Ultra-narrow optical inhomogeneous linewidth in a stoichiometric rare earth crystal

0.67 MB·

by  R. L. Ahlefeldt

Ultra-narrow optical inhomogeneous linewidth in a stoichiometric rare earth crystal
R. L. Ahlefeldt,1,2 M. R. Hush,3 and M. J. Sellars4
1Department of Physics, Montana State University, Bozeman, MT 59717, USA
2Laser Physics Centre, Research School of Physics and Engineering,
The Australian National University, Canberra 0200, Australia
3School of Engineering and Information Technology,
University of New South Wales at the Australian Defence Force Academy, Canberra 2600, Australia
4Centre for Quantum Computation and Communication Technology,
Research School of Physics and Engineering, The Australian National University, Canberra 0200, Australia
(Dated: July 26, 2016)
We have obtained a low optical inhomogeneous linewidth of 25 MHz in the stoichiometric rare
earth crystal EuCl .6H O by isotopically purifying the crystal in 35Cl. With this linewidth, an
3 2
important limit for stoichiometric rare earth crystals is surpassed: the hyperfine structure of 153Eu
6
is spectrally resolved, allowing the whole population of 153Eu3+ ions to be prepared in the same
1
hyperfine state using hole burning techniques. This material also has a very high optical density
0
and can have long coherence times when deuterated. This combination of properties offers new
2
prospects for quantum information applications. We consider two of these, quantum memories and

l quantum many body studies. We detail the improvements in the performance of current memory
u
protocols possible in these high optical depth crystals, and how certain memory protocols, such as
J
off-resonant Raman memories, can be implemented for the first time in a solid state system. We
5
explainhowthestrongexcitation-inducedinteractionsobservedinthismaterialresemblethoseseen
2
in Rydberg systems, and describe how these interactions can lead to quantum many-body states

that could be observed using standard optical spectroscopy techniques.
]
h
p PACSnumbers: 03.67.Hk,32.70.Jz,78.40.Ha,61.72.S-
-
t
n
a The hyperfine levels of rare earth ions have exception- tions. Very narrow inhomogeneous linewidths have been
u allylongcoherencetimes, asmuchas6hoursin151Eu3+ observed in rare-earth doped crystals by reducing the
q [1]. Additionally, these hyperfine levels are addressable dopant concentration to the ppm level and by isotopi-
[
through an intermediary optical level, allowing high fi- cally purifying the host. The most well-known exam-

2 delityspinstorageandreadoutusingopticalpulses[2,3]. ple is YLiF [12–14]. When isotopically purified in 7Li
4
v Because of these properties, doped rare earth crystals to remove broadening caused by isotopic disorder, this
3
have received considerable attention for quantum mem- material has optical inhomogeneous linewidths as low as
1
ory applications [2–6]. 16 MHz for Er3+ [15] and 10 MHz for Nd3+ [16]. To
0
5 Allthespin-wavequantummemorydemonstrationsto achieve such narrow lines, it was necessary to use ex-
0 tremely low rare earth dopant concentrations, around
datehaveusedrare-earthdopedcrystalswithlowconcen-
. 3 ppm. So although these crystals are much lower dis-
1 trations, ranging from 0.001 to 0.05% [2–4, 7], resulting
0 in low optical densities of the order of 1 cm−1. In addi- order than current memory materials, their optical and
6 spatial densities are low, and little advantage is gained
tion, partly as a consequence of the disorder introduced
1 from their narrow lines for quantum memory purposes.
by the rare earth dopant, these crystals exhibited inho-
:
v mogeneous linewidths of the order of GHz, much greater In this paper, we show that small inhomogeneous
i
X than the hyperfine structure and the available Rabi fre- linewidths can be achieved at the same time as high op-
quencies. As a result, spectral hole burning techniques ticalandspatialdensitiesbyisotopicallypurifyingama-
r
a werenecessarytocreatethenarrowspectralfeaturesthat terial that is stoichiometric, rather than doped, in the
would allow memory demonstrations. The use of these rare earth ion. The linewidth reduction is sufficient in
techniques, combined with the low initial optical den- our chosen material, EuCl .6H O, that the rare earth
3 2
sity of the crystal, severely reduces the number of ions hyperfine structure is resolved. Reaching this limit in
that can contribute to the operation of the memory (the the high optical depth regime has broad-reaching impli-
usable optical depth), limiting its efficiency and storage cations for quantum memories. It also opens new ap-
density [8–10]. Because of these limitations, only two plications, and in particular we discuss the use of these
quantummemorydemonstrationstodatehavesurpassed materialsformanybodyphysicsstudies,whicharemade
theno-cloninglimit,andinbothcasesaverylargeinter- possible because the linewidth is also smaller than the
action length was required to obtain a sufficient optical nearest-neighbor ion-ion interactions [17].
depth to store even a single mode [4, 11].
EuCl .6H O is a good starting point in the quest to
3 2
Narrowlinewidth,highopticaldensitymaterialswould achieve ultra-narrow linewidths because it already has a
thereforebeverybeneficialforquantummemoryapplica- verynarrow, 100MHzopticallinewidthwithoutisotopic
2
that D is responsible for 1.4 MHz of the inhomogeneous
broadening seen in natural abundance crystals. Assum-
ing the broadening scales linearly with the relative mass
difference, the concentration and the abundance, we ex-
pect that 17O and 18O contribute 2 MHz to the in-
≈
homogeneous broadening, 37Cl 60 MHz, and 151Eu3+
≈
10 MHz. These numbers are approximate, but clearly
≈
indicate that 37Cl is likely to be the major source of
broadening in EuCl .6H O, and that the best method
3 2
for reducing the linewidth is to isotopically purify the
crystal in 35Cl.
We grew a crystal isotopically purified in 35Cl from
a water solution at just above room temperature. The
startingmaterialwas6gofEu35Cl .6H Othathadbeen
3 2
prepared from Na35Cl and 99.999% EuCl .6H O. The
3 2
nominalisotopicpuritywas99.67%. Sufficientwaterwas
added to saturate the solution at 30◦C. A crystal was
FIG. 1. The first shell of Eu3+ ions (gray) in EuCl .6H O.
3 2
The C symmetry axis is vertical. The Eu3+ ions are la- grown out of the solution over 1 week after lowering the
2
beled by their distance from the central ion. Ligand ions Cl temperature to 29◦C. The growth rate during this time
(green), O (blue) and H (red) are only shown for the central wasnotconstantasthehotplateusedforgrowthonlyhas
ion. Our previous measurements suggest that the static in- atemperaturestabilityof 1◦C.Anunstablegrowthrate
teractionbetweenionsseparatedby6.53˚AalongtheC axis ±
2 canleadtoinclusionsandothergrowthdefects. Because
is >40 MHz.
the base linewidth in this material is so low, the effect of
these rare growth defects can start to be seen as small
macroscopic variations in the inhomogeneous linewidth
purification[18], and good coherence times when deuter-
of the order of 20 MHz over millimeter-sized regions of
ated [19]. This makes it an excellent quantum memory
thecrystal. Weexpectthatthemajorityofthesedefects
candidate in its own right.
and the associated macroscopic variations in broadening
EuCl .6H O is a monoclinic crystal with a single rare
3 2 can be removed by improving the temperature stability
earthsiteofC sitesymmetry[20,21]. Theenvironment
2 of the growth process.
of an Eu3+ ion in EuCl3.6H2O is shown in Figure 1. It The excitation spectrum of the 7F 5D transition
0 0
haseightdirectligands–sixwatermoleculesandtwoCl →
wasmeasuredwithaCoherent699-29ringdyelaserwith
ions at distances between 2.4 and 2.8 ˚A. Also shown are
the crystal at 4 K in a helium bath cryostat. Because
the first shell of Eu3+ neighbors.
EuCl .6H O is hygroscopic, the crystal was mounted in
3 2
The 7F0 5D0 transition of EuCl3.6H2O at a small helium-gas-filled chamber to avoid exposure to
→
579.703nm(vacuum)showsastructuredlinespreadover air or vacuum. The laser beam was orientated parallel
600 MHz, with each component line approximately 100 to the C axis to minimize absorption. Even along this
2
MHz wide. The structure of the line can be completely direction, the absorption is high, and a confocal imag-
explained by a combination of the hyperfine structure of ingsystemwasusedtocollectfluorescenceonlyfromthe
the two europium isotopes and shifts caused by different front face of the crystal. In this setup, achromatic 10 cm
isotopes occupying the nearest neighbor ligand positions lenses were used for objective and imaging lenses, and
[18]. These isotope shifts can be large, up to 2 GHz for the emission was focused onto the end of a 62.5 µm mul-
Eu3+ ions neighboring D ions (2H), and we expect that timode fiber serving as the pinhole.
isotopesoccupyingmoredistantsitescontributesubstan- Figure 2 shows the excitation spectrum of
tially to the inhomogeneous broadening. Eu35Cl .6H O. There is a 200 MHz Eu3+ isotope
3 2
Thecontributionofthedifferentisotopestothebroad- shift in EuCl .6H O, leading to two sets of peaks:
3 2
ening can be estimated simply. It depends on the con- around0MHzfrequencyoffsetarethosedueto151Eu3+,
centration of that element in the crystal, the abundance while at higher frequencies are those due to 153Eu3+.
of the isotope relative to the dominant isotope, and the These sets of peaks are split by the hyperfine inter-
perturbationtothelatticecausedbysubstitutingtheiso- action. For 153Eu3+, which has hyperfine splittings
tope. This latter quantity depends on the relative mass approximately twice as large as 151Eu3+, this hyperfine
difference of the isotope and the dominant isotope, thus structure is well resolved. In Fig. 2, we have labeled
Dcausesthelargestperturbationand151Eu3+ thesmall- each peak for 153Eu3+ with the transition that generates
est. it.
Wehavemeasuredtheinhomogeneousbroadeningrate The inhomogeneous linewidth of each line in the spec-
due to D as 91 MHz/% concentration [18], suggesting trum is 25 5 MHz. The instrumental broadening due
±
3
rb.units) 0.81 110397..90 eee123 (g3→eg11)→eg12→e2 gg31→→ee32 tttlaihahfleleeitfieiggsmt11ieme→→x,ecaigtoee2vf3dastaleribnvadydenrastagiswtl2siuooh→mnofi.uperetlAs3di,osstnso:ruvafmaenornrisn9iotEg0ipo%uatnCicsovla3feal.rnt6yfihHdeel2load1Onn5g3swrEwhfuheyfip3ipce+theldroifihovonnaenessr
a
nalintensity( 00..46 1577340E..50u87 ggg123 gg23→→ee12 g2→e3 cdigmne3een.ntatshGseieutriyvreoeenodfntftitftrhohheereecgEorp3ysurcseC→itplallaa3lr.te6ceo3adHrnl2sfieOtnbraeeet(nuo3pgrvuet×ehmris1tp90h>e8−ad%t94)i0wn,o0teft0ohhtcegham3vep,e−eiao1pan.nrkdesvoaaipotrtueitcshilanyel
Sig 0.2 (g1→e3) Combined with Eu35Cl .6H O’s other properties, this
3 2
extremely high optical density makes this crystal very
0
200 0 200 400 attractive for quantum memory applications. The low
−
Opticalfrequencyoffset(MHz) optical density of current memory crystals, of the order
of 1 cm−1, has severely limited the quantum memory
FIG. 2. Excitation spectrum of the 7F →5D transition in performance in demonstrations to date. An increase in
0 0
isotopicallypureEu35Cl3.6H2O.Theenergylevelstructureof optical density can improve aspects of the performance
the 7F ground and 5D excited states for 153Eu3+ is shown
0 0 of all spin-wave storage quantum memory protocols for
ontheupperleft,wherethesplittingsaregiveninMHz. The
rareearthcrystals, whichcomprisetheatomicfrequency
positions of each transition between the 153Eu3+ ground and
comb (AFC) [22], the gradient echo memory (GEM)
excitedstatesareindicatedbyredlinesonthespectrum. The
weak transitions are bracketed. [23, 24] and Raman-type protocols such as electromag-
netically induced transparency (EIT) [25, 26]. Here,
we briefly describe the improvements in memory perfor-
to instability in the laser scan is less than 5 MHz. As mancethatcanbeexpectedfromthehighopticaldensity
describedearlier,weexpectthatabout10MHzofthere- and other properties of Eu35Cl .6H O.
3 2
maining linewidth is due to 151Eu3+, with about 3 MHz The quantum memory efficiency for all the protocols
due to the extra O and H isotopes. Therefore, isotopic above is directly dependent on the optical depth [9, 27].
purification of the other elements in the crystal will re- The efficiency in memory demonstrations to date has
ducethelinewidthtotheorderof10MHz. Furtherpurifi- been limited by the low optical density to less than 80%
cation also has the added advantage that it can be used [4, 11], with most demonstrations being well below the
totunesomeofthecrystalproperties. Forexample,fully no-cloninglimit, 50%. Thehighopticaldensityavailable
deuterating the crystal will increase the coherence times in Eu35Cl .6H O means a memory efficiency of above
3 2
[19], while altering the 50:50 europium isotope ratio can 90% should be easily achievable, exceeding the highest
be used to tune the Eu3+ ion-ion interactions. memory efficiency seen, 87% in Rb gas [28].
At 25 MHz, the inhomogeneous broadening has al- The high optical depth of Eu35Cl .6H O also allows
3 2
ready reached an interesting limit: it is smaller than a much high spatial multiplexing capacity than current
the 153Eu3+ hyperfine structure, as well as the static materials. Eu35Cl .6H O will show appreciable absorp-
3 2
excitation-induced interactions between Eu3+ ions. This tion over 1 µm, allowing the creation of a dense set of
regimeisveryusefulforcertainquantuminformationap- spatial voxels, each capable of storing a mode at high
plications. We will discuss two of these: quantum mem- efficiency.
ories and quantum many-body dynamics. Efficiency and spatial multiplexing capacity are im-
TherearetwopropertiesofEu35Cl .6H Othatareim- proved across all protocols. Improvements to other per-
3 2
portantforboththeseapplications. First,longcoherence formancemetricsarepossibledependingontheprotocol.
timesontheopticalandhyperfinetransitions. Anoptical For example, while the GEM and EIT protocols allow
coherence time of 700 µs [19] is obtainable with deuter- higherinitialefficiencythattheAFCprotocol,theband-
ation, while the zero first order Zeeman (ZEFOZ) tech- widthisdependentontheopticaldepth,sothereiseven-
nique can be used to get very long hyperfine coherence tually a trade-off between efficiency and bandwidth or
times. Second, the ability to optically pump the major- spectral/temporal multiplexing capacity [9]. This trade-
ity of 153Eu3+ ions into a single hyperfine state, which off is alleviated by a very high optical depth, allowing
is possible because of the narrow linewidth. This results large bandwidth, high efficiency storage. For GEM, a
in a higher optical depth, and initializes the ions in a high optical density should allow the bandwidth limit,
well-defined state, which is the capability that enables the ground state hyperfine splitting, to be reached. This
many body investigations and certain memory protocols limit is generally considered to apply to all spectral-
in this system. To estimate the proportion of the popu- holeburning based memories like GEM and AFC. How-
lation that can be pumped into a single hyperfine state, ever, for a material like Eu35Cl .6H O in which the hy-
3 2
we use a simple rate equations model in which the crys- perfinestructureisresolved,thislimitationisliftedinthe
4
GEM protocol [4], allowing much larger memory band- shortranges,iftherewerestrongoff-diagonalinteractions
widths. we would expect to see the linewidth of the spectrum in-
The ability to resolve the hyperfine structure present crease as the ion density increases due to the contribu-
inEu35Cl .6H Oalsoallowsnewmemoryprotocolstobe tion of these interactions. However, in our experiments
3 2
implemented in this material. In particular, off-resonant we did not see any significant difference in the linewidth
Ramanschemes[29,30]becomepossibleforthefirsttime of the bulk line in Fig. 2), where the Eu3+ ion density
in a solid state system. These protocols require a high is high, and the satellite lines due to 18O (not visible in
optical depth, and the ability to completely empty one the figure), where the Eu3+ density is very low. Hence,
hyperfinestateovertheentirespectralwidthoftheinho- wecanestimatetheshortrangeoff-diagonalinteractions
mogeneousline,whichisonlypossiblewhenthehyperfine are no larger than 5 MHz, the accuracy of our linewidth
structure is completely involved. Off-resonant Raman measurements, which is a factor of 10 smaller than the
protocolshaveanumberofadvantagesovertheresonant largest observed diagonal interaction. Therefore, in ei-
schemesdescribedabove,suchaslowernoisebecausethe ther regime, we expect the static shift interaction will
excited state is never populated. dominate the many body dynamics observed.
Similar to Raman memories, the second quantum in- As the diagonal interaction dominates, a close ana-
formation application we will consider, quantum many logue for Eu35Cl .6H O among cold atom systems is an
3 2
body dynamics, is enabled in Eu35Cl .6H O by the high optical lattice of Rydberg atoms [33, 34], and the many-
3 2
optical density and small optical inhomogeneous broad- body effects predicted for Rydberg systems should also
ening. Inthismaterial,theEu3+atomsareclosetogether be observable in our rare earth ion setting. Currently,
and can have interactions much stronger than the resid- the primary experimental signature used to verify the
ual inhomogeneity in the system. The result is a lattice presence of Rydberg interactions is the blockade effect
of interacting Eu3+ atoms, the ideal platform for inves- [35, 36]: exciting one atom in the system pushes nearby
tigating many-body quantum phenomena. atoms out of resonance with the exciting field. Since the
The interactions that dominate in this material will ion-ion distances and the associated blockade region are
determine what many-body states can be observed. We much smaller in solid state systems, the spatial imaging
are interested in interactions on the optical transition methodsusedtostudyRydbergsystemsarenotapplica-
between the 7F ground state and the 5D electronic ble, and spectral imaging methods must be used.
0 0
excited state. We assume the 153Eu3+ population has The blockade effect could be indirectly observed
been prepared in the g state using the holeburning through the suppression of excitation [36] or EIT spec-
3
method described above. Two Eu3+ ions separated by troscopy[37]. Todirectlydeterminetheblockaderegion,
a distance r can interact through a variety of com- a spectrally narrow sub-ensemble of ions can be excited,
plex mechanisms including direct electric multipole in- and then the shifts caused by this excitation can be ob-
teractions or exchange, a wavefunction-overlap mecha- served in the optical spectrum [17]. The geometry of the
nism that is often mediated by intervening ligands (su- interaction strengths can be determined from the spec-
perexchange). Regardless of the mechanism, there are trum and used to infer the exact size of the blockade
two qualitatively different parts of the interaction. The region. Lastly, although the size of the blockade region
first is a diagonal interaction producing a static shift to is likely to be well below the diffraction limit of light,
the electronic levels H /h = V(r)e ,e e ,e . This sub-wavelength imaging is possible by using a spectro-
d 3 3 3 3
| (cid:105)(cid:104) |
interaction is the nearest-neighbor version of the in- spatialmethod[38],inwhichanelectricormagneticfield
teraction that commonly leads to instantaneous spec- gradient creates a large spatial variation in the optical
tral diffusion in rare earth crystals [31, 32]. We pre- transitionfrequencyoveraregionmuchsmallerthanthe
viously measured these nearest neighbor interactions to diffraction limit.
be on the order of 40 MHz in EuCl .6H O [17], larger After verification and quantification of the blockade
3 2
than the inhomogeneous linewidth. The second interac- region, there are a variety of many-body states theoreti-
tion is an off-diagonal interaction, of the form H /h = callypredictedtoexistforRydbergsystemsthatcouldbe
o
T(r)e ,g g ,e +T∗(r)g ,e e ,g . investigated in rare earth crystals. For example, param-
3 3 3 3 3 3 3 3
| (cid:105)(cid:104) | | (cid:105)(cid:104) |
Using our experimental measurements, we can esti- agneticstateswithshortrangequantumcorrelations[39]
mate the relative strength of the off-diagonal T and and the so-called devil’s staircase of crystalline phases
diagonal V interactions in two different regimes: long [40–43]. More general many-body phenomena have also
and short range. At long range, we can assume the beenpredicted,butareyettobeconfirmed,suchasquan-
dipole-dipole interaction will dominate. Hence, the rel- tum critical behavior [44], fermionic transport [45], col-
ative strength of the interactions will be the ratio of lectivejumps[46]andnon-equilibriumdynamicaltransi-
the static d = 1.6 10−33 C.m and transition tions [47].
trans
×
d = 1.0x10−32 C.m dipole moments squared [17]. Recently, anomalous broadening has been observed in
static
Thus, the diagonal interaction will be d2 /d2 =42 lattices of Rydberg atoms prepared with a two-photon
static trans
times stronger than the off-diagonal interactions. At transition, which gets rapidly larger with increasing
5
atomic density [48]. This broadening will not be present [5] J. Dajczgewand, J.-L. Le Gou¨et, A. Louchet-Chauvet,
intherareearthioncrystalbecauseaconventionalsingle and T. Chaneli`ere, Opt. Lett. 39, 2711 (2014).
photon transition is used to access the interacting states [6] E. Saglamyurek, J. Jin, V. B. Verma, M. D. Shaw,
F.Marsili,S.W.Nam,D.Oblak, andW.Tittel,Nature
whicharespectrallydistinct. Thismeansthattheserare
Photon. 9, 83 (2015).
earth ion crystals may be able to probe coherent inter-
[7] M. Afzelius, I. Usmani, A. Amari, B. Lauritzen,
acting dynamics in the dense atomic regime, which now
A. Walther, C. Simon, N. Sangouard, J. Mina´ˇr,
appears to be unavailable in Rydberg systems. H. de Riedmatten, N. Gisin, and S. Kro¨ll, Phys. Rev.
HerewehaveconcentratedontheuseofEu35Cl .6H O Lett. 104, 040503 (2010).
3 2
[8] A. V. Gorshkov, A. Andr´e, M. Fleischhauer, A. S.
for two quantum information applications, quantum
Sørensen, andM.D.Lukin,Phys.Rev.Lett.98,123601
memories and quantum many body studies. The low
(2007).
disorder and high optical density of this material could
[9] J. Nunn, K. Reim, K. C. Lee, V. O. Lorenz, B. J. Suss-
also be useful for other applications, such as optical de- man, I. A. Walmsley, and D. Jaksch, Phys. Rev. Lett.
laylineprotocolslikethetwolevelAFC[22],andDLCZ- 101, 260502 (2008).
type repeater protocols [49, 50]. In addition, it is likely [10] P. Jobez, N. Timoney, C. Laplane, J. Etesse, A. Ferrier,
that similar properties are obtainable in other stoichio- P.Goldner,N.Gisin, andM.Afzelius,Phys.Rev.A93,
032327 (2016).
metric rare earth materials. Having a range of materials
[11] D.Schraft,M.Hain,N.Lorenz, andT.Halfmann,Phys-
is particularly useful for quantum many body studies, as
ical Review Letters 116, 073602 (2016).
the variation in crystal structure and types of interac-
[12] N.I.Agladze,M.N.Popova,G.N.Zhizhin,V.J.Egorov,
tion should provide a way to probe different many body and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
effects. [13] R.M.Macfarlane,A.Cassanho, andR.S.Meltzer,Phys.
Rev. Lett. 69, 542 (1992).
In conclusion, we have shown that EuCl .6H O iso-
3 2 [14] E. Chukalina, M. Popova, S. Korableva, and R. Ab-
topically purified in 35Cl has an optical inhomogeneous
dulsabirov, Phys. Lett. A 269, 348 (2000).
linewidth for the 7F0 5D0 transition of Eu3+ of [15] C. Thiel, T. Bo¨ttger, and R. Cone, J. Lumin. 131, 353
→
25MHz,thelowestofanystoichiometricrareearthcrys- (2011).
talandoneofthelowestinhomogeneouslinewidthsmea- [16] R.M.Macfarlane,R.S.Meltzer, andB.Z.Malkin,Phys.
sured in any material. Isotopic purification of the other Rev. B 58, 5692 (1998).
elements in the crystal, in particular Eu3+, will further [17] R. L. Ahlefeldt, D. L. McAuslan, J. J. Longdell, N. B.
Manson, andM.J.Sellars,Phys.Rev.Lett.111,240501
lower this linewidth. The small linewidth and high opti-
(2013).
caldepthmeanthismaterialwouldbeagoodsystemfor
[18] R.L.Ahlefeldt,A.Smith, andM.J.Sellars,Phys.Rev.
quantummemories. Combinedwiththeseproperties,the B 80, 205106 (2009).
strong excitation induced frequency shifts between near- [19] R.Ahlefeldt,N.Manson, andM.Sellars,J.Lumin.133,
est neighbors suggest that many-body physics analogous 152 (2013).
to that seen in Rydberg systems can be observed. [20] N. K. Bel‘skii and Y. T. Struchkov, Sov. Phys. Crystal-
logr. 10, 15 (1965).
This work was supported by the Australian Re-
[21] D. L. Kepert, J. M. Patrick, and A. H. White, Aust. J.
search Council Centre of Excellence for Quantum Com- Chem. 36, 477 (1983).
putation and Communication Technology (Grant No. [22] M.Afzelius,C.Simon,H.deRiedmatten, andN.Gisin,
CE110001027). MRH acknowledges funding from an Phys. Rev. A 79, 052329 (2009).
Australian Research Council (ARC) Discovery Project [23] A. Alexander, J. Longdell, M. Sellars, and N. Manson,
J. Lumin. 127, 94 (2007).
(project number DP140101779). MJS was supported
[24] G. Hetet, J. J. Longdell, A. L. Alexander, P. K. Lam,
by an Australian Research Council Future Fellowship
and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
(Grant No. FT110100919). The authors thank E. A.
[25] M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65,
Goldschmidt for helpful discussions. 022314 (2002).
[26] S. E. Harris, J. E. Field, and A. Imamog˘lu, Phys. Rev.
Lett. 64, 1107 (1990).
[27] M. R. Hush, A. R. R. Carvalho, M. Hedges, and M. R.
James, New J. Phys. 15, 085020 (2013).
[1] M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. [28] Y.-W. Cho, G. T. Campbell, J. L. Everett, J. Bernu,
Bartholomew,S.E.Beavan,S.M.Wittig,J.J.Longdell, D. B. Higginbottom, M. T. Cao, J. Geng, N. P. Robins,
and M. J. Sellars, Nature 517, 177 (2015). P. K. Lam, and B. C. Buchler, Optica 3, 100 (2016).
[2] P. Jobez, C. Laplane, N. Timoney, N. Gisin, A. Fer- [29] K.F.Reim,J.Nunn,V.O.Lorenz,B.J.Sussman,K.C.
rier,P.Goldner, andM.Afzelius,Phys.Rev.Lett.114, Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley,
230502 (2015). Nature Photon. 4, 218 (2010).
[3] M. Gu¨ndo˘gan, P. M. Ledingham, K. Kutluer, [30] S. A. Moiseev, Phys. Rev. A 88, 012304 (2013).
M. Mazzera, and H. de Riedmatten, Phys. Rev. Lett. [31] G.Liu,M.Joubert,R.Cone, andB.Jacquier,J.Lumin.
114, 230501 (2015). 38, 34 (1987).
[4] M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, [32] G.K.LiuandR.L.Cone,Phys.Rev.B41,6193(1990).
Nature 465, 1052 (2010). [33] S. E. Anderson, K. C. Younge, and G. Raithel, Phys.
6
Rev. Lett. 107, 263001 (2011). Daley, New J. Phys. 12, 103044 (2010).
[34] M. Viteau, M. G. Bason, J. Radogostowicz, N. Malossi, [43] G. Pupillo, A. Micheli, M. Boninsegni, I. Lesanovsky,
D. Ciampini, O. Morsch, and E. Arimondo, Phys. Rev. and P. Zoller, Phys. Rev. Lett. 104, 223002 (2010).
Lett. 107, 060402 (2011). [44] H. Weimer, R. Lo¨w, T. Pfau, and H. P. Bu¨chler, Phys.
[35] Y. O. Dudin and A. Kuzmich, Science 336, 887 (2012). Rev. Lett. 101, 250601 (2008).
[36] D.Tong,S.M.Farooqi,J.Stanojevic,S.Krishnan,Y.P. [45] B. Olmos, R. Gonza´lez-F´erez, and I. Lesanovsky, Phys.
Zhang,R.Coˆt´e,E.E.Eyler, andP.L.Gould,Phys.Rev. Rev. Lett. 103, 185302 (2009).
Lett. 93, 063001 (2004). [46] T.E.Lee,H.Ha¨ffner, andM.C.Cross,Phys.Rev.Lett.
[37] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weath- 108, 023602 (2012).
erill,M.P.A.Jones, andC.S.Adams,Phys.Rev.Lett. [47] M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and
105, 193603 (2010). I. Lesanovsky, Phys. Rev. Lett. 113, 210401 (2014).
[38] S. Schiller and R. L. Byer, J. Opt. Soc. Am. A 9, 683 [48] E.A.Goldschmidt,T.Boulier,R.C.Brown,S.B.Koller,
(1992). J. T. Young, A. V. Gorshkov, S. L. Rolston, and J. V.
[39] I. Lesanovsky, Phys. Rev. Lett. 106, 025301 (2011). Porto, Phys. Rev. Lett. 116, 113001 (2016).
[40] H. Weimer and H. P. Bu¨chler, Phys. Rev. Lett. 105, [49] L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller,
230403 (2010). Nature 414, 413 (2001).
[41] T. Pohl, E. Demler, and M. D. Lukin, Phys. Rev. Lett. [50] P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E.
104, 043002 (2010). Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301
[42] J. Schachenmayer, I. Lesanovsky, A. Micheli, and A. J. (2010).