficiency ~100% Have exceptional coherence properties:

Optical T2 ~ 4 ms observed

Spin coherence up to 30 s

Be surprisingly sharp; h ~ 75 Hz observed

Vary slowly in frequency from material to material

Can be “compositionally” tuned

These properties can be achieved at

number densities of 1018/cm3 or more.


Principal Transitions for Spectral Hole Burning and Lasers

Echo, HoleBurning, and QIP Commercial

Solid State Lasers


Optical Linewidths of Ions in CrystalsRoom temperature

Lines are homogeneously broadened by phononsh = 60 – 1000 GHz 2 – 30 cm-1

Crossover to inhomogeneous broadening occurs ~ 77 K Strain and inhomogeneity

Narrowest homogeneous transitions occur forLowest component of Ground multiplet to lowest component of an Excited

multiplet

Low temperatures ~1.5 to 10 K (cryocoolers or helium)

inh = 1 - 30 GHz, or more depending on ion concentration

inh > 200 – 300 GHz with disorder

h = 15 Hz to a few kHz, in favorable cases that are lifetime-limited ~ 75 Hz observed in several crystal systems in our laboratory

Er3+:Y2SiO5 and Eu3+:Y2SiO5

Provides TREMENDOUS ratio: inh / h ~ 105 ... 108


Excite a subset of ions with a narrow-band laser

Excited ions are temporarily or permanently removed from the absorbing population

inh: 10’s to 100’s of GHz

h: as low as ~ 50 Hz

inh / h ~ 105 ... 108

Persistent Holes Weeks to indefinite

Transient Holes 10 ms lifetimes

abs

orp

tion

frequency

Spectral hole

inh

h

fLaser

Spectral Hole Burning … and Spectral Recording


Spectral hole burning allows tailoring the line shape for Quantum Memory Protocols such as CRIB & AFC

inh: 10’s to 100’s of GHz

h: as low as ~ 50 Hz

inh / h ~ 105 ... 108

Persistent Holes Weeks to indefinite

Transient Holes 10 ms lifetimes

abs

orp

tion

frequency

Spectral hole

inh

h

fLaser

Spectral Hole Burning … and Spectral Recording


Spectral Hole Burning Mechanisms & Lifetimes

Two-level saturation• Population storage in the excited state (ms to ns or less)

• Er3+:Y2SiO5 with lifetime T1 = 11 ms

• h = 75 Hz – several kHz possible

Optical pumping of hyperfine levels in Eu3+:Y2SiO5 • h = 120 Hz to several kHz

• Hole lifetime > 2 weeks in our lab

Local ion rearrangement• Tm3+:CaF2:D- and Er3+:CaF2:D- where interstitial D- moves• Hole lifetime appears indefinite based on activation energy

Gated spectral hole burning – ideal case• Two-photon photoionization • UV Photoemission used to explore options


Applications of Spectral Hole BurningSpatial-Spectral Holography – “S2” or “4 - d Holography”

Time- and space-domain holographySynthesis of • Spectral hole burning• Spatial holography and Fourier optics

Optical Signal Processing• High bandwidth spectrum analysis • Radar signal processing

beyond electronic bandwidths• Correlation and Convolution

of optical pulse trains• True-time delay for phased arrays

Optical Storage• Spectral holes = bits • Buffers at 1.5 microns, etc.

Laser Frequency Stabilization to Ultra-Narrow Spectral Holes

Crystal

Phase d ArraySSH TTD Controlled

Phased Array

N f( )

f

Crystal


Phased Array

N f( )

f

N f( )

f


Applications of Spectral Hole BurningSpatial-Spectral Holography – “S2” or “4 - d Holography”

Time- and space-domain holographySynthesis of • Spectral hole burning• Spatial holography and Fourier optics

Optical Signal Processing• High bandwidth spectrum analysis • Radar signal processing

beyond electronic bandwidths• Correlation and Convolution

of optical pulse trains• True-time delay for phased arrays

Optical Storage• Spectral holes = bits • Buffers at 1.5 microns, etc.

Laser Frequency Stabilization to Ultra-Narrow Spectral Holes

Crystal


Phased Array

N f( )

f

Crystal


Phased Array

N f( )

f

N f( )

f

That Work Led Naturally to Quantum Information & Slow Light


Rare Earth Ion HamiltonianFree ion (Slater-Racah) ‑ Full rotation symmetry

1. Central field splits configurations ~ 105 cm-1 (10 eV)2. Within lowest configuration 4fN

Non-central field ~ 104 cm-l (1 eV)Spin-orbit coupling ~ 103 cm-l (0.1 eV)

3. Eigenfunctions of form:

built up from products of single-electron basis states

Weak crystal field (Bethe) ‑ Local site symmetry1. Free ion levels split ~ 100 - 200 cm-1 (10 - 20 meV)2. Eigenfunctions of form

(Sometimes, summation over J is important)

Hyperfine and superhyperfine splittings – kHz to GHz

Orbit-lattice interaction – Non-radiative relaxation, thermal line shifts, etc.

JMJ

LML

SMS

LML

SMS

LML

SMS

JMJ

,,,,

JJ

MJ

JM

JMJJ


Free ion (Slater-Racah) ‑ Full rotation symmetry1. Central field splits configurations ~ 105 cm-1 (10 eV)2. Within lowest configuration 4fN

Non-central field ~ 104 cm-l (1 eV)Spin-orbit coupling ~ 103 cm-l (0.1 eV)

3. Eigenfunctions of form:

built up from products of single-electron basis states

Weak crystal field (Bethe) ‑ Local site symmetry1. Free ion levels split ~ 100 - 200 cm-1 (10 - 20 meV)2. Eigenfunctions of form

(Sometimes, summation over J is important)

Hyperfine and superhyperfine splittings – kHz to GHz

Orbit-lattice interaction – Non-radiative relaxation, thermal line shifts, etc.

Rare Earth Ion Hamiltonian

JMJ

LML

SMS

LML

SMS

LML

SMS

JMJ

,,,,

JJ

MJ

JM

JMJJ

Important for QIS


Role of Symmetry in Choice of Host MaterialFree ion (Slater-Racah) ‑ Full rotation symmetry

Eigenfunctions of form:

Weak crystal field (Bethe) ‑ Local site symmetry

1. Free ion levels split ~ 100 - 200 cm-1 (10 - 20 meV)

2. Eigenfunctions of form

Local point symmetry often forbids optical transitions from lowest component of Ground multiplet to lowest component of Excited multiplet - but those are the ones we need !

Branching ratio among hyperfine levels for optical and RF transitions also depends on symmetry (and direction of applied fields) and is critical for state preparation and other aspects.

JMJ

LML

SMS

LML

SMS

LML

SMS

JMJ

,,,,

JJ

MJ

JM

JMJJ


Material Design and Characterization Tasks

Active Ions & Transitions• Operating wavelength range • Lowest to lowest transition allowed• Dynamical properties

• Gap to next lower multiplet• Magnetic g factors

• Storage times (optical & hyperfine)

Host Materials • Specific wavelengths & compositional

tuning• Bandwidth by control of disorder • Low nuclear magnetism• Phonons impact decoherence

Spectral Coverage • Absorption spectrum

• lamp absorption for big picture of ion’s energy level structure

• laser absorption for precision• watch out for hole burning distortions • watch out for optical density distortions • watch out for leakage around sample

• Photon echo-excitation spectrum

Decoherence and Bandwidth• Photon echoes• Spectral diffusion by stimulated

photon echoes• Time-resolved spectral hole

burning• Large parameter space

• concentration• magnetic field magnitude• magnetic field direction• temperature• light direction• light polarization• electric field effects

• ODNMR, ODEPR, PENDOR, etc.

Crystal GrowthMaterial OptimizationDevice Demonstrations

Large Scope & Critical Part of System Design for QIS & SSH


Specialized Requirements (& Tradeoffs)No material currently solves all problems for all protocolsProtocols evolve, too

Long decoherence times T2 – optical and magnetic sublevel• Hosts, fields, & potentially magic angles (Pr3+:Y2SiO5)• Controlling spectral diffusion

Inhomogeneous broadening• Narrow 1-10 MHz for CRIB • Broad for AFC protocols

Hyperfine structure with long decoherence timePermanent ground state electric dipoles for CRIB – symmetryNice to have optically-resolved hyperfine structure (very rare)Large oscillator strengths for relevant optical transitionsNeed better understanding of mechanisms of inhomogeneous

broadening• Crystal growth, strain, defects – defect chemistry, growth chemistry, …


Magnetic Hyperfine Interactions – Odd Electron Case

Hamiltonian

Hhfs = J I J where J is an atomic constant

Er3+ 162 (0.14%), 164 (28.2%), 166 (33.6%), 168 (26.8%), 170 (14.9%)

All I = 0 No HFS 167 (22.94%)

I = 7/2 1st Order HFS

Kramers Degeneracy of Electronic States All Levels Are Magnetic


Electric Hyperfine Interactions – Even Electron CaseHamiltonian for Electric Quadrupole & Pseudo-Quadrupole Interactions

Heq = P [(IZ2 - I(I+1)/3) + (IX

2 – IY2)/3]

+ h N I (1 - ) B

Flurin Könz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, Phys. Rev. B. 68, 085109 (2003)

151Eu3+:151Eu3+: Y2SiO5 I = 5/2

Hole Burning Spectrum

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).

141Pr3+: Y2SiO5 - 100% I = 5/2

C1 Symmetry Site – Singlet Lowest No Electronic Moment,

Only Pseudo-Quadrupole

Crystal field levels &Hyperfine splittings


Investigated: 0.001%, 0.005%, 0.02%, 0.1% Er3+ concentrations and also co-doped with 1% and 2% Eu3+ to induce weak disorder

Grown by: of Bozeman, MT

• Active ion is Er3+

• Er3+ replaces Y3+ on sites of C1 symmetry

• Transient hole burning by population storage gives hole lifetime: T1 ~ 11 ms

• T ~ 1.5 – 5 K to minimize phonon & spin-flip broadening

Site 1

4I13/2

4I15/2

T1 ~ 11 ms1.53614 m

41 cm-191 cm-1

0 cm-1

39 cm-1 84 cm-1102 cm-1

0 cm-1

• • •

• • •

Basic Spectroscopic Properties of Er3+:Y2SiO5

Opt. Lett. 22, 871-873 (1997)

J. Lumin. 94-95, 565-568 (2001)

Proceedings of SPIE Vol. 4988, 51-61 (2003)

Physical Review B 73, 075101 (2006)

Physical Review B 74, 075107(2006)


Broadening Er3+:Y2SiO5 for Increased Processing Bandwidthby Introduction of Eu3+

Site 1, D2 Polarization Highlighted Below

* Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic bi-phase codes, Appl. Phys. Lett. 81, 3525-3527 (2002)

Controlled compositional disorder in Er3+:Y2SiO5 for wide bandwidth hole burning material at 1.5 m, Böttger, Thiel, Cone, and Sun, Phys. Rev. B 77, 155125 (2008).

0.005%Er3+:Y2SiO5 *

Er conc inh abs. coeff.

0.005% 0.5 GHz 7 cm-1

0.02%Er3+:1%Eu:Y2SiO5


0.02% 12.5 GHz 1.14 cm-1

0.02%Er3+:2%Eu:Y2SiO5


0.02% 21.5 GHz 0.6 cm-

1


Suppress and manage spin-flip broadening using:

• Er3+ dopant concentration (range dependent interactions)

• Temperature (thermal population)

• Magnetic field (maximize level splitting)

• Magnetic field direction (maximize level splitting)

Er3+-Er3+ Interaction Dynamics and Spectral Diffusion

Time

Spectral hole evolves with time

Spectral hole broadens

Hole area may be conserved

Time

Spectral hole evolves with time

Spectral hole broadens

Hole area may be conserved

Successfully modeledPhysical Review B 73, 075101 (2006)

4I15/2: Z1

4I13/2: Y1

Levels shifted dynamically

Er3+ optical center Neighboring ground state Er 3+ ions(not to scale)

spin-flip

spin-flip

+

direct-phonon driven

4I15/2: Z1

4I13/2: Y1

Levels shifted dynamically

Er3+ optical center Neighboring ground state Er 3+ ions(not to scale)

spin-flip

spin-flip

+

direct-phonon driven


5 10 15 20 25 30 35 40

0.01

0.1

1

T = 0 s

T = 7 s

T = 10 s

T = 15 s

T = 20 s

T = 35 s

T = 50 s

T = 70 s

T = 100 s

T = 200 s

T = 700 s

T = 2000 s

T = 10000 s

No

rma

lize

d E

ch

o In

ten

sity

t12

- delay (s)

1 2 3stimulated

photon echo

photonecho

step t12 T

time

0 121

1122

Spectral Diffusion Theory:

2( ) exp exp 4

1 exp( )h SD

TI t I t

T

Rt RT

Stimulated Echo t12- Decay


Magnetic field suppresses

spectral diffusion

J. Lumin. 94-95, 55 (2001)

hInitial linewidth

SDSaturated linewidth

R – Rate of perturbations

T – Waiting time

1 10 100 1000 10000

0

20

40

60

80

100

120

140

160

0.02 % Er3+:Y2SiO

5

T = 1.6 K

(k

Hz)

T (s)

B = 0.8 T B = 1.5 T B = 1.75 T B = 2 T B = 2.25 T B = 3 T

12 1 exp( )h SD RT

Spectral Diffusion: Magnetic Field Dependence


B

D1

D2b

k

0 20 40 60 80 100 120 140 160 180 200

103

104

105

0

2

4

6

8

10

12

14

16

140.6 O

B //

D2

B //

D1

B //

D1 0.001 % Er3+:Y

2SiO

5, 1-544-Top

site 1, B = 3 T, T = 1.6 K

Line

wid

th (

Hz)

Angle (degrees)

0.005 % Er3+:Y2SiO

5, 7-167

site 1 & 2, B = 0.5 T, T = 5 K

g -

fact

or

excited state site 1 ground state site 1 ground state site 2 excited state site 2

time

- pulse

/ 2 - pulse

photon echo

MT

1 hom

step t12

Angle Dependent g-Factors and Linewidth h


Achieving 30 sec Hyperfine Coherence for Pr3+ & Eu3+

Controlling spectral diffusion • No first-order magnetic moment for electronic singlet states (unlike Er3+)• Local field fluctuations arise from ligand nuclear moments• Nuclear Zeeman splittings too small to allow “freezing out” spin fluctuations

Solution is to find magnetic fields and field directions where hyperfine Zeeman splittings are “stationary”

Dynamic decoherence control of a solid-state nuclear-quadrupole qubit, E. Fraval, M. J. Sellars, J. J. Longdell, Phys. Rev. Lett. 95, 030506 (2005).

Method of extending hyperfine coherence times in Pr3+:Y2SiO5, E. Fraval, M. J. Sellars, J. J. Longdell, Phys. Rev. Lett. 92, 077601 (2004).

Hyperfine interaction in ground and excited states of praseodymium-doped yttrium orthosilicate, J. J. Longdell, M. J. Sellars, N. B. Manson, Phys. Rev. B 66, 035101 (2002).


Er3+:LiNbO3 & Tm3+:LiNbO3 PapersJ. Lumin. 130, 1603-1609 & 1598-1602 (2010)

Large energy splittings—Er3+:LiNbO3 has a Favorable Energy Level Structure

Oscillator strength concentrated in desired 4I15/2 (1) to 4I13/2 (1) transition

ErEr3+3+:LiNbO:LiNbO33 Energy Levels Energy Levels

Er3+:LiNbO3

4I13/2

4I15/2

1.532 m

62 cm-187 cm-1

0 cm-1

63 cm-1132 cm-1156 cm-1

0 cm-1

• • •

• • •

Crystal Field Splittings


Photon echo spectroscopy is a powerful probe of optical decoherence, spectral

diffusion, and superhyperfine interactions

Optical Decoherence Measurements Optical Decoherence Measurements

Distribution A: approved for public release; distribution unlimited

Decays are non-exponential—Indicates presence of strong spectral diffusion over timescale of measurement

Echo modulation observed for timescales of a few s—Indicates strong superhyperfine coupling to 93Nb and 7Li nuclei in host and large inhomogeneity

Some motional narrowing can be observed at longest timescales when t ~ 1/R

MT

1 hom

time

- pulse

/ 2 - pulse

photon echo


Stimulated photon echo techniques provide an exceptionally powerful tool to characterize time-dependent broadening and probe spectral diffusion dynamics

Time Evolution of Linewidth Time Evolution of Linewidth

Use stimulated echo decays to measure the effective linewidth over a wide range of timescales

Spectral diffusion causes echo decay shapes and decoherence rates to evolve over time

Use spectral diffusion model to fit decays and extrapolate to linewidth at t12=0 —allows us to probe broadening independent of decoherence during t12

Distribution A: approved for public release; distribution unlimited

step t12

time

321

T23

photon

echo

stimulated

photon echo

step t12

time

321

T23

photon

echo

stimulated

photon echo


Ion - Ion InteractionsRare Earth - Rare Earth Interactions

1. Electronic exchange2. Magnetic dipole-dipole3. Electric multipole-multipole (includes electric dipole-dipole)4. Virtual phonon exchange

Pair Symmetry Typically Not Unique

Laser-Induced “Instantaneous Spectral Diffusion”

G. K. Liu and R. L. Cone, Phys. Rev. B 41, 6193-6200 (1990).References on Rare Earth - Rare Earth Interactions

R. L. Cone and R. S. Meltzer, Ion-Ion Interactions and Exciton Effects in Rare Earth Insulators, Chapter 8 in Spectroscopy of Crystals Containing Rare-Earth Ions, Ed. by A. A. Kaplyanskii and R. M. Mafarlane (North Holland, 1987).

S. Hufner, Optical Spectroscopy of Lanthanides in Crystal Matrix, Ch. 8 in Systematics and the Properties of the Lanthanides, Ed. S. P. Sinha, (D. Reidel Publ. Co., Dordrecht, 1982).

S. Hufner, Optical Spectra of Transparent Rare Earth Insulators (Academic Press, New York, 1978).

R. L. Cone and W. P. Wolf, Phys. Rev. B 17, 4162 (1978). W. P. Wolf, J. Phys. (Paris) 32, C1‑26 (1971).

J. M. Baker, Rep. Prog. Phys. 34, 109 (1971).

W. P. Wolf and R.J. Birgeneau, Phys. Rev. 166, 376 (1968).

Hz level to 10 cm-1 (300 GHz)


Experimental demonstrations

- storage of sub-nanosecond qubits using AFC

- time-variable storage (of classical data) in spin states using AFC

- 69% efficiency quantum storage with CRIB

WT et al., ISOMQIS (2010); Afzelius et al., PRL (2010); Hedges et al., Nature (2010).


Ti:Tm:LiNbO3 waveguides

N. Sinclair, WT et al., J. Lumin. (2010), C. Thiel, RLC et al., J. Lumin. (2010)

Thulium

- 795 nm zero phonon absorption line, hom ~200 kHz @3K

- large, polarization and wavelength dependent optical depth (min~2.2/cm @ 3K & 795.5 nm)

- T1(3H4)=80 s

- optical pumping into magnetic ground-state sublevels (T1~sec @ B=150G & T=3K)

LiNbO3:

- no inversion symmetry -> Stark shifting of resonance lines

- “telecommunication” material, waveguide fabrication well mastered

Waveguide

- large Rabi frequencies

- fast switching of large electric fields using closely spaced electrodes

- simplified integration with fibre optic components and into networks

80 s

2.4 ms


The setup

T=2.9K B=133 G

Oscilloscope

Laser AOM pol. mod. PBS

Detector Ti:Tm:LiNbO3 waveguide

fibre-to-fibre coupling loss ~10dB

- prepare AFC (2 ms long pulse sequences)

- wait 1.5 ms (19 T1)

- send data to be stored

- register transmitted and recalled data

- prepare AFC (2 ms long pulse sequences)

- wait 1.5 ms (19 T1)

- send data to be stored

- register transmitted and recalled data

P l

time frequency

795.5 nm

≥300 ps

Width ~1/

80 s

2.4 ms


Storage of classical data – 20 ns long pulses

internal≈ 1.25 %

0.00

0.02

0.04

0.06

0.08

0.10

op

t. p

ow

er (

au)

Time (ns)

Transmitted light

Recalled light

-100 0 100 200

0 20 40 60 80 100

0

1

2

3

4

5

6

7

Op

tica

l De

pth

Frequency (MHz)

Frequency comb

d0

d1

e d1

Fd1

F

2

e 7

F 2e d0

F=2, d0~1.1, d1~1.6

-> ~ 1.6 %

F=

De Riedmatten et al., Nature (2008)


Storage of sub-ns time-bin qubits

- AFC preparation using 300 ps long pulses -> GHz-width AFC

- 0.4 photons/qubit before cryostat, 500 ps duration of each temporal mode

- 30 to 60 ns storage time

T=2.9K B=133 G

TDC

Laser AOM pol. mod. PBS

Si- APDTi:Tm:LiNbO3

waveguide

795.5 nm

Sta

rt

Stop

|>=|t0>+ei|t1>

xx0x1

px

Time-bin qubit


Storage of sub-nanosecond time-bin qubits

- 700 ps duration output pulses

- internal efficiency 4.5 %

- out = Fin+(1-F)in

F = Pcorrect/(Pwrong + Pcorrect)

= 0.989/0.994

> Fclassical(max) = 2/3

200 300 400

0

500

1000

1500

late bin counts : 347

early bin counts :2

early bin counts : 366

late bin

Cou

nts

Time (ns)

early bin

late bin counts : 4

Separation between the bins 30 ns

Storage time : 65 ns

|>=|t0>+ei|t1>


Two-path interferometer/projection onto qubit states

h

D1

1

0

1e0 i

Interference

data

- comb spacing determines moment of recall

- two superposed combs -> two recalls

- difference between minima and maxima determines fidelity with target state


Two-path interferometer/projection onto qubit states

-50 0 50 100 150 200 250 300 350 400

0

100

200

300

400

500

600

- state V = 96.4%+ state V = 97.4%

|s> + |l> storage |s> - |l> storage

Co

un

ts

Grating relative phase (degrees)

Double grating visibility curveDouble grating read-out

Fmean=(1+Vmean)/2 = 0.985 > 2/3


AFC memory with variable storage time

0/1 T time

outputcontrol fields

0TsT

Inte

nsity input

Afzelius et al., PRL (2010)

- Material: Pr:YSO, 3H4 <-> 1D2 transition @ 606 nm

- AFC determines storage time (in opt. coherence) of 4 sec

- Transfer to ground state coherence -> variable storage time

17 MHz

10 MHz

4.8 MHz

4.6 MHz

inpu

t

cont

rol f

ield

s

outp

ut

±1/2

±3/2

±5/2

±1/2

±3/2

±5/2


AFC memory with variable storage time

Tot

al s

tora

ge t

ime

0 5 10 15 20

0

1

2

3

4

5

6

TS

(a)

Inte

nsity

(ar

b. u

nits

)

Time (s)

TM=9.6 µs

TM=11.6 µs

TM=14.6 µs

TM=19.6 µs

Output pulses

0/1 T time

output

control fields

0TsT

Inte

nsit

y input

Afzelius et al., PRL (2010)

Storage time limited by inhomogeneous broadening of spin transition


Efficient CRIB-type quantum memory

140 KHz wide spectral feature

140 dB tall

longitudinal broadening (gradient echo) to 1.6 MHz, 15 dB tall

Hedges et al, Nature (2010), Slide stolen from Mathew Sellars and modified


Gradient Echo efficiency

Input pulse duration: 600 ns

First: 69 2% (switched 1.4 s)

Second: 45 2%(switched at 2.1 s)

Noise analysis proves quantum nature

Hedges et al, Nature (2010), Slide stolen from Mathew Sellars and modified


Conclusion- Building on the past 50 years, CRIB & AFC photon-echo quantum

memory in RE crystals becomes competitive with other approaches

- RE crystals also suitable for other protocols (slow light, DLCZ,..)

- Photon-echo quantum memory feasible in gases

- Still much to be done, protocols, materials, and material knowledge has to improve in parallel

- Workable quantum memory may soon exist


Thank youMontana State University, Bozeman, MT

C. W. Thiel, R. M. Macfarlane, Y. Sun, T. Böttger, M. J. M. Leask, R. W. Equall, and W. R. Babbitt

Air Force Office of Scientific ResearchNational Science FoundationScientific Materials Corporation, Bozeman, MT

Ralph Hutcheson & R. W. Equall

University of Calgary, Calgary, ABE. Saglamyurek, N. Sinclair, C. La Mela, J. SlaterNSERC, GDC, iCORE

University of Paderborn, Paderborn, GermanyM. George, R. Ricken, W. Sohler


Quantum memory

- A synchronization device for quantum data

- A key ingredient for a quantum repeater

Lvovsky, Sanders, WT, Nature Photonics (2010); Simon et al., quant-ph (2010)

|>QM

BSM

QM

E E

QM

BSM

QM

E E

QM

BSM

QM

E

BSM BSM


Photon storage using two-pulse photon-echoes

Massar & Popescu, PRL (1995); Ruggiero et al, PRA (2009); Sanguard, WT et al., PRA (in oress)

u

v

w

-Time-bin qubit (single photon) input: spontaneous emission adds significant noise

- Pecho = Pnoise

out = Fin+(1-F)in

F = tr(inout)

= (Pecho + Pnoise)/(Pecho + 2Pnoise) = 2/3

= Fclassical(max)

P(x) P(x)

x x

|>=|0>+ei|1>


Storage of classical data- 500 ps long pulses

550 ps

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

46 48 50 52

0

1

2

Second order echo

Echo

Inte

nsi

ty (

au)

Time (ns)

Transmitted

FWHM=71018 ps

Inte

nsi

ty (

au)

Time (ns)

opt.

pow

er (

au)

op

t. p

ow

er

(au

) internal≈ 4.5 %

710 ps

AFC preparation using 300 ps long pulses -> AFC spectral width > GHz

[email protected] [email protected] rufus l. cone department for physics montana state university...

Documents

quantum information

quantum information

quantum states of light

quantum data lvovsky

quantum computer qip

detection of quantum

yag lasers

based storage of light