MSc in Pho onics PHOTONICSBCN
Uni e si a Poli ècnica de Ca alunya (UPC)
Uni e si a Au ònoma de Ba celona (UAB)
Uni e si a de Ba celona (UB)
Ins i u de Ciències Fo òniques (ICFO)
h p://www.pho onicsbcn.eu
Mas e in Pho onics
MASTER THESIS WORK
SPECTRAL PROPERTIES OF AN EFFICIENT
ENTANGLED PHOTON SOURCE BASED ON
BULK PPKTP
Daniel Pé ez Gumà
Supe ised by D . Vale io P une i, (ICFO)
P esen ed on da e 1s Sep embe 2011
Regis e ed a
Spec al p ope ies o an e icien en angled pho on
sou ce based on bulk PPKTP
Daniel P´e ez Gum`a
ICFO - Ins i u de Ci`encies Fo `oniques, Medi e anean Technology Pa k, 08860
Cas ellde els (Ba celona), Spain
E-mail: [email p o ec ed]
Abs ac . The main objec i e o his hesis is o s udy and cha ac e ize he spec al
p ope ies o spon aneous pa ame ic down con e sion (SPDC) gene a ed in bulk
pe iodically poled po assium i anyl phospha e (PPKTP). The wo k ca ied ou
is an essen ial s ep owa ds he implemen a ion o a high b ig hness pho on-pai
sou ce o long dis ance quan um key dis ibu ion (QKD) expe imen s in a ee-space
en i onmen .
Keywo ds. Quan um key dis ibu ion,spon aneous pa ame ic down con e sion,PPKTP
1. In oduc ion and mo i a ion
Nowadays socie y needs o as and secu e communica ions is undeniable. Up o
he p esen ime communica ion and c yp og aphy echniques a e being used aking
ad an age o ou knowledge abou he ealm o classical physics. In his con ex classical
elec odynamics is he solid g ound in which all cu en communica ion sys ems a e
based: wi i local a ea ne wo ks, mobile communica ions, op ical ne wo ks, blue oo h,
e c. . . Howe e , quan um physics has become an in ensi ely s udied esea ch ield o e
he las cen u y. I u ns ou some scien i ic and echnological b eak h oughs sugges
ha cu en classical c yp og aphy could be de ea ed by nea - u u e quan um sys ems.
This is he eason why he scien i ic communi y is pu suing he c ea ion o quan um
communica ion sys ems.
1.1. The end o classical c yp og aphy
Classical c yp og aphy su e s om wo main laws: ei he he secu i y o a p o ocol is
no uncondi ional (i.e. 100% secu e) o he key exchange be ween he pa ies is e y
unp ac ical.
The i s issue is usually ela ed o public-key sys ems, whe e he secu i y o he
key is based on wha is called a one way unc ion. One-way unc ions a e ma hema ical
ope a ions ha a e e y easy o compu e in one way, bu e y di icul o e e se.
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 2
An example o his echnique is he widely used RSA p o ocol whe e he secu i y is
based on he di icul y o inding he p ime ac o s o la ge in ege s. Finding he p ime
ac o s o a numbe using a classical compu e is a p oblem ha has exponen ially
g owing complexi y wi h espec o he key leng h. Howe e , i has been demons a ed
ha he e exis s a leas one ou ine (Sho ’s algo i hm) implemen able in a quan um
compu e ha can sol e his one-way unc ion in polynomial ime. The e o e, he pa h
owa ds quan um compu a ion ende s classical public-key sys ems.
The second issue is usually ela ed o sec e -key sys ems. In his case he secu i y
o he da a is based on he assump ion ha only he wo pa ies in ol ed know he
key. This is e y unp ac ical because one en i y migh wan o exchange in o ma ion
secu ely wi h many pa ies, he e o e needing many di e en keys. Mo eo e , only he
ace- o- ace key exchange would be 100% secu e, which is expensi e and ime consuming.
QKD can sol e he p oblems men ioned be o e. Thanks o he laws o quan um
mechanics, he secu i y o he keys is assu ed and hei c ea ion is emo ely nego ia ed.
Quan um p o ocols a e based on he exchange o quan um pa icles be ween he wo
pa ies namely Alice and Bob. A se ies o measu emen s o he s a es o such pa icles
by Alice and Bob enable he c ea ion o he secu e key [2].
1.2. Ou line o he p ojec
In sec ion 2 he design o he en angled pho on sou ce is desc ibed. The nume ical model
and i s main pa ame e s a e commen ed as well. In sec ion 3 he expe imen al se -up
is shown and discussed. Finally in sec ion 4 he esul s ob ained in he labo a o y a e
analyzed and compa ed wi h he nume ical model.
2. Theo y
Cu en ly, SPDC is he mos widely used physical p ocess o c ea e en angled pho on
pai s. This phenomenon is pu ely quan um, aking place a he pa icle le el. SPDC
can be unde s ood as a spon aneous decay o one pho on a eling in a nonlinea op ical
medium in o a pai o lowe ene gy pho ons called signal and idle . The p ocess is
allowed only when ene gy and momen um a e conse ed. The ene gy conse a ion can
be exp essed in e ms o he pho on ene gy as
¯hωp= ¯hωs+ ¯hωi(1)
whe e ωp,s,i is he angula equency o he pump, signal and idle pho ons
espec i ely. The echnique aiming a achie ing momen um conse a ion is called phase
ma ching. The e a e wo app oaches ha can ul ill he momen um conse a ion law:
bi e ingence and quasi phase ma ching (QPM). In his p ojec he QPM app oach has
been chosen mainly because o wo ad an ages wi h espec he bi e ingence echnique.
Fi s , he highes nonlinea coe icien o he c ys al can be used (in ou c ys al we
will exploi d33). Secondly, aligning he di ec ion o p opaga ion wi h one o he
c ys allog aphic axes, he beam does no su e he walk-o e ec because he wa e ec o
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 3
and he poyn ing ec o a e pa allel. The e o e, he beam is be e con ined and as a
consequence he nonlinea in e ac ion is mo e e icien .
The QPM is achie ed in ou case by means o a e oelec ic pe iodic poling
echnique o he PPKTP c ys al. The pe iodically e e sed c ys allog aphic axes
o ien a ion enables he phase misma ch compensa ion be ween he pump, signal and
idle . The domain in e sion is enginee ed applying s ong elec ic ields by means o
pa e ned elec odes. The ini ial design o he pho on sou ce de e mined a alue o
3.425µm o he poling pe iod.
The pe iodically poled c ys al s uc u e has he key ole in he momen um
conse a ion equa ion. The phase ma ching condi ion o a collinea in e ac ion can
be w i en as [3]
kp=ks+ki+2π
Λ(2)
whe e kp,s,i a e he pump, signal and idle momen a and Λ is he poling pe iod o
he PPKTP c ys al. The e o e, he momen a misma ch can be exp essed as
∆k= 2π np(λp, T)
λp
−ns(λs, T)
λs
−ni(λi, T)
λi
−1
Λ!(3)
whe e he dependence o he e ac i e indices np,s,i wi h espec o he wa eleng h
and he empe a u e ha e been w i en. Using a con inuous wa e (CW) pump, he
spec um o he SPDC is [1]
S(λs,i)∝sinc2∆kL
2(4)
whe e Lis he leng h o he PPKTP c ys al, and ∆kis he exp ession (3). The
SPDC p ocess in ou expe imen s co esponds o ype 0 (pump,signal and idle ha e
he pola iza ion along he zaxis o he c ys al).
En anglemen is c ea ed by c ossing he c ys allog aphic z-axis o wo iden ical
PPKTP c ys als a 90 deg ees wi h espec o each o he . Signal and idle om he i s
and second c ys als a e supe posed and he elec ic ield can be w i en as a quan um
supe posi ion o bo h con ibu ions, ha ing o hogonal pola iza ions due o he c ys al
o ien a ions. The mos gene al o m o he quan um s a e gene a ed in his con igu a ion
may be w i en as
|Hsi ⊗ |Hii+eiφ |Vsi ⊗ |Vii(5)
whe e Hand Vs and o he ho izon al and e ical pola iza ions, and he
subindices e e o signal o idle wa eleng hs. The phase φcan be con olled o p oduce
di e en Bell s a es. The quali y o he en anglemen depends on he indis inguishabli y
o he ield coming om he i s and he second c ys al. Any measu able p ope y being
di e en lowe s he amoun o en anglemen . Fo his eason, a igo ous cha ac e iza ion
o he SPDC spec a as well as compa ison wi h he model calcula ion will be p esen ed
in he ollowing.
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 4
The nume ical model is an implemen a ion in MATLAB o he spec um p o ile o
SPDC shown in equa ion (4). The unknown pa ame e s needed o be ound in o de o
cha ac e ize he se -up a e he e ac i e index o he pump np(λp, T) and he e ec i e
leng h o he c ys als Le . In sec ion 4 he me hods ollowed o ind hese pa ame e s
a e de ailed.
3. Se -up
The expe imen al se -up is shown in igu e 1. Two di e en lase s we e ixed, one
being single-mode and he o he mul i-mode. The ligh is coupled in o single mode
ibe s (SMFs). The lase is selec ed connec ing he desi ed ibe wi h he launching ibe
(do ed-line ibe s indica e ha hey a e used o no depending on he expe imen ). The
pola iza ion o he pump is con olled wi h he qua e -wa e pla e (QWP) and he hal -
wa e pla e (HWP). The luo escence il e p e en s possible long-wa eleng h adia ion
o c oss he c ys al and each he a alanche pho odiodess (APDs). The ocusing lens
plus he collima ing lens enable o p ope ly ocus he pump beam inside he c ys al.
The pump cu il e plays he same ole as he luo escence il e , bu in his case he
pump beam is blocked. In bo h cases he goal is p o ec ing he APDs om high powe
adia ion. Finally he wa eleng h di ision mul iplexe (WDM) spli s he SPDC ield in
wo di e en ibe s, being one co esponding o he signal and he o he o he idle .
Fo he expe imen s in which he spec um o he SPDC is eco ded, he ligh is sen
di ec ly o a monoch oma o .
Figu e 1. Se -up o he expe imen s. Two di e en pumping lase s can be used, one
being single mode and he o he mul imode. The beam is p ope ly ocused inside he
PPKTP c ys al wi h a ocusing and collima ing lenses. Two di e en SPDC de ec ion
s ages a e used, one being he monoch oma o ( o spec al analysis) and he o he
he WDM plus he APDs ( o pho on coincidences analysis)

Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 5
4. Resul s
4.1. The mal and wa eleng h expansion o he e ac i e index o he pump
The sellmeie equa ions used [4] [5] in he nume ical model ha e p e iously been epo ed
o ha e limi ed applicabili y in he pump wa eleng h egion [6], and only apply o signal
and idle . Since he PPKTP is hea ed a di e en empe a u es inside he o en and
pumped wi h a mul imode lase , a he mal and wa eleng h expansions o he e ac i e
index a e needed o comple e he nume ical model. Fi s he 4 h o de wa eleng h
expansion is compu ed a a ixed empe a u e (50℃). The ixed wa eleng h a ound
which he polynomial expansion is calcula ed co esponds o he single mode lase cen e
wa eleng h: 405.42nm.
In igu e 2(a) he esul is shown. As i can be seen he cen e wa eleng hs o he
di e en modes ma ch, which alida es he polynomial exp ession ound. The spec al
ampli udes p o ided by he simula ion seem o be unp ecise. The eason is ha he
mul imode pump spec um has a noisy beha io which a ec s he empo al e olu ion
o he ampli udes o he modes. Since he spec um eco ding p ocess in ol es a ime
in eg a ion, he inal ampli ude has a andom componen .
(a) (b)
Figu e 2. (a) Mul imode spec al in ensi y o SPDC a 50℃used o compu e he
wa eleng h expansion o he e ac i e index (b) Mul imode pump spec um o he
wa eleng h expansion expe imen
Once he wa eleng h dependence o he index o e ac ion is known, he he mal
coe icien s a e compu ed. The me hod o do i consis s o ma ching he signal and
idle cen e wa eleng hs wi hin a su icien ly wide ange o empe a u es. The e e ence
empe a u e is 50℃because he wa eleng h expansion has been calcula ed a his alue.
The single mode lase is used his ime. The 2nd o de expansion p o ides a e y good
ag eemen be ween he simula ion and he expe imen al da a as i can be seen in igu e 3.
To check ha he he mal and wa eleng h expansion wo k ine oge he , a
mul imode SPDC spec um is eco ded expe imen ally and simula ed a 48.3℃. Figu e 4
con i ms a good ag eemen o he join expansion wi h he expe imen .
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 6
Figu e 3. Expe imen ally obse ed cen e wa eleng hs o signal and idle pho ons as a
unc ion o empe a u e. Simula ed da a shown using he op imized he mal expansion
o he pump e ac i e index
Figu e 4. Mul imode SPDC spec um a 48.3℃o he 20mm PPKTP c ys al.
The cen e wa eleng hs o he mul iple peaks a e ma ched, he e o e his expe imen
alida es he he mal-wa eleng h join expansion o he index o e ac ion a he pump
wa eleng h egion.
The exp ession o he pump e ac i e index wi h he mal and wa eleng h
expansions can be inally w i en as
np(λ, T) = np(λ0, T0) + A(T−T0) + B(T−T0)2+C(λ−λ0) +
D(λ−λ0)2+E(λ−λ0)3+F(λ−λ0)4(6)
whe e T0= 50℃and λ0= 405.42nm.
4.2. Bandwid h
Ha ing analyzed he cen e wa eleng h o he peaks, he o he impo an pa ame e om
he communica ions poin o iew is he spec al ull wid h hal maximum (FWHM).
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 7
Like he cen e wa eleng h, he FWHM is empe a u e dependen [1], bu also he leng h
o he c ys al de ines he bandwid h. The longe he c ys al he na owe he peaks.
F om expe imen s eco ded o di e en empe a u es we de e mined he e ec i e leng h
o he c ys als. The speci ica ions o he manu ac u e only assu e ha he e ec i e
leng h is highe han 90% o he physical leng h, bu do no p o ide he exac alues.
In igu e 5 he FWHM o signal and idle a e depic ed o he L= 6.2mm c ys al as a
unc ion o empe a u e. The simula ion ma ches he expe imen al esul s a almos all
empe a u es. Only o e y low empe a u es nea he degene acy poin he simula ion
p o ides sligh ly highe alues han he expe imen s. The e ec i e leng h ha p o ides
a be e i ing o he expe imen co esponds o 98% o he physical leng h.
Figu e 5. Expe imen al FWHM o signal and idle as a unc ion o he empe a u e
o he 6.2mm PPKTP c ys al. The e ec i e leng h ha be e i s he simula ion
wi h he expe imen al poin s co esponds o Le = 6.08 (98% o he physical leng h)
In [1] he esul o he heo e ical FWHM wi h espec o he c ys al leng h is
p o ided. I u ns ou he bandwid h o he signal/idle is in e sely p opo ional o he
c ys al leng h. A nume ical simula ion has been ca ied ou o check he ag eemen o
he expe imen al esul s wi h he nume ical model. In igu e 6 he FWHM dependency
wi h espec o he c ys al e ec i e leng h is shown a T= 50℃. Fo la ge c ys al
leng hs he non negligible 1.2nm esolu ion o he monoch oma o s masks he eal 1
L
dependence, and he expe imen ally eco ded FWHMs a e sligh ly highe han he alues
ob ained wi h heo y.
4.3. Angle de uning
Up o now he beha io o he sys em wi h espec o empe a u e, c ys al leng h and
pump wa eleng h ha e been analyzed. Ano he ole ance ha needs o be es ed is he
angle o incidence o he pump beam. The quali y o he op omechanics used o ix
he componen s ely on he ole ance o misalignmen s. To check his issue a sweep
o he angle o incidence o he pump has been pe o med. The cen e wa eleng h o
he idle peaks is shown in igu e 7. The highes cen e wa eleng h co esponds o
Spec al p ope ies o an e icien en angled pho on sou ce based on bulk PPKTP 8
Figu e 6. FWHM o signal and idle a 50℃in on o he e ec i e leng h o he
PPKTP c ys al. Expe imen al da a is shown o he 20mm c ys al (18mm e ec i e
leng h) and he 6.2mm c ys al (6.08mm e ec i e leng h).
no mal incidence, which means ha he poling pe iod seen by he beam co esponds
o he alue p o ided by he manu ac u e . When he incidence angle is de uned (bo h
posi i ely and nega i ely), he e ec i e poling pe iod inc eases and his modi ies he
QPM equa ion, o cing signal and idle o mo e apa as hey do when he empe a u e
o he c ys al is inc eased.
Figu e 7. Expe imen al cen e wa eleng h d i as a unc ion o he ho izon al angle
o incidence o he pump beam. This e ec is caused, as a i s app oxima ion, by he
inc ease o he e ec i e poling pe iod when he incidence o he pump is no no mal
o he inpu ace o he c ys al.
4.4. E iciency o he sou ce using a WDM
One o he in e es ing pa ame e s o he sou ce is he numbe o pho ons pe second
emi ed. The highes b igh ness (coincidences[MHz]/pump powe [mW]) eco ded du ing
he p ojec was 5.66MHz
mW , ha ing a spec al b ig hness (coincidences[MHz]/pump powe