# Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-I parametric downconversion in PPLN.

**ABSTRACT** A periodically poled lithium niobate (PPLN) crystal has been used as an efficient source of non-collinearly generated polarization-entangled photon pairs at 810 and 1550 nm. The PPLN crystal was endowed with a specially designed poling pattern and the entangled photons were generated via the nonlinear optical process of spontaneous parametric down conversion (SPDC). A novel design based on overlapping two concurrent type-I quasi-phase-matching structures in a single PPLN crystals produced correlated pairs of alternatively polarized photons in largely separated spectral regions. The phase of the resulting two-photon state is directly linked to parameters of the nonlinear grating. Continuous tunability of the generated Bell state, from Phi(+) to Phi(-), has been demonstrated by translating a slightly wedged crystal perpendicular to the pump beam.

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**ABSTRACT:**We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a dual-periodically poled crystal. Compared with the usual forward-wave type source, this source, in the backward-wave way, has a much narrower bandwidth. With a 2-cm-long bulk crystal, the bandwidths of the example sources are estimated to be 3.6 GHz, and the spectral brightnesses are more than 100 pairs/(s GHz mW). Two concurrent quasi-phase-matched spontaneous parametric down-conversion processes in a single crystal enable our source to be compact and stable. This scheme does not rely on any state projection and applies to both degenerate and non-degenerate cases, facilitating applications of the entangled photons.Physical Review A 12/2011; 84(5). · 3.04 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We propose to integrate the electro-optic (EO) tuning function into on-chip domain engineered lithium niobate (LN) waveguide. Due to the versatility of LN, both the spontaneously parametric down conversion (SPDC) and EO interaction could be realized simultaneously. Photon pairs are generated through SPDC, and the formation of entangled state is modulated by EO processes. An EO tunable polarization-entangled photon state is proposed. Orthogonally-polarized and parallel-polarized entanglements of photon pairs are instantly switchable by tuning the applied field. The characteristics of the source are theoretically investigated showing adjustable bandwidths and high entanglement degrees. Moreover, other kinds of reconfigurable entanglement are also achievable based on suitable domain-design. We believe tailoring entanglement based on domain engineering is a very promising solution for next generation function-integrated quantum circuits.Scientific Reports 01/2014; 4:4812. · 5.08 Impact Factor - SourceAvailable from: export.arxiv.org
##### Article: Generation and manipulation of entangled photons in a domain-engineered lithium niobate waveguide

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**ABSTRACT:**We propose to integrate the electro-optic tuning function into polarization-entangled photon pair generation process in a periodically poled lithium niobate (PPLN). Due to the versatility of PPLN, both the spontaneously parametric down conversion and electro-optic polarization rotation effects could be realized simultaneously. Orthogonally-polarized and parallel-polarized photon pairs thus are instantly switchable by tuning the applied field. The characteristics of the source are investigated showing adjustable bandwidths and high entanglement degrees. Moreover, other kinds of reconfigurable entanglement are also achievable based on suitable domain-design. We believe the domain engineering is a very promising solution for next generation function-integrated quantum circuits.07/2013;

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Non-collinear and non-degenerate

polarization-entangled photon

generation via concurrent type-I

parametric downconversion in PPLN

Hugues Guillet de Chatellus∗, Alexander V. Sergienko, Bahaa E. A.

Saleh and Malvin C. Teich

Quantum Imaging Laboratory,

Department of Electrical & Computer Engineering and Department of Physics

Boston University, 8 Saint Mary’s Street

Boston, Massachusetts 02215

∗Laboratoire de Spectrom´ etrie Physique, CNRS-Universit´ e Joseph Fourier

140 avenue de la physique, BP 87

38402 Saint Martin d’H` eres, France

AlexSerg@bu.edu

Giovanni Di Giuseppe

Department of Physics

University of Camerino, Via Madonna delle Carceri, 9

I-62032 Camerino, Italy

Abstract:

been used as an efficient source of non-collinearly generated polarization-

entangled photon pairs at 810 and 1550 nm. The PPLN crystal was endowed

with a specially designed poling pattern and the entangled photons were

generated via the nonlinear optical process of spontaneous parametric down

conversion (SPDC). A novel design based on overlapping two concurrent

type-I quasi-phase-matching structures in a single PPLN crystals produced

correlated pairs of alternatively polarized photons in largely separated

spectral regions. The phase of the resulting two-photon state is directly

linked to parameters of the nonlinear grating. Continuous tunability of the

generated Bell state, from Φ+to Φ−, has been demonstrated by translating

a slightly wedged crystal perpendicular to the pump beam.

A periodically poled lithium niobate (PPLN) crystal has

© 2006 Optical Society of America

OCIS codes: (270.0270) Quantum optics; (190.4410) Nonlinear optics, parametric processes.

References and links

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1.Introduction

Spontaneous parametric downconversion (SPDC) [1] has been widely used as a source of cor-

related and entangled photon pairs in many quantum optics experiments. Applications of such

optical states include tests of basic quantum mechanics [2, 3], precise optical measurements

[4,5],quantumimaging[6,7,8,9],andquantuminformation[10],amongothers.Theencoding

of quantum information using polarization has served as a reliable technique for implementing

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such nonclassical effects as quantum teleportation [11, 12], quantum dense coding [13], and

secure quantum key distribution (QKD) [14, 15, 16].

Practical quantum cryptography is expected to benefit from the availability of a compact

and efficient source of polarization entanglement between photons whose frequencies are well

separated, particularly when one of the wavelengths falls in the telecommunication window

near 1550 nm and the other lies in the visible region [16]. The entangled-photon QKD protocol

relies on the joint (coincidence) detection of the photon pair at two spatially separated nodes.

The benefit arises because of the superior performance of Si photon-counting detectors in the

visible region relative to InGaAs detectors in the infrared. In particular, double-wavelength

entanglementenhancestheoverallefficiencyoftheentangled-photonQKDschemebyallowing

the visible photon to be detected locally, with a low-noise detector at Alice’s node, while the

infrared photon is transmitted to Bob’s site via a low-loss optical fiber. The detection of the

visible photon effectively serves to herald the arrival of its infrared partner at the remote node,

which has a noisier InGaAs detector, thus allowing the observer to narrow the detection-time

window and thereby increase the signal-to-noise ratio for the overall process.

Various efforts to construct compact and efficient sources of polarization entanglement suit-

able for practical use have been reported over the past decade. Historically, the most commonly

used scheme makes use of type-II SPDC in a bulk beta-barium borate (BBO) crystal; this pro-

vides polarization entanglement along two particular non-collinear directions in space [17].

However, this approach suffers from a low efficiency of entangled-pair production because of

the poor overlap of the two orthogonally polarized SPDC cones. The group-velocity mismatch

between the two orthogonal polarizations in the birefringent nonlinear crystal destroys the tim-

ing indistinguishability of two photons; this must be restored by making use of an additional

birefringent element to compensate for the longitudinal walk-off acquired inside the nonlinear

material.

The overlap of the two orthogonally polarized SPDC cones can be improved by pumping

the crystal in the direction of one of its principal axes, which generates entanglement around a

whole revolution cone [18]. However, the use of type-II phase matching to generate polarization

entanglement with this approach is restricted to the degenerate case, where the frequencies of

the signal and idler photons are coincident.

The need for additional compensation optics can be avoided by using type-I SPDC, for which

temporalwalk-offisnegligible.Apolarization-entangledstatecanbeengineeredbymakinguse

of fully overlapping correlated-photon outcomes from separate nonlinear interactions in two

thin type-I nonlinear crystals placed immediately adjacent to each other; downconversion with

orthogonalpolarizationsemergesfromthecrystalpairwhenpumpedbyasinglebeampolarized

at 45◦[19]. The photon pairs are generated along any set of directions that are symmetric with

respect to the axis of the pump beam, and this leads to high efficiency. The close spacing

of the crystals renders the otherwise independent processes indistinguishable, thus creating a

polarization-entangledstate.Aprincipallimitationofthisapproachisthatthenonlinearcrystals

must be rather thin to preserve the indistinguishability of pairs in the non-collinear case. Also,

an additional birefringent plate must be placed in the path of the pump beam to tune the phase of

a Bell-state. An extension of this approach that makes use of two orthogonally oriented PPKTP

crystals has led to the collinear generation of nondegenerate polarization-entangled pairs [20].

Instead of pumping two nonlinear crystals with a single pump beam, it is also possible to

produce polarization entanglement by pumping a single nonlinear crystal with two counter-

propagating pump beams [21, 22]. However, such implementations require additional optics.

External optical elements are also often required to spatially separate the photons of a pair

because, traditionally, nonlinear interactions in PPLN utilize a collinear geometry of interacting

waves. Finally, the fine tuning of an output state, and the switching from one polarization Bell-

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state to another, requires the insertion of auxiliary birefringent elements in the outgoing beams.

Is it possible to create a compact single-crystal source, pumped by a single beam, that gen-

erates polarization-entangled photon pairs, with well separated frequencies in a non-collinear

geometry, that does not requires additional optics for tuning the output state? We demonstrate,

both theoretically and experimentally, that a specially engineered periodically poled crystal

(PPC) can serve as just such a source when suitably prepared.

The organization of the remainder of this paper is as follows. We first demonstrate the possi-

bility of designing a poling pattern in a PPC that allows the generation of polarization-entangled

states via the overlap of two different, but concurrently existing, type-I nonlinear interactions

in the same crystal. The resulting two-photon state is then determined; its phase is shown to

be directly linked to the profile of the periodic nonlinearity in the PPC. This suggests the pos-

sibility of tuning the phase of the outgoing two-photon state by forming a wedged PPC and

translating it in the field of the pump laser. While we have established that this technique is

applicable for an arbitrary periodically poled nonlinear material, we select periodically poled

lithium niobate (PPLN) for the first demonstration. In particular, we generate non-degenerate

polarization-entangled photon pairs at 810 and 1550 nm directly from a single PPLN crystal

with two overlapping type-I parametric interactions. We examine the spatial and spectral char-

acteristics of the emerging photons that are required for indistinguishability between the two

contributing processes. A Bell-state measurement that demonstrates the nonclassical behavior

of the ensuing two-photon state is reported. Finally, we demonstrate the tuning the state from

Φ+to Φ−by a simple translation of the crystal.

2. Generation of entanglement in a PPC: Theoretical considerations

2.1.

Periodically poled crystals, which make use of quasi-phase matching [23], are suitable for

achieving parametric oscillation [24], frequency up-conversion [25] and, in a conventional con-

figuration, SPDC [18, 20, 21, 26]. Here we provide a general description of SPDC in a PPC

that elucidates the design of our special poling patterns.

We consider the simple case of a plane-wave pump traveling along the x direction in a non-

linear medium that occupies a volume V between x = 0 and x = L, which is periodically poled

with spatial period Λ. As always, the components of the second-order susceptibility tensor can

be written as

χ(2)

q

where the summation is over all spatial wavevectors q associated with the Fourier spectrum of

the spatial profile of the periodically modulated nonlinearity. In a one-dimensional PPC, q is

directed along x. The Fourier transform of the nonlinear profile can be reduced to

Two-photon state produced by SPDC in a PPC

ijk(r) =∑

? χ(2)

ijk(q)eiq·r,

(1)

? χ(2)

ijk(q) =1

Λ

?+Λ/2

−Λ/2

dxχ(2)

ijk(x)e−iq·r.

(2)

The finiteness of the nonlinear medium is accounted for by the integration over the volume of

the crystal. The wavevectors q are the spatial harmonics of the modulation. In the general case

of an infinite PPC, they can be written as q = n·q0where |q0| = q0= 2π/Λ is an elementary

vector of the reciprocal lattice, and n is an integer.

Accommodating the various components of the second-order nonlinear tensor, the two-

photon state produced by SPDC can be written as [1]

?

|ψ(2)? ∼

Vdr

?

dt ∑

tensor

χ(2)

psi(x)? E+

p(r,t)? E−

s(r,t)? E−

i(r,t)|vac?,

(3)

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where? E−

sand? E−

iare the field operators of the signal and idler, respectively:

?

?

The classical pump field is specified by the complex amplitude

?

The quantities Ep, Es, and Eirepresent the spatial modes of the pump, signal, and idler fields

respectively. The polarizations of the three photons are denoted as p, s, and i, respectively; they

can be ordinary (o) or extraordinary (e). The magnitude of the pump wavevector is |kp(ωp)| =

kp(ωp)=2πnp(ωp)ωp/c where ωpis the pump frequency and np(ωp) is the refractive index of

a p-polarized monochromatic wave of frequency ωpin the nonlinear crystal. Similar relations

can be written for the signal and idler waves.

In the case of a plane-wave, the SPDC state becomes

? E−

? E−

s(r,t) =

dωs

?

?

ωs

ns(ωs)Ese−iks(ωs)·reiωsta+

ωi

ni(ωi)Eie−iki(ωi)·reiωita+

s(ωs,ks(ωs)),

(4)

i(r,t) =

dωi

i(ωi,ki(ωi)).

(5)

E+

p(r,t) =

dωp

?

ωp

np(ωp)Epeikp(ωp)·re−iωpt.

(6)

|ψ(2)? ∼

?

?

dωsdωpδ(ωp−ωs−ωi)

?

∑

tensor

n=+∞

∑

n=−∞

? χ(2)

psi(nq0)

?np(ωp)ns(ωs)ni(ωi)

(7)

×

Vdrei(kp(ωp)−ks(ωs)−ki(ωi)−nq0)·r

???1ωs,ks(ωs)

? ??1ωi,ki(ωi)

?.

The double summation suggests the possibility of producing at least two independent photon

pairs in the same spectral (ωs,ωi) and spatial (ks(ωs),ki(ωi)) modes, and therefore to the pos-

sibility of constructing an entangled state, provided that energy and momentum are conserved.

As an example, we consider the case where the nonlinear tensor has two nonvanishing compo-

nents, χ(2)

the maximally polarization-entangled Bell state

|Φ? = (|e,e?+eiφ|o,o?)/√2,

where the first term is enabled by the χ(2)

nonlinear tensor, respectively.

Several conditions must be fulfilled for a polarization-entangled state to be synthesized:

1. Energy must be conserved: ωp= ωs+ωi.

eeeand χ(2)

eoo. The crystal can then be pumped by an e-polarized pump beam to produce

(8)

eee, and the second by the χ(2)

eoo, components of the

2. Momentum must be conserved, i.e., a pair of integers nee,noomust exist that satisfy the

quasi-phase matching conditions:

ke(ωp)−ke(ωs)−ke(ωi) = neeq0

ke(ωp)−ko(ωs)−ko(ωi) = nooq0.

(9)

3. A spatial mode of the e-polarized signal photon of a pair must overlap with the spatial

mode of the o-polarized signal photon of the same frequency from the second interaction,

and vice versa (see Fig. 1).

4. The production rates (intensities) of the two processes must be the same.

The process of designing polarization-entangled states from two concurrent nonlinear interac-

tions is therefore closely related to the choice of nonlinear interaction geometries, in combina-

tion with the physical parameters of the selected nonlinear medium.

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1

Λ Λ Λ Λ

χ χ χ χ(2)

(2)(2)

(2)( ( ( (x) ) ) )

x

PPLN

y

z

Pump 532 nm

1550 nm

810 nm

2

π π π π

-π π π π

α α α α

Fig. 1. Principle of generating polarization-entangled pairs at 810 and 1550 nm. Two sys-

tems of cones (e and o polarized) are caused to overlap. Entangled pairs are collected along

the directions labeled 1 and 2, always on opposite sides of the pump beam. The two inserts

illustrate the definitions of the fundamental parameters of the PPC: the period Λ and the

(angular) duty cycle α.

2.2.

The production of entangled states of the type (|e,e?+eiφ|o,o?)/√2 is particularly interesting

because it can be achieved by the direct overlap of two type-I interactions. As indicated above,

this avoids the necessity of birefringent compensation following the crystal [19], and results

in a more compact source of entangled photons. In particular, we consider 810 and 1550 nm

photons produced by SPDC with a monochromatic laser pump at 532. This choice is motivated

by the fact that QKD implementations with both photons at 1550 nm are particularly difficult

to realize [27], principally because of the poor efficiency of existing InGaAs single-photon de-

tectors at this wavelength. Because of the technological maturity of Si single-photon detectors

in the visible spectrum, in contrast, a hybrid 810/1550 nm configuration can provide a good

alternative, provided that the distance traveled in the fiber by the 810-nm photon is sufficiently

short [16].

With respect to the material, periodically poled lithium niobate (PPLN) has proven to be an

efficient and versatile choice for realizing quasi-phase matching in the context of a nonlinear

three-wavemixingprocess. Anumericalsimulation wascarriedoutto determinetheparameters

(spatial pitch and duty cycle) of the PPLN crystal suitable for satisfying the four requirements

set forth earlier. A practical and feasible PPLN crystal design is achieved with a spatial pitch

Λ=27.5µm and angular duty cycle 33◦(see Fig. 1). In this case, the emission directions of the

pairfromthee→e+einteraction,phase-matchedwiththefourthorderofthenonlineargrating,

are coincident with the emission directions of the pair from the e → o+o interaction, phase-

matched with the zeroth order of the poling period. Zeroth order signifies that the interaction is

made possible by natural bulk birefringent phase-matching in lithium niobate.

ExploitingthetemperaturedependenceoftheSellmeierequationsforlithiumniobateleadsto

Selection of physical parameters

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scattering angles for e-polarized 810 nm and 1550 nm photons (which are, in general, different)

that coincide with the angles of corresponding o-polarized 810 nm and 1550 nm photons at

100◦C (see Fig. 1). The reduced duty cycle of the poling enables the equalization of the pair

production rates for the two participating interactions, since the nonlinear coefficient associated

with the first interaction (d33= 16 pm/V) is substantially larger than the coefficient associated

with the second interaction (d31= 2.9 pm/V).

2.3.

To simplify the calculation of the two-photon entangled state generated in the previously de-

fined configuration, we restrict our consideration to wavevectors produced in the x–y plane.

Since the interior angles between the signal and idler wavevectors, and the direction of the

pump (i.e. the x axis), are small (2.6◦and 5◦, respectively), we make use of a paraxial ap-

proximation that enables us to eliminate the transverse dependence of the wavevectors. A more

complete description of the SPDC phase-matching parameters that includes the transverse be-

havior of the wavevectors in a strongly non-collinear geometry can indeed be provided by using

a methodology described elsewhere [28].

In the simplified case considered here, however, the two-photon state produced in the x–y

plane by the e → e+e interaction can be written as

|ψ(2)

? χ(2)

We choose to spread the signal and idler frequencies around their central values ω0

correspondingtothewavelengthsof810and1550nm,respectively.Energyconservationallows

us to write ωs= ω0

and ke(ωi) = ke(ω0

waves at 810 nm and 1550 nm in the PPLN crystal, respectively. Because the quasi-phase

matching condition is simply ke(ωp)−k0

? χ(2)

Writing Dee= 1/us,e−1/ui,e, the integration leads to

ee ? ∼ −1

L

ne(ωp)ne(ω0

Amplitude and phase of the two-photon state

ee ? ∼

?

eee(4q0)

dωsdωpδ(ωp−ωs−ωi) ×

?L

(10)

?ne(ωp)ne(ωs)ne(ωi)

0

dxei(ke(ωp)−ke(ωs)−ke(ωi)−4q0)x|1ωs,ke(ωs)?|1ωi,ke(ωi)?.

sand ω0

i,

s+ν and ωi= ω0

i)−ν/ui,e, where us,eand ui,eare the group velocities for the e-polarization

i−ν. The wavevectors are then ke(ωs) = ke(ω0

s)+ν/us,e

e(ωs)−k0

?L

e(ωi) = 4q0, the two-photon state becomes

|ψ(2)

ee ? ∼

eee(4q0)

?

ne(ωp)ne(ω0

s)ne(ω0

i)

0

dxe−i(1/us,e−1/ui,e)ν·x|1ωs,ke(ωs)?|1ωi,ke(ωi)?.

(11)

|ψ(2)

? χ(2)

eee(4q0)

?

s)ne(ω0

i)

e−iνDeeL/2sinc(νDeeL/2)|1ωs,ke(ωs)?|1ωi,ke(ωi)?. (12)

Similarly, taking Doo= 1/us,o−1/ui,o, the two-photon state produced by the e → o+o inter-

action is

? χ(2)

The state incorporating both pairs [Eq. (8)] is maximally entangled if contributions from both

nonlinear processes are totally indistinguishable over their spectral bandwidths:

?????

|ψ(2)

oo? ∼ −1

L

eoo(0)

?

ne(ωp)no(ω0

s)no(ω0

i)

e−iνDooL/2sinc(νDooL/2)|1ωs,ko(ωs)?|1ωi,ko(ωi)?. (13)

? χ(2)

eee(4q0)

?

ne(ωp)ne(ω0

s)ne(ω0

i)

sinc(νDeeL/2)

?????=

?????

? χ(2)

eoo(0)

?

ne(ωp)no(ω0

s)no(ω0

i)

sinc(νDooL/2)

?????. (14)

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Page 8

φ φ φ φ1 1 1 1

φ φ φ φ2 2 2 2

Fig. 2. Left: input face of the poled crystal. The spatial period is 27.5µm. Note the highly

unbalanced duty cycle between the ferroelectric domains. The red arrow represents the

normal to the input face while the blue arrow is the normal to the domain walls. Right:

the two-photon state phase φ is modified by simply changing the transverse position of the

input beam.

The accuracy of this indistinguishability requirement can be estimated by constructing an over-

lap integral of these two functions over ν. In the case of an 8-mm-long PPLN crystal, the

agreement is close to 95%. Under these conditions, the necessity of using birefringent compen-

sation following the crystal is essentially obviated, in contrast to the situation for type-II-based

SPDC sources. Introducing the notation

?χ?(2)

psi(q) =

? χ(2)

psi(q)

?

np(ωp)ns(ω0

s)ni(ω0

i)

,

(15)

the equality of the pair-production rates is readily expressed as |?χ?(2)

is determined to be

φ = −ν(Dee−Doo)L/2+arg??χ?(2)

For the 8-mm-long PPLN crystal, the variation of the phase arising from frequency disper-

sion within the spectral width of the signal and idler waves is found to be negligible. For

a 2 nm-bandwidth signal, the phase change is estimated to be less than 0.13 rad. Thus the

first frequency-dependent term in Eq. (16) is essentially zero. (Note that this discussion is

not necessary for the degenerate case of equal signal and idler central frequencies.) Hence,

the phase of the two-photon state is governed principally by the second term in Eq. (16),

arg??χ?(2)

the pairs is generated via harmonic zero (bulk phase matching without modulation), the phase

of the entangled state depends solely on the relative position of the rectangular poling structure

within the nonlinear crystal. A straightforward and direct way to tune the output state is then to

shift the relative phase φ by translating a wedged sample perpendicular to the field of the pump

beam, as depicted in Fig. 2. This highlights another advantage of generating entanglement us-

ing PPCs: the entangled state structure can be easily controlled because it is governed only by

the intrinsic properties of the poled crystal.

eee(4q0)| = |?χ?(2)

eoo(0)|.

The phase between the two processes that contribute to the joint two-photon entangled state

eee(4q0)−?χ?(2)

eoo(0)?.

(16)

eee(4q0)−?χ?(2)

eoo(0)?, which is directly linked to the phase properties and spatial profile

of the periodically modulated nonlinearity in the poled crystal. In the special case when one of

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Page 9

Fig. 3. Movie size: 350 K. Image from the CCD camera that collects the 810-nm SPDC

rings as crystal temperature is varied. The bandwidth of the interference filter is 10 nm. The

ring that disappears at 130◦C is the extraordinary polarized one. The movie illustrates the

versatility of using periodically poled structures for applications that exploit non-collinear

geometries.

3. Experiment

3.1.

We developed procedures and an experimental protocol for poling lithium niobate crystals. A

z-cut 0.5-mm-thick lithium niobate sample (1”×1”) is patterned with a 3µm-thick photoresist

layer (Shipley 1813) using standard lithographic techniques. The photomask pattern consists

of a rectangular grating with a 27.5-µm period. The angular duty cycle of the pattern is 25◦,

leading to 2µm-wide openings in the resist. This value is selected to be smaller than the the-

oretical value (33◦), in anticipation of domain spreading during poling. The boundaries of the

grating are oriented along the y-axis of the lithium-niobate crystal. The length of the grating is

12 mm and its width is 5 mm. A 20-nm-thick layer of nickel-chromium is deposited by e-beam

evaporation atop the photoresist pattern to improve nucleation during the poling process, as

well as the homogeneity of the domains [29]. The crystal is then inserted in a poling chamber

filled with liquid electrolyte (a saturated solution of LiCl), and a high-voltage pulse is applied

for a duration of 60 msec to flip the domains. After the poling, the sample is cut to a size 8×5

mm and its sides are polished. The input edge is polished at a slight angle with respect to the

domains to enable the phase of the two-photon state to be altered by a simple translation of the

crystal in the pump beam, in accordance with the illustration provided in Fig. 2.

Poling of the crystal

3.2.

We characterize the spatial and spectral properties of SPDC by pumping the PPLN crystal with

an e-polarized, 150-mW, frequency-doubled CW Nd:YAG laser beam that is slightly focused at

the center of our sample by means of a 400-mm focal length lens. The PPLN crystal is mounted

in an oven with an adjustable temperature between 25 and 230◦C. The crystal temperature

serves to fine tune the SPDC output. To facilitate the direct observation of SPDC, a collection

lens (f = 38 mm) is placed at distance f from the crystal. A dichroic mirror and a long-pass

filter remove the residual 532-nm pump light, and the SPDC beam is sent through a 810-nm

Characterization of the parametric downconversion

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16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10068

Page 10

804 804808 808812 812816816 820820

0.00.0

0.2 0.2

0.40.4

0.60.6

0.8 0.8

1.01.0

Signal wavelength (nm)Signal wavelength (nm)

e-e+e interaction

e-o+o interaction e-o+o interaction

Normalized spectrum

e-e+e interaction

Normalized spectrum

Fig. 4. Relative spectra of the 810-nm photons for the two processes (e → e+e and e →

o+o) collected through a narrow pinhole that serves as a spatial filter (see text for details).

interference filter (∆λ =10 nm). A polarization analyzer allows the polarization of the outgoing

photons to be adjusted. A telescope comprising two lenses reduces the size of the beam so that

the 810-nm photons suitably impinge on a commercial uncooled silicon CCD camera.

The temperature-dependent SPDC pattern at 810 nm is displayed in Fig. 3. At 60◦C, the

rings representing the two processes are seen to overlap. The crystal was initially designed

to achieve overlap at 100◦C; the discrepancy likely arises from the difference between the

temperature-dependent Sellmeier coefficients quoted in the literature and those for the actual

sample used in our experiments. As the temperature is increased, the diameter of the e-polarized

pattern decreases dramatically while the o-polarized pattern changes far less. This asymmetry is

aresultofthefactthatthephase-matchingconditionforthee→e+einteractionissubstantially

more sensitive to temperature than is that for the e → o+o interaction.

To compare the relative intensities of the orthogonally polarized 810-nm beams from the two

interactions, we direct all emitted photons to a photodiode surface using a 2f–2f configuration.

The intensity of the pump beam is ramped up to 750 mW and the analyzer is successively set

along the e and o directions. Following a 10-nm-wide interference filter centered at 810 nm, the

optical power was observed to be 90±10 nW in both cases, revealing a similar pair-production

rate from both interactions.

To evaluate the degree of spectral overlap for the spatially overlapping photons from the

two interactions, a 0.5-mm-diameter pinhole is placed at the center of the 810-nm beam, at

a distance of 50 cm from the crystal. The beam is then sent to a spectrometer coupled to a

cooled CCD camera, which records the spectra. The normalized spectra for both polarizations

are presented in Fig. 4. They display significant overlap, although the full-width half-maxima

(FWHM) differ slightly as a result of the differing bandwidths of the two interactions. This par-

tial spectral distinguishability can potentially lead to a degradation of entanglement. However,

this can likely be obviated by modifying the poling design.

3.3.

To demonstrate the nonclassical behavior of the polarization-entangled two-photon state, we

carry out a Bell-state measurement using the experimental arrangement schematized in Fig. 5.

Bell-state measurement and phase tuning

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Page 11

FC

x

y

z

FC

Si

65 mW, 532 nm

vides spatial selection for the 810 nm photons. The 1550-nm photons are collected through

a similar system (half-wave plate, Glan-Thompson prism and pinhole) and are coupled into a

single-mode telecommunications-wavelength fiber. This fiber leads to an InGaAs single-photon

counting detector (idQuantique), which, in turn, is triggered by the Si detector. A coincidence

circuit based on a time-to-amplitude converter and a multichannel analyzer monitors the coinci-

dence rate. A Bell-state measurement is performed using half-wave plates to select the required

polarization projections.

The observed experimental results are presented in Fig. 6. From the number of single counts

at 810 nm and from the quantum efficiency of the Silicon avalanche photodiode (about 80%),

we can estimate a pair production close to 108pairs/nm bandwidth/sec/steradian per mW of

pump. It is apparent from this figure that the singles rate at 810 nm is rather flat (within ≈

3%) indicating a well-balanced presence of both polarizations in the channel. However the

coincidence rate is slightly higher when the 1550-nm analyzer is in the horizontal position -i.e.

along y- (triangles) rather than in the vertical position -i.e. along z- (squares). This indicates a

greater collection efficiency for the 1550-nm photons from the e → o+o interaction than from

the e → e+e interaction. When the 1550-nm analyzer is set at 45◦(circles), the coincidence

rate exhibits modulation with a visibility of 75% as the 810-nm waveplate is rotated. This

value is larger than the usual Bell-threshold of 70.7% and is sufficient for demonstrating the

nonclassical nature of the two-photon polarization state. However, the contributions from the

two concurrent type-I nonlinear interactions must be further equalized before this source can

be used in a practical QKD setting. We estimate the modification of visibility arising from the

intensity mismatch of the nonlinear processes to be approximately 85%. The spectral mismatch

also contributes to the degradation of the purity of the state.

To demonstrate the tunability of the entanglement source, we set both analyzers at 45◦and

record the rate of coincidence as the PPLN crystal is translated perpendicularly to the pump

beam. The results are illustrated in Fig. 7. The coincidence rate changes from a maximum to a

minimum, demonstrating that the phase φ varies from 0 to π. The two-photon entangled state

PPLN

60° C

trigger

TAC

λ/ / / /2 + GT prism

λ/ / / /2 + GT prism IF

SM fiber

@1550 nm

MM fiber

Fig. 5. Experimental arrangement for the Bell-state measurement. IF = interference filter at

810 nm (FWHM = 10 nm), λ/2= half-waveplate, GT = Glan-Thompson prism, FC = fiber

coupler, MM = multimode, SM = single-mode, Si = silicon APD photon-counting module,

idQuantique = InGaAs photon-counting detector, TAC = time-to-amplitude converter.

The intensity of the 532-nm pump beam is reduced to 65 mW and the beam waist is narrowed

to 100µm to enable observation of the change of phase when the crystal is translated in the

pump beam. After passing through a λ/2-waveplate, a Glan-Thompson prism, and a 10-nm-

bandwidth filter centered at 810 nm, the photons are coupled into a multimode fiber that leads

to a passively quenched Si single-photon counting module (Perkin-Elmer). The pinhole pro-

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16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10070

Page 12

0 4590135180

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Singles 810 nm /100

Counts (10 s)

Analyzer 810 nm (degrees)

Analyzer 1550 nm @ 0

Analyzer 1550 nm @ 90

Analyzer 1550 nm @ 450

0

Fig. 6. Results of a Bell-state measurement. Top: singles rate at 810 nm as a function of

the orientation of the polarization analyzer in the 810-nm path with respect to the z axis.

Bottom: coincidence rates for three different settings of the 1550-nm analyzer.

is effectively adjusted from Φ+= (| e,e?+ | o,o?)/√2 to Φ−= (| e,e?− | o,o?)/√2 with a

translational shift of ≈ 200 µm. This clearly demonstrates the ability to tune the phase of an

outgoingentangledstatebymodulatingthephysicalpropertiesofthenonlinearpolingpatternin

PPLN. Note that the visibility of the two-photon interference could be improved by decreasing

the wedge angle of the nonlinear crystal : a substantial loss in the visibility (close to 85%) of

the two-photon interference results from the convolution of the pump beam (waist = 100µm)

with the transverse profile (i.e. along y) of the nonlinear pattern (400µm period).

4.Conclusion

We have carried out a theoretical and experimental study of non-collinear and non-degenerate

optical parametric down conversion in a periodically poled lithium niobate crystal, demonstrat-

ing the feasibility of constructing a compact source of two-photon polarization entanglement

in the 810–1550-nm spectral regions. A specially designed nonlinear poling pattern enables the

overlap of two concurrent type-I down conversion interactions in a single PPLN crystal in such

a way that pairs of alternatively polarized photons become indistinguishable and thereby con-

tribute coherently to the formation of a two-photon polarization-entangled state. This approach

eliminates the traditional external compensation optics. We showed further that the phase of

the ensuing entangled state can be continuously adjusted by simply translating the nonlinear

crystal relative to the pump beam.

Although this first experimental test of entangled-state production using two concurrent type-

I nonlinear interactions in a PPLN crystal is most promising, a number of improvements must

be effected before it can be adopted for use in a practical QKD implementation. The design of

the periodically poled crystal can be improved quite easily: reducing the crystal length should

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16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10071

Page 13

0 100 200300400500 600700800

0

200

400

600

800

1000

1200

1400

1600

1800

Counts (10 s)

Translation of the crystal (µ µ µ µm)

Singles 810 nm /100

Coincidences (both analyzers @ 45

0)

Φ Φ Φ Φ+ + + +

Φ Φ Φ Φ+ + + +

Φ Φ Φ Φ− − − −

Φ Φ Φ Φ− − − −

Fig. 7. Demonstration of the tunability of the output two-photon state. Both analyzers are

set at 45◦andthe crystalis translatedperpendicularly tothe pump beam.Top:singlesrate at

810 nm. Bottom: coincidence rate. The translation distances at which Φ+and Φ−emerge

are shown.

ameliorate the spectral mismatch between the two nonlinear contributions, and a wider poled

pattern relative to the pump beam waist should lead to a higher degree of entanglement. Finally,

it will be useful to more accurately control the duty cycle of the nonlinear profile to better

equalize pair production and to enhance the coherence of the state. The symmetry of collecting

the 1550 nm photons can be improved by modifying the fiber-coupling optics.

We believe that our results demonstrate a significant potential for periodically poled crys-

tals with specially designed patterns as sources of entanglement. The possibilities offered by

multiple concurring nonlinear interactions offer a roadmap for the implementation of compact,

sophisticated devices. The approach set forth here can be extended, for example, to the design

and construction of bidimensional nonlinear PPLN structures that allow direct access to the

simultaneous manipulation of polarization and frequency entanglement [30].

Acknowledgments

This work was supported by a U.S. Army Research Office (ARO) Multidisiplinary Univer-

sity Research Initiative (MURI); by the Center for Subsurface Sensing and Imaging Systems

(CenSSIS), an NSF Engineering Research Center; by the National Science Foundation (NSF);

by the Defense Advanced Research Projects Agency (DARPA); and by the David & Lucile

Packard Foundation. G.D.G. also acknowledges financial support from the Ministero della In-

struzione, dell’ Universit` a e della Ricerca (PRIN-2005024254 and FIRB-RBAU01L5AZ) and

the European Commission through the Integrated Project ”Qubit Applications” (QAP), contract

No. 015848, funded by the IST directorat.

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Received 8 June 2006; revised 13 September 2006; accepted 28 September 2006

16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10072