Ion-photon entanglement and quantum frequency conversion with trapped Ba$^+$ ions

2.1 MB·

by  James D. Siverns

*
Ion-photon entanglement and quantum frequency conversion with trapped Ba+ ions
J. D. Siverns, X. Li and Q. Quraishi*
Army Research Laboratory, Adelphi, MD 20783 and
Joint Quantum Institute, University of Maryland, College Park, MD 20742∗
(Dated: compiled January 12, 2017)
Trappedionsareexcellentcandidatesforquantumnodes,astheypossessmanydesirablefeatures
ofanetworknodeincludinglong-lifetimes,on-siteprocessingcapabilityandproducephotonicflying
qubits. However, unlike classical networks in which data may be transmitted in optical fibers and
therangeofcommunication readily extendedwith amplifiers, quantumsystemsoften emit photons
7 thathavelimitedpropagationrangeinopticalfibersand,byvirtueofthenatureofaquantumstate,
1 cannotbenoiselesslyamplified. Here,wefirstdescribeamethodtoextractflyingqubitsfromaBa+
0
trapped ion via shelving to a long lived, low-lying D-state with higher entanglement probabilities
2 comparedwithcurrentstrongandweakexcitationmethods. Weshowaprojectedfidelityof≈89%of

n theion-photon entanglement. Wecompare several methodsof ion-photon entanglement generation
a andshowhowthefidelityandentanglementprobabilityvariesasafunctionofthephotoncollection
J optic’s numerical aperture. We then outline an approach for quantum frequency conversion of the
0 photons emitted by theBa+ ion to the telecom range for long-distance networking and to 780 nm,
1 for potential entanglement with Rubidium based quantum memories. Our approach is significant
for extending the range of quantum networks and for development of hybrid quantum networks

] compromised of different typesof quantum memories.
h
p
PACSnumbers:
-
t
n
a I. INTRODUCTION fied [12], however, two-node entanglement swapping can
u serve as a quantum repeater to transfer quantum infor-
q
mation [13].
[ Trapped ions are a well-established system in which

many of the desirable features for quantum information
1
v processing have been demonstrated [1], such as long-
3 lived quantum coherence [2, 3] and storage and retrieval It would be advantageous if emerging quantum net-
8 of quantum states using photons on scalable platforms works could exploit existing telecom optical fiber in-
7 [4]. From the first work [5] demonstrating a quantum frastructures. In this case, long-distance quantum net-
2 gate with one trapped ion to the engineering of quan- workingrequiresphotonic flying qubits at telecomwave-
0
tum states with 14 ions [6], efforts are now underway to lengthsforlow-losstransmission. However,trappedions,
.
1 establish networks of remotely situated trapped ion sys- similar to other types of quantum memories like neutral
0 tems[7]. Twoquantumnodesareconnectedwhenentan- atoms or nitrogen vacancy centers, typically emit pho-
7
glement has been established via a joint measurementof tons which have high attenuation when propagated in
1
single photons (flying qubits), emitted by each quantum optical fibers, as such memories emit either in in the ul-
:
v nodeseparately[8]. Thenodesactasquantummemories, traviolet (UV), visible or near-IR regime. Optical fre-
Xi emitting photons entangled with the ion’s internal state quency conversion via nonlinear processes is well estab-
[9]. Entanglement between nodes can be established via lished and may be used to obtain more desirable wave-
r
a Bell-state measurements. Such quantum networks may lengths. Quantum frequency conversion (QFC)[14] of
beusedforteleportationbetweenthenodes,evenifthere single photons has been demonstrated using atomic va-
isnoa-prioriknowledgeofthestatetobeteleported[10]. pors [15], photonic crystal fibers [16] and crystals such
Lab-based networks connected by approximately 1 km aslithium niobate[17,18]. Recentworkhas shownQFC
optical fibers have demonstrated entanglement but the intotelecomwavelengthsfromsinglephotonsemittedby
flying qubit wavelenghts are incommensurate with low quantum memories such as quantum dots [19] and neu-
loss,long-distancepropagationinopticalfiber[11]. Mod- tral atoms [20]. Importantly, the quantum nature of the
ern telecommunication (telecom) networks utilize well- photonispreservedinthequantumfrequencyconversion
established networks of optical fibers linking remotely process [14, 20, 21]. In addition, creating entanglements
situated nodes. Unlike classical approaches to extend- between different types of memories in a hybrid quan-
ing these data ranges using optical amplifiers, quantum tum network allows for each system’s unique properties
information can neither be cloned nor noiselessly ampli- to be utilized [22]. Here, we present an approach to ex-
tract polarization entangled photonic flying qubits from
a 138Ba+ trapped ion memory and outline a scheme for
quantum frequency conversion for long-distance and hy-
∗Electronicaddress: *[email protected] brid quantum networking.
2
mass, m, and charge, e, which, for a linear Paul trap,
is given by [39, 40]
e2V2η2
ψ = 0 x2+y2 , (1)
4mr4Ω2
RF (cid:0) (cid:1)
whereΩ /2πistheRFfrequency,r istheion-electrode
RF
distance and V is the amplitude of the RF voltage ap-
0
pliedtothetrap. Confinementoftheionalongthez-axis
canbe achievedbythe introductionofapotentialinthis
direction created from various static voltage electrodes.
Thegeometricfactorη [40]isequaltooneforaperfectly
hyperbolic electrode geometry and less than one as the
geometry strays from this perfect form. Ions trapped in
FIG.1: (a)Schematicofthebladetrap. Thedistancebetween this pseudo-potentialwill undergo secular motionwith a
the upper (segmented into five static voltage electrodes) and
frequency given by [39, 40]
lower (RF) blades is ∼260 µm and the width of the central
electrode(labeledDC3)is∼250µmatitstip. Forillustration
purposes, the inset shows a close up photograph of the trap eV0η
ω = . (2)
withmoredetailoftheelectrodesegmentation. Thesegments s √2mr2Ω
RF
of the rf blade they are electrically shorted together creating
oneelectrode. (b)Diagramshowingthetrapgeometryinthe We use a linear four-blade trap as shown in Fig. 1(a).
x-yplanewiththelightconeofthe0.6NAlens(half-angleof Such traps possess a node in the ponderomotive poten-
◦
around 37 ) shown in blue. tialalongthe axisof the trapallowingeither a singleion
or a chainof ions to be trapped. Confinement along this
node is providedby applying static voltagesto the outer
II. ION TRAPPING AND PHOTON segments of the electrodes. These traps typically have
EXTRACTION depths of 1 eV to 10 eV, corresponding to 105K. It is
≈
possible to achieve ion temperatures of approximately 1
Trapped ions confined in radio frequency (RF) Paul mK by applying a single laser cooling beam with mo-
traps are versatile quantum systems from which flying mentum projections in all three motional directions of
qubitsmaybeextractedwithahighquantumcorrelation the ion. Hence, the ion can remain tightly confined in
between the trapped ion memory and flying qubit [9]. the trap allowing for repeated interrogation by optical
Such systems have applications in frequency standards beams for single photon production.
[23, 24], quantum information processing [4, 25, 26], To increase the ion-photon entanglement probability,
quantum simulations [27–30] and quantum networking collection optics must capture as much spontaneously
[31–33]. Networking two-individual nodes has been im- emitted light as possible. We have custom-designed our
plemented over a distance of meters [8, 34, 35]. Here, apparatuswithaparticularlyhighcollectionapertureop-
we propose a method for near deterministic ion-photon tic. The physical arrangement of the blades allows for
entanglement production using continuous wave (CW) collection up to 10% (numerical aperture (NA) of 0.6)
≈
excitation and compare this approach to methods using of the light emitted from ions in the trap as shown in
strong [36] and weak excitation [9]. Strong excitation Fig.1(b). Similarlensesintegratedwithblade-trapshave
methods require a laser pulse with sufficient intensity to substantially improved ion-photon entanglement proba-
excitetheionwithnearunityprobability. Typically,this bilities [35].
is achievedwith the use ofa modelockedpulse laser[36].
The approach outlined here has a higher entanglement
probability comparedwith both strongand weak excita- B. Ion state preparation and ion-photon
tionschemes[9,37,38]. Thefidelity,althoughlowerthan entanglement
other schemes, provides a higher entanglement probabil-
itywhichcouldbeusedforthedemonstrationofaproof- A qubit is represented by the two Zeeman levels in
of-principle quantum network node without the need for the S ground state of a 138Ba+ ion with 0 =
1/2
additional experimental overhead involved with strong m = 1/2 and 1 = m =+1/2 as show| ni in
j j
excitation schemes. |Fig. 2(−a). Tihe groun|distate,|S , is spliit into two Zee-
1/2
manlevelsbyapplyingamagneticfieldwhichdefinesthe
direction of the quantization axis. It is possible, as we
A. Ion trapping background show below, to produce a single 493 nm photon with its
polarization entangled with the qubit states 1 and 0
| i | i
RF voltages applied to trap electrodes provide a suit- viashelvingintheD level. TheD levelislong-lived
3/2 3/2
able ponderomotive pseudo-potential to trap ions of (lifetime of 80 sec) allowing for effective shelving.
3
folTlohweinigont-hprheoetostnepesn.taFnigrlsetmly,enttheisiopnroidsuinceitdiaulisziendginthtoe (A) P1/2 mj=-1/2 mj=1/2 σ+650 nm
π
the m = +3/2 (m = 3/2) state in the D level, 650 nm
j j 3/2
using π-polarized 493 lig−ht along with π and σ+ (σ−)
polarized650nmCWlasers. Secondly,theionisexcited
from the D state to the P state via a σ− (σ+) po- π π D Initialized state
larized 6503n/m2 beam. Initiall1y/,2the ion is only excited to 493 nm 493 nm 3/2 mj=-3/2 mj=-1/2
the P1/2 state Zeeman level mj = +1/2 (mj = −1/2). mj=1/2 mj=3/2
Theeffectsofmultipleexcitations,includingthosetothe 0
oFpinpaolslyit,ethZeeeiomnacnalnevspelowntiallnbeeoudsilsycudsesceadyifnrosmectthioenexIIcCite1d. S1/2 mj=-1/2 mj=11/2
state, P , to the ground state, S , via two dipole-
transitio1n/2allowed paths correspond1i/n2g to either a π or (B) P1/2 mj=-1/2 mj=1/2
σ+ polarized photon. Observation in the direction per-
pendicular to the quantization axis means it is possible
± σ-
to view σ and π photons as horizontal H and verti- 650 nm
| i
cal V polarizationsrespectively,yielding anion-photon Initialized state
enta|ngiled state given by 493 nmσ+ D3/2 mj=-3/2
π mj=-1/2
1 1 493 nm mj=1/2 mj=3/2
Ψ = V 1 + H 0 . (3)
G
| i √2| i| i √2| i| i S 0
1/2 1
The state givenby Eqn. 3 takes into accountboth the mj=-1/2 mj=1/2
intensity pattern of the emitted σ+ and π polarizations,
with the latter being greaterby a factoroftwo whenthe FIG. 2: (a) The transitions required for initializing a 138Ba+
sphericalpolarangle, θ, of the emitted photons, with re- ioninthem =+3/2stateintheD level. (b)The650nm
j 3/2
specttothedipoleaxis,isequaltoπ/2. Alsoincludedare σ−transitionrequiredforthegenerationofthe493nmphoton
theClebsch-Gordancoefficientsofthetransitions,shown and production of the ion-photon entangled state given in
in Fig. 3(a). equation 3.
This intensity pattern difference arises from our ob-
servationdirectionwith respectto the quantizationaxis.
The flying qubit in this state carries with it informa-
PhotonsemittedfromtheP toS transitionhavethe
1/2 1/2
unnormalisedpolarizationstates, π and σ± ,whichare tion about the atom’s state, meaning that a measure-
| i | i mentofonepolarizationcorrelatestoaparticularatomic
given by
state. Interferencebetweenphotonsfromasimilarlypre-
paredremotequantummemorynodewouldgenerateen-
π = sinθ θˆ (4) tanglement between the two nodes, forming a quantum
| i − (cid:12) E network. Two prominent factors which would degrade
(cid:12)
and (cid:12) the purity of the ion-photon entangled state include re-
excitation from the D level and polarization mixing,
3/2
as discussed in sections IIC1 and IIC2 respectively.
e±iφ
σ± = cosθ θˆ i φˆ (5)
(cid:12)(cid:12) (cid:11) √2 (cid:16) (cid:12)(cid:12)(cid:12) E± (cid:12)(cid:12)(cid:12) E(cid:17) C. Fidelity of ion-photon entanglement
respectively,where φ is the azimuthalangle with respect
to the dipole axis and θˆ and φˆ are the respective unit
The target state given by Eqn. 3, is produced by de-
vectors. ItcanbeseenfromEqns. 4and5thatwhenthe
cay from the m =1/2 state of the P level to the two
angleθ issettoπ/2thetwopolarisationsareorthogonal j 1/2
S ground states via two paths with Clebsch-Gordan
[9] and, after taking into account the relevant Clebsch- 1/2
coefficients shown in Fig. 3(a) (solid blue line). Factors
Gordan coefficients, we obtain Eqn.3.
whichdegradethepurityoftheion-photonentanglement
It shouldbe noted that initializationinto the opposite
includere-excitationfromtheD levelandpolarization
Zeeman level of the D (m = 3/2) is driven by σ+ 3/2
3/2 j − mixing due to the large collection angle. In the former
polarizationofthe650nmbeam. Thisresultsincoupling
case, rather than a pure state, a mixed state is obtained
to the m = 1/2 Zeeman level in the P level and
j − 1/2 affecting the ability of the scheme to generate the de-
produces an ion-photon entangled state given by
siredentanglement. A common measure of the extent to
whichthe desiredtargetstate is obtainedis givenby the
1 1 fidelity. Belowweanalyzethefidelityunderre-excitation
Ψ = H 1 + V 0 . (6)
| Bi √2| i| i √2| i| i and polarization mixing.
4
1. Effect of multiple excitations on state fidelity photon entanglement created with this scheme will be
given by the mixed state
P1/2 mj=-1/2 mj=1/2 Ψ = PG Ψ + PB Ψ (7)
m G B
P +P | i P +P | i
G B G B
where P and P are the probabilities of the scheme
G B
creating the ion-photon entangled states Ψ and Ψ
G B
| i | i
respectively, and are given by the following geometric
series
S D
1/2 mj=-1/2 mj=1/2 3/2mj=-3/2 mj=-1/2 mj=1/2 mj=3/2 Br
493
P = 0.844 (8)
G 1 (C2Br ) ≈
− 1 650
Br Br C2
P = 493 650 2 0.103. (9)
B 1 (C2Br ) ≈
− 3 650
FIG.3: DiagramshowingtheClebsch-Gordancoefficientsfor
transitions betweenthe(a) ground-stateS andP levels 1.00
1/2 1/2
and(b)theP andmeta-stableD level. (c)Asimplified
1/2 3/2
energy level diagram showing the branching ratio from the
excited P level to theS and theD level [41]. 0.95
1/2 1/2 3/2
y
t
i
l
e
Theexcitationschemepresentedhere(Fig.2)isunlike
d 0.90
some [9, 37] usedfor ion-photonentanglementas the ex- Fi
citation(at650nm)isatanentirelydifferentwavelength
thanthe emittedphoton(at493nm). This is clearlyad-
0.85
vantageousintermsoffilteringbackgroundlight,butalso
servestoimproveion-photonentanglementprobabilities.
Re-attempts at successful entanglement can occur after 0.0 0.2 0.4 0.6 0.8 1.0
failed attempts during the same experiment cycle, albeit NA
at the expense of the fidelity.
The ratio of a CW pulse duration, ∆t, to the natural FIG. 4: The fidelity of the ion-photon entangled state as a
linewidth, τ, gives the probability of double excitation, functionofNAisshownfortheschemeoutlinedinSectionIIB
p = 1 exp( ∆t/τ). If we assume a worst case sce- (solid), weak and strong (both dashed) excitation methods.
γ
nario of−contin−uous (∆t ) exposure to 650 nm σ− The weak and strong excitation methods fall on the same
light, then p 1. Th→e r∞e-excitation occurs because upper(dashed) curve.
γ
→
there is an appreciable probability (approximately 27%,
seeFig.3)oftheiondecayingbacktotheD3/2 manifold, HereBr493andBr650arethebranchingratiosfromthe
although not exclusively into the initialized state shown P1/2statetothegroundstateandD3/2staterespectively,
in Fig. 2(a). The decay back to the D3/2 manifold hap- andC1, C2 andC3 arethe C-Gcoefficientsofthe decays
pensviathreepossiblechannelsemittingeitheraσ+,σ− shown in Fig. 3. This means that a 493 nm photon will
orπ photon,withthe Clebsch-Gordan(C-G)coefficients be emitted bythe ionwithasuccessof 94.7%,making
≈
shown in Fig. 3 [41]. theschemeneardeterministic,albeitwithalowerfidelity
forthetargetstatewhencomparedwithweakandstrong
If the ion decays back to the initialized state shown
excitationmethodsasshowninFig. 4. Whenunsuccess-
in Fig. 2(a), we would proceed as already described in
ful, the ion will have been pumped into a dark state in
Section IIB without any effect on the fidelity. If the
the D level.
decayisviaaπ photon(tothem =+1/2Zeemanlevel, 3/2
j
Here, we examine the effect of these re-excitations by
withC-Gcoefficientof 1/3)thenthe subsequent650
− using the metric of fidelity, defined as [42]
nm excitation will be to tphe mj = 1/2 Zeeman level of
−
theP state. Any493nmdecaytothegroundstatewill
1/2
result in the ion-photon entangled state given by Eqn. 6
F = Ψ Ψ , (10)
beingcreatedinsteadofthedesiredstategivenbyEqn.3. h |i| i
If the decay is via a σ+ photon (to the mj = 1/2 level, where Ψ is the intended pure state and ρ is the density
− | i
with C-G coefficient 1/6), the ion will go dark and no matrix of the created state. The fidelity of the mixed
ion-photon entanglempent will occur. Therefore, the ion- state,Ψm,createdbythisschemewiththeintendedpure
5
state,Ψ ,canbe calculatedto be 0.89. Althoughthis
G
≈
scheme yields a lower fidelity than standard strong and
1
weakexcitationmethods(bothcanachievefidelitiesnear F =Fmax 0.24(Ω/4π) Fmax 0.24 NA2 (12)
tounity),itallowstheusertoproduceion-photonentan- − ≈ − (cid:18)4 (cid:19)
glement with a higher probability and in the case of the
strongexcitationmethod,withouttheneedforadditional where Fmax is the maximum fidelity achievable. For
pulsedlaserapparatus. Byadoptingthis methodwewill the method outlined in section IIB, the fidelity Fmax ≈
0.89,soweobtainafidelityF =0.87forNA=0.6. For
have the ability to perform proof-of-principle quantum 0.6
comparison, also shown are curves for a weak excitation
networkingexperimentswithquantumfrequencyconver-
method[37]andastrongexcitationmethod[36](dashed
sion of the emitted photon.
line). Both have the same fidelity as both have Fmax
near unity.
The approach presented here does not reach the high
2. Effect of polarization mixing due to collection solid-angle
fidelities (unity with a NA of zero) achieved with these
on state fidelity
othertwoschemes,however,itdoesyieldahigherproba-
bilityofentanglementcomparedtotheothertwoschemes
Ion-photon entanglement is useful as a resource for as shown below. For improved fidelities, achieved by
quantum networking, as the photon carries information avoiding multiple excitations, using a single pulse from
about the atomic state to a remote site. To optimize a pulsed laser is a desirable approach even though the
networkingprotocolswewishtocapturephotonsfromas entanglement probability is reduced.
manyentanglementtrialsas possible. However,the pho-
tonisemittedfromtheP levelspontaneouslyintothe
1/2
full solid angle 4π. There are a variety of approaches to 3. Probability of ion-photon entanglement with D
3/2
optimize collectionincluding opticalcavities[43, 44] and initialization
in-vacu [45, 46] and ex-vacu [35] high NA lenses. High
NAlensescanhavesuchalargecollectionanglethatthe Using a highNA lens increasesthe probability of pho-
±
σ polarized light typically has a projection on the π ton capture and hence, the ion-photon entanglement
polarized light when viewed in a horizontal and vertical probability. This higher entanglement probability is
polarization basis. Here we examine how this projection shown in Fig. 5 and is given by
reduces the fidelity of the ion-photon entanglement.
We plan to integrate an ex-vacu 0.6 NA lens into our
setup which is designed to collect approximately 10% of NA2
P =P P (13)
e s
the light and is AR coatedfor both 493 nm and 650nm. 4
Ex-vacu high NA collection reduces complexity of the
where P is the probability of excitation to the P-level
in-vacuum trap assembly and readily allows for optical e
and P is the probability of decay to the S-level. For the
corrections with additional free-space optics. Although, s
curves shown, the weak and strong excitation methods
in-vacuoopticscanprovideamoremodular,compactand
haveP equalto0.2and1respectivelyandbothhaveP
scalablesolutionforfuture nodesofapotentialquantum e s
equalto0.7304,setbythebranchingratio[Fig.3(c)]. For
network[45,47]. Theanalysisbelowholdsforbothtypes
themethodoutlinedinSectionIIBwhereweinitializein
of lenses.
the D level, the product, P P = 0.947 (as shown in
The fraction of emitted photons collected by a lens 3/2 e s
Section IIC1) meaning re-excitation increases the prob-
with numerical aperture, NA, is given by
ability of obtaining anentangledstate. For anNA =0.6
an ion-photon entanglement probability of P = 0.085
canbe obtained. Itisnotablethattheexcitationscheme
Ω 1
NA2. (11) outlined in Section B has a reasonable fidelity but the
4π ≈ 4
highest entanglement probability. For proof-of-principle
experimentsthiswouldbeappropriatetotransmitquan-
From Eqn. 11 it is clear to see that a lens with a high
tum information to a remote site.
NAwillresultinthecollectionofahigherfractionofthe
photons emitted from an atom. However,as can be seen
in Eqns. 4 and 5, if the spherical polar angle, θ, is not TABLE I: Comparison of excitation schemes with fidelity,
equal to π/2 then there will be a loss of orthogonality F0.6, and ion-photon entanglement generation probability,
between the σ and π light emitted from the atom, when P0.6, evaluated at NA=0.6.
viewed in a Cartesian basis. In this case, the fidelity of
Excitation scheme PePs P0.6 Fidelity,F0.6
the collected ion-photon entangled state varies from the
D excitation 0.947 0.085 0.87
ideal ion-photon entangled state. For CW excitation of 3/2
Weak excitation 0.146 0.014 0.98
the ion as outlined in IIB, the fidelity of the entangled
Strong excitation 0.730 0.068 0.98
state as a function of the collection lens’s NA (Fig. 4,
solid trace) is given by [9]
6
0.25
A. Quantum frequency conversion (QFC)
ty background
bili0.20
a
b Quantumfrequency conversion[14] is a nonlinearpro-
ro0.15 cess and relies on parametric oscillations of a material’s
P
electronic susceptibility, χ. With sufficiently intense op-
t
n
e0.10 ticalpumpfields,thehigherordercomponentsofχbegin
m
todominateandmodulatethematerial’spolarizibilityas
gl
n0.05 a function of the applied field, given by
a
t
n
E0.00
P =ε χ(1)E +ε χ(2)E E +ε χ(3) E E E +
0.0 0.2 0.4 0.6 0.8 1.0 i 0 ij j 0 ijk j k 0 ijkl j k l ···
Xj Xjk Xjkl
NA
(14)
where ε is the free space electric permittivity, E de-
0 ijkl
FIG.5: Theentanglementprobabilityoftheschemeoutlined
notes the electric field, and χn is a rank n+1 tensor.
in Section IIB (solid), weak excitation method (dotted) and
In a media with a large χ(2) coefficient, the secondor-
strong excitation method (dashed) as a function of NA.
der term in Eqn. 14 can dominate with a strong pump
field, allowing the non-linear three-wave mixing (TWM)
process to occur. Here the generation of the frequency
ω = ω ω is expected, where ω is the frequency
2 1 p 1
±
of the light to be converted and ω is the frequency of
p
III. QUANTUM FREQUENCY CONVERSION
the high intensity pump. The plus sign corresponds to
OF SINGLE PHOTONS
sum frequency generation(SFG), or upconversion,while
the minus sign means difference frequency generation
(DFG), or downconversion. Examples of a TWM pro-
Trapped ions can serve as excellent quantum mem- cess include frequency doubling in lithium niobate (LN),
ories, however, they often emit in optical frequency beta-barium-borate(BBO) and lithium triborate (LBO)
ranges that have substantial attenuation even in ded- crystals where ω =ω and ω =2ω . With quasi-phase
p 1 2 1
icated wavelength-specific optical fibers. For instance, matching (QPM), TWM can be achieved in periodically
Yb+ ions arehighly desirablequbits, but they emit pho- poled materials like lithium niobate and potassium ti-
tons at 369 nm which have approximately 70 dB/km at- tanyl phosphate (KTP) even when ω =ω .
p 1
6
tenuation in commercially available single mode fibers. Itisalsopossibletoperformfour-wavemixing(FWM)
Although Ba+ wavelengths (493nm, 650 nm) have im- in centrosymmetric media as the second order term in
proved fiber transmission over this Yb+ emission wave- Eqn.14iszeroduetosymmetryandthe thirdorderχ(3)
length, there is still substantial attenuation, as shown in term can dominate, when subject to two pump lasers
Fig. 6. of sufficient intensity. χ(3) media such as silicon ni-
tride (SiN) microresonators [50] and optical fibers can
Quantum frequency conversion [14] may be imple- both support FWM [51]. Recent work in SiN [52] has
mentedtoconvertphotonsfromtheionintothetelcomm shown conversionefficiencies on par with those observed
regime for low loss propagation through optical fibers in PPLNs, however, not at a low enough noise rate re-
therefore extending the range of quantum networking quired for the relatively low photon rates emitted by
from lab-based two-node setups [36, 48]. Additionally, atomic quantum memories.
spectrally mismatched photons may be frequency con- Frequency conversion at the single photon level with
vertedto establisha hybridquantumnetworkcomprised sufficiently low dark counts has been shown using TWM
of two different types of quantum memories [49]. The in periodically poled waveguides [20]. Given expected
frequencyconversionmustpreservethequantumproper- photon data rates [35], we plan to use a TWM process
tiesandindeed,QFCexperimentsofsinglephotonshave for frequency conversionof the Ba+ ion photons.
shown that the quantum state of the single photon was In the case of periodically poled materials suitable for
preserved after QFC [16, 17]. TWM, the quasi-phase matching can be achieved when
Here,wepresentanapproachforQFCofBa+ ionpho-
tonsemittedat493nmand650nm. The493nmphotons k k k 2πm/Λ=0 (15)
1 p 2
− − −
willbeconvertedintothenearinfra-red(NIR)regimefor
potentialnetworkingwithaneutralatombasedquantum where k =ω n /c, k =ω n /c, k =ω n /c, m is the
1 1 1 2 2 2 p p p
memory and the 650 nm photons will be converted into polingorderandΛisthepolingperiod. QPMisachieved
the telecom regime for long-distance quantum informa- by periodically-poling the materialand yields more than
tion transmission. anorderofmagnitudeimprovedconversionefficienciesas
7
100
n crystal to reduce transmission loss and to ensure better
o
i (a) spatialmodeconfinementofallthe opticalbeams within
t
c thePPLN.Anotherdesirablefeatureofthesecrystalsare
a
r 493 nm theobservedlownoisecounts,suitableforthesignallevel
f
n 10-1 emitted by atomic quantum memories [20].
o
i Giventhat we are interestedin convertingand detect-
s
s ing single photons, noise photons at ω and ω must
i 1 2
m 780 nm (5%) be minimized as they can spoil the ion-photon entan-
ns 10-2 glement , considering current entanglement probabili-
a 1550 nm (18%) ties [35]. The primary sources of noise are spontaneous
r
t Raman scattering (SRS) and spontaneous parametric
n
o downconversion (SPDC). The SRS scattering can pro-
t
o 10-3 duce Raman peaks ofnoise sitting atopa noise pedestal.
h
p 0 5 10 15 These effects are significantly minimized by ensuring ω2
isgreaterthanω andbysufficientω ω detuning[18].
p 2 p
−
fiber propagation distance (km) TheSPDC noisemaybe minimizedbyensuringthatthe
pumpwavelengthis the longestwavelengthinthe TWM
process [18] so that parasitic photons are produced at
n 100
o lower frequencies than either the input ω1 or converted
i
t signalω . Afinalstepinminimizingnoisefromthepump
c 2
a 650 nm (b) isdoneusingopticalfilters,alongwithopticalprismsand
r
f fiber Bragg gratings [20], to ensure that the background
n 10-1
o is significantly lower than the converted signal. Conver-
i
s sionofcoherentlightat369nmhasbeendonetotelecom
s
i wavelengths with a single-stage DFG process, but with
m 1259 nm (15%)
s ωp greater than ω2 [55], resulting in SPDC noise at the
n 10-2 target telecom photon, and also in a two-stage process
a
r [56] with higher poling period and, therefore, reduced
t

n conversionefficiencies[57]. Toobservealong-livedmem-
o
1259 nm (1%) ory entangled with either a visible or telecom photon,
t
o
h 10-3 it should be possible to generate local entanglement be-
p 0 5 10 15 tweenYb+ andBa+ [58]andthendoQFConthephoton
emitted by the Ba+ ion.
fiber propagation distance (km)
FIG.6: Photontransmissionfractionasafunctionofdistance B. Proposed quantum frequency conversion for
thoughwavelengthspecificfiberofphotonsderivedfromBa+ long distance and hybrid networking with Ba+ ions
ions. Representative quantum frequency conversion efficien-
ciesaregiveninparenthesis. (a)(greentrace)Transmissionof Ba+ has two strong dipole transitions (493 nm, 650
493nmphotonswithafiberlossof-50dB/km. (orangetrace)
nm) from the P state. We begin by discussing fre-
1/2
Transmissionof780nmphotonswithafiberloss-3.5dB/km,
quency conversion of the 493 nm photons. In a single
fromfrequencyconverted493nmphotons. (redtrace)Trans-
DFG stage, the 493 nm photon may be combined with
mission of 1550 nm photons with a fiber loss -0.18 dB/km,
fromfrequencyconverted780nmphotons(∼18%QFCvalue a strong pump beam at 1343 nm (ωp/2π = 223 THz) to
produce a photon at 780 nm (ω /2π = 384 THz). This
reportedin[20])(b)(redtrace) Transmission of650nmpho- 2
tons (fiber loss of -15 dB/km). (blue trace) Transmission of target wavelength is chosen to match the 780 nm D2
1259nmphotonswithafiberlossof-0.3dB/kmfrom650nm transition in neutral 87Rb atoms. The pump laser may
photons. be frequency stabilized to match the 780 nm photon to
the 87Rb D2 transition. The similarity of the temporal
profiles of the photons emitted from Ba+ and Rb-based
comparedagainstconversionusingthe largestcoefficient quantum memories, means that entanglement between
that can be phase-matched with birefringence [53]. them might be created via Bell state measurements [59],
Most work in quantum frequency conversion has been therefore creating a hybrid ion-neutral two-node quan-
done using TWM in periodically-poled lithium niobate tum network that utilizes properties of each memory.
(PPLN) because it can be readily engineered to yield For long-distance communication through optical
high conversion efficiencies over a range of input wave- fibers, we can envisage using a second DFG conversion
lengths, especially with waveguides fabricated in them. stage to convert the 780 nm photon to 1551 nm, with
Using a reverse proton exchange (RPE) technique [54] a a pump at 1569 nm. Indeed, 780 nm photons from Rb-
waveguidemaybeburiedbeneaththesurfaceofthebulk based quantum memories have already been converted
8
into the telecom regime [20, 60]. In Fig. 6(a) we show Forefficientcouplingofbothω andω intothenonlin-
1 p
the propagation losses through wavelength specific fiber earwaveguide,weplantoimplementafreespacescheme
given conservative estimates on the QFC efficiencies. with a silver-coated, off-axis, parabolic mirror with a 15
Given the high propagation loss of 493 nm in optical mm focal length, as shown in Fig. 7. This gives us the
fiber, it is advantageous to do a single stage conversion abilitytosimultaneouslycouplethevisiblelightand1343
efficiency to 780 nm for propagation over approximately nm light into the respective fundamental modes of same
0.5 km even with a modest 5% QFC efficiency. waveguide [62]. Parabolic mirrors are excellent for fo-
ABa+ion’s650nm(ω /2π=461THz)photoncanbe cusing beams ofvastly differentwavelengthsto the same
1
convertedinto the telecom regime in a single DFG stage spot, as they posses no chromatic aberration. Before
with the same CW pump laser at 1343 nm. The con- the parabolicmirror,the two collimatedbeams are com-
verted photon will be at 1259 nm (ω /2π =238 THz), binedonadichroicmirrorthatreflectssignalsat493nm
2
near the beginning of the telecom o-band. Although or 650 nm and passes the 1343 nm pump. The waists
thereisasmallerprobabilityoftheionemittinga650nm of the beams are chosen to match the mode field diame-
photonovera493nmphoton(seeFig.3),weonlyneeda ter (MFD) ofthe fundamentalmode ofthe relativecolor
single DFG stage to obtain a telecom photon. However, inside the waveguide.
two-stage conversion is also possible as shown in recent To align the beams into the waveguide, we first put
work of conversion from 650 nm to 1550 nm [61]. In the two colors into a wavelength-division multiplexing
Fig.6(b) we show the propagation losses through wave- (WDM) fiber combiner and put the output near the fo-
length specific fiber of 650 nm and the target frequency cus of the parabolic mirror. The output is then back-
converted photon given a modest conversion efficiency. propagated through the setup. We adjust WDM along
Two different values of QFC efficiency are plotted to il- withtheparabolicmirrorona3-axistranslationstageto
lustrate the crossing points between ω and ω at which collimate both colors simultaneously. We then separate
1 2
conversion is beneficial. The approach outlined here for the two colors with a dichroic mirror, and couple each
single-stageconversionof eachBa+ ionallowsfor hybrid beam into their relative fiber. As a result, if we send
and long-distance quantum communication. each color back through the fibers, they will be focused
InTableIIwesummarizetherelevantpotentialconver- at the same spot after the parabolic mirror. The WDM
sionpossibilities. AlthoughPPLNcrystalshavetypically isthenexchangedwithanonlinearchipinatemperature
shownthebestQFCperformance,wewillusePPKTPfor controlled oven. By only adjusting the nonlinear chip’s
the 493 nm conversionas it has a higher photorefractive position with a 5-axis translation stage, we can couple
damagethreshold. The damagethresholdis notrelevant both beams into the same waveguide.
forsinglephotoninputto thePPKTPbutisrelevantfor
the coherent light levels needed for initial alignment.
TABLE II:QFC materials and frequencies
Conversion ω1/2π ω2/2π ωp/2π Device
(THz) (THz) (THz)
493 nm → 780 nm 608 384 223 PPKTP
650 nm → 1259 nm 461 238 223 PPLN
780 nm → 1550 nm 384 193 191 PPLN
FIG.7: Diagram showing theproposed DFGsetup. The sig-
C. Planned experimental approach for visible nalandpumpbeamsarecollimated outofeachfiberwithan
photon frequency conversion asphericlens. Theirpolarizationareadjustedwithhalf-wave-
plates (HWP) to vertical, i.e., perpendicular to the PPKTP
chip surface with waveguides. The two beams are combined
Previously we established a frequency converter setup
onadichroicmirrorbeforebeingsimultaneouslyfocusedinto
for a neutral atom wavelength [62]. We can extend this
thewaveguidebyaparabolicmirror. Residualpumpandsig-
approachtotheBa+ wavelengthsofinteresthere. Toob- nal are filtered to allow measurement of the converted pho-
serve frequency conversion (and hence obtain the QFC tons.
conversion efficiency), we plan to use CW tunable ex-
ternal cavity diode laser (ECDL) sources. One ECDL Therearevariousfreespacecouplingschemesthatuse
is at the input frequency ω (493 nm or 650 nm) and other focusing optics, e.g., aspheric lens, grin lens, etc.
1
the other at the pump ω (1343 nm), seeding a single However, in order to simultaneously couple both colors
p
frequency Raman fiber amplifier. The seed laser can be well, one either has to pre-shape one of the beams or to
locked to a transfer cavity, so that the converted photon custom design the lens to be diffraction limited for both
is on resonance with the Rb transition. ω and ω . It is also possible to write WDM waveguides
1 p
9
before the PPKTP/PPLN waveguide. This way, opti- that although high numerical aperture lenses can im-
cal fibers carrying each color can be directly attached to prove the photon collection efficiency, they can act to
the input of the corresponding WDM waveguide. Such degradethequalityoftheion-photonentanglementstate
miniaturized setups have excellent coupling efficiencies due to polarization mixing. We proposed quantum fre-
and are highly scalable. However, they are wavelength quencyconversionsoftheBa+ ionwavelengthswithonly
specific and typically not commercially available. one pump laser to drive both conversion processes. The
ForQFCofsinglephotonsfromtheBa+ ion,theback- method outlined would produce photons available either
groundnoisefromthepumplaserneedstobecarefullyfil- forhybridquantumnetworkingorlong-distancequantum
tered. Narrowbandpass filters along with optical prisms communicationutilizing existing telecom fiber networks.
and fiber Bragg gratings [20] can be used to ensure that
the background is significantly lower than the converted
signal. The final single photon detection can be per-
IV. FUNDING INFORMATION
formed with a superconducting nanowire single photon
detector, which can achieve more than 95% quantum ef-
Funding provided by the Army Research Laboratory
ficiency in the telecom regime [63].
(ARL) under Cooperative Agreement (W911NF-14-2-
0101) and ARL’s Center for Distributed Quantum In-
D. Summary formation.
Establishing a long-distance network using quan-
tummemoriesinvolvesentanglementgenerationbetween V. ACKNOWLEDGEMENTS
nodes. Photons entangled with quantum memories are
excellent carriers of quantum information. Our ap-
We thank Chris Monroe for the use of the ion trap
proach to extract flying qubits from a Ba+ ion provides
bladesshowninourtrapphotographandwethankMar-
high entanglement probabilities between the photon and
tin Lichtman for a thorough reading of the manuscript.
ion compared with current weak and strong excitation
schemes,however,atthelossofsomefidelity. Weshowed
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