Photorefractive effect in LiNbO$_3$-based integrated-optical circuits for continuous variable experiments

Abstract

We investigate the impact of photorefractive effect on lithium niobate integrated quantum photonic circuits dedicated to continuous variable on-chip experiments. The circuit main building blocks, i.e. cavities, directional couplers, and periodically poled nonlinear waveguides are studied. This work demonstrates that, even when the effect of photorefractivity is weaker than spatial mode hopping, they might compromise the success of on-chip quantum photonics experiments. We describe in detail the characterization methods leading to the identification of this possible issue. We also study to which extent device heating represents a viable solution to counter this effect. We focus on photorefractive effect induced by light at 775 nm, in the context of the generation of non-classical light at 1550 nm telecom wavelength.

Full text

Photorefractive effect in LiNbO3-based integrated-optical circuits for continuous
variable experiments
Fran¸cois Mondain,1Floriane Brunel,1Xin Hua,1´
Elie Gouzien,1Alessandro Zavatta,2, 3 Tommaso
Lunghi,1Florent Doutre,1Marc P. De Micheli,1S´ebastien Tanzilli,1and Virginia D’Auria1, ∗
1Universit´e Cˆote d’Azur, CNRS, Institut de Physique de Nice (INPHYNI),
UMR 7010, Parc Valrose, 06108 Nice Cedex 2, France.
2Istituto Nazionale di Ottica (INO-CNR) Largo Enrico Fermi 6, 50125 Firenze, Italy
3LENS and Department of Physics, Universit`a di Firenze, 50019 Sesto Fiorentino, Firenze, Italy
(Dated: July 23, 2020)
We investigate the impact of photorefractive effect on lithium niobate integrated quantum pho-
tonic circuits dedicated to continuous variable on-chip experiments. The circuit main building
blocks, i.e. cavities, directional couplers, and periodically poled nonlinear waveguides are studied.
This work demonstrates that, even when the effect of photorefractivity is weaker than spatial mode
hopping, they might compromise the success of on-chip quantum photonics experiments. We de-
scribe in detail the characterization methods leading to the identification of this possible issue. We
also study to which extent device heating represents a viable solution to counter this effect. We focus
on photorefractive effect induced by light at 775 nm, in the context of the generation of non-classical
light at 1550 nm telecom wavelength.
Keywords: Quantum communication, Continuous variables, Nonlinear integrated photonics, Lithium niobate
I. INTRODUCTION
With the development of quantum information tech-
nologies, photonic circuits are attracting an increasing
interest as platforms for future out-of-laboratory realiza-
tions. Strong light confinement in waveguides guarantees
efficient quantum state generation and manipulation in
miniaturized structures which enables a progressive in-
crease in architecture complexity thanks to high system
stability and scalability [1, 2].
Lithium niobate (LiNbO3) waveguides are particularly
well adapted to quantum photonics, featuring easy in-
and out-coupling to single-mode fibers, high nonlinear
frequency conversion efficiencies, electro-optical proper-
ties, and low propagation losses [3]. Largely used in single
photon regime, LiNbO3chips are now moving also toward
applications to continuous variable (CV) quantum optics,
where quantum information is coded on light continuous
spectrum observables. CV quantum states produced at
telecom wavelengths (around 1550 nm) for quantum com-
munication and computing [4] can be deterministically
produced in LiNbO3by spontaneous parametric down
conversion (SPDC) of near-infrared light (775 nm) [5] and
unambiguously discriminated by on-chip homodyne de-
tection [6, 7]. In comparison to single photon regime,
CV experiments require higher pump powers at the in-
put of the downconverters. In such a condition, LiNbO3
is likely to be affected by photorefractive effect: impu-
rities and defect centers in the crystal cause a small ab-
sorption of the light traveling along the waveguide. The
photogenerated charges move out of the illuminated area
and get trapped at the edges of the waveguide. The
∗Virginia.DAuria@univ-cotedazur.fr
resulting space-charge field leads to a refractive index
modification that changes the spatial beam profile of the
guided mode [8]. This can cause, in multimode waveg-
uides, a coupling between the spatial modes (mode hop-
ping) [9, 10]. Metal doping (magnesium, zinc, indium,
or hafnium) can be employed to mitigate photorefrac-
tivity but the fabrication techniques are not yet mature
enough for being used in complex circuits [11, 12]. Pho-
torefractive effect is partially or completely suppressed
by operating undoped congruent LiNbO3at high work-
ing temperatures [13], so as to increase charges’ mobility.
However, higher temperature becomes rapidly unprac-
tical and a compromise must be found between pump
power and device temperature.
This paper bridges material science and quantum pho-
tonics aspects. It investigates LiNbO3photonic circuits
in working conditions that, although below the appear-
ance of mode hopping, are submitted to photorefrac-
tive effect. We study the impact of photorefractivity
on the main building blocks of CV experiments in sit-
uations where the induced alteration is weak and by
performing dedicated tests on the components. We fo-
cus on the on-chip generation and detection of squeezed
light, i.e. of optical quantum states exhibiting a noise
level below the classical limit on one of their CV observ-
ables [14]. Squeezed states lie at the very heart of many
CV quantum-information protocols and are crucial for
the heralded generation of non-Gaussian optical states
as required for universal quantum computing [4]. At the
same time, they are very sensitive to losses as well as to
generation or detection imperfections, hence they repre-
sent an extremely pertinent case-study for the analysis
of unwanted effects occurring in integrated photonic sys-
tems. In the following, we illustrate the consequences
of photorefractive effect on crucial elements of squeez-
ing experiments, such as integrated cavities, directional
arXiv:2007.11375v1 [quant-ph] 22 Jul 2020

2
couplers, and PPLN sources, components having already
been successfully implemented on LiNbO3CV complex
photonic circuits [6, 7, 15]. We will highlight, as a func-
tion of the pump power level and chip temperature, the
careful optimization necessary to avoid a degradation of
the squeezing.
II. SAMPLE FABRICATION AND
CHARACTERIZATION SETUP
Ion-diffusion currently represents the most reliable
technique to fabricate photonic integrated circuits on
LiNbO3[16]. Depending on the specific fabrication pro-
cedure, the sensitivity to photorefractive effect varies.
Proton-exchanged (PE) waveguides exhibit the highest
robustness to photorefractivity but suffer from a strong
degradation of electro-optic and nonlinear optic proper-
ties that make them not suitable for integrating complex
circuits. Annealed proton-exchanged (APE) and reverse
proton-exchanged (RPE) waveguides allow to partially
recover the material properties at the price of higher sen-
sitivity to photorefractive effect. Eventually, titanium in-
diffused waveguides benefit from non-degraded LiNbO3
properties but are strongly affected by photorefractivity,
because of lower dark conductivity [9, 17].
In this context, soft proton exchange (SPE) technique is
particularly convenient for quantum photonics, both in
single photon [3] and CV regimes [7]: it prevents degra-
dation of the material properties during the manufac-
turing process leading to nonlinear efficiency better than
those of APE structures. In addition, it allows higher
refractive index jumps providing a more efficient optical
confinement with respect to RPE [3].
In this work, we will explore photorefractive effects in
SPE waveguides. In this regard we note that photore-
fractivity of SPE structures is close to the one observed
in APE and RPE waveguides [18]. More in general, we
stress that, although the specific numerical results are
valid only for SPE waveguides, characterization strate-
gies and considerations developed here can be generalized
to devices fabricated via any ion-diffusion technique.
In our analysis, we use in-house photonic integrated cir-
cuits, fabricated by means of 72 hours SPE at 300°C
in benzoic acid buffered with lithium benzoate. More
details about the fabrication technique can be found
in [3, 19]. Typical transmission losses yield 0.1 dB/cm
(1 dB/cm) at 1550 nm (775 nm). All the studied channel
waveguides are 6 µm-wide, single-mode at telecom wave-
lengths, and slightly multimode at 775 nm, where pho-
torefractivity can therefore cause mode hopping.
The experimental setup developed for the investigation
of photorefractive effect is presented in Fig.1: it employs
a narrowband tunable laser at 1550 nm as a probe and a
tunable laser at 775 nm as a pump inducing the photore-
fractive space-charge field. Probe and pump beams are
multiplexed through the same optical fiber and coupled
to the sample under test (SUT). Both optical sources are
FIG. 1. Schematics of the characterization setup used to in-
vestigate photorefractivity in LiNbO3quantum photonic cir-
cuits. The probe beam is delivered by a EXFO T100S-HP
tunable laser; the pump by a M-Squared SolsTiS laser. PC:
fiber polarization controllers. WDM: fiber wavelength divi-
sion multiplexer. SUT: sample under test, i.e. integrated cav-
ity, directional coupler or periodically poled nonlinear waveg-
uide. Light sensors are Coherent OP-2 Vis and OP-2 IR.
Residual pump power on the probe beam detector is avoided
thanks to the dichroic mirror (DMLP950T-Thorlabs), whose
transmission at 775 nm is less than 0.1%. Isolators after the
probe and the pump lasers are not represented on the scheme.
operated in continuous wave regime (CW) and have their
polarization independently controlled. At the output of
the SUT, light is collected by a lens, its spectral compo-
nents separated using a dichroic mirror, and focused onto
suitable photodetectors. The temperature of the system
is stabilized by an active loop with an error of ±5 mK.
We note that in our working conditions, photothermal
drift only induces changes of ∼10−7/K in the refractive
index [20]; this effect can be neglected compared to the
one induced by photorefractivity, that is approximately
three order of magnitude more important (see below).
III. CAVITY EFFECT
A. Waveguide cavity made of chip’s end-facets
To date, the highest levels of squeezing have been ob-
tained thanks to SPDC in resonant systems such as op-
tical parametric oscillators [21]. Integrated optics opens
the possibility of fabricating monolithic squeezers that
are more compact and stable than their bulk optics ana-
logues, working either in single-pass or resonators. This
concept has been recently validated by the realisation
PPLN waveguides on ZnO-doped substrate that was used
to demonstrate single-mode squeezing at 1550 nm, with
a noise reduction of about -6 dB in single pass configu-
ration [22]. At the same wavelengths, squeezing of -5 dB
has been measured at the output of a Ti-indiffused PPLN
waveguide resonator [15] pumped with 30 mW of CW
powers at 775 nm. The observation of stronger squeezing
values in such a resonant device was prevented by the oc-
curence of photorefractive effect at higher SPDC pump
powers.
Beside instabilities caused by the appearance of mode
hopping of the pump beam, photorefractive effect can
indeed impact cavity based devices even at weaker power

3
conditions. More specifically, the waveguide refrac-
tive index variation, ∆n(t), induced by photorefractiv-
ity can result in a phase shift and, possibly, in a detun-
ing from perfect cavity resonance that can degrade the
squeezing level [23]. This effect can also affect efficient
squeezing production in LiNbO3in single-pass configu-
rations [5, 7, 24, 25] where parasitic cavity effects can
arise from Fresnel’s reflections at the end-facets of the
waveguide; here, we focus on the effects of these para-
site cavities. To his end, we take as SUT a 15 mm long
SPE waveguide with end-facets polished perpendicular
to light propagation direction and uncoated. The prop-
agating modes indices are nef f (@1550 nm)=2.13 and
nef f (@775 nm)=2.18. Corresponding Fresnel’s coeffi-
cients at the waveguide interfaces are Rwg→air ≈0.14
(0.13) per facet at 1550 nm (775 nm), and the device acts
as a parasitic Fabry-Perot interferometer (FPI) with a
low finesse F=1.30 and a FWHM of 20 pm [26]. The
cavity enhancement to squeezing generation due to Fres-
nel’s reflections at the sample facets is incremental. At
the same time, a photorefractive-induced detuning from
cavity resonance can result in an overall degradation of
the device transmission and give rise to instabilities.
B. Phenomenological description
The complexity of the dynamics of the system is well
illustrated in Fig. 2 that shows the transmission trace of
the probe at 1550 nm, when the SUT working tempera-
ture is 30°C. Here, green regions indicate the time-slots
FIG. 2. Transmitted power of a 1550 nm wavelength probe
signal as a function of time, measured in a channel waveguide
with normal polished end-facets. Red regions indicate when
a pump beam at 775 nm is injected in the waveguide. Green
regions indicate when the pump beam is off. Between 25 s and
85 s, pump mode hopping affects the transmission of the probe
beam. The power drop at 20s is due to unwanted mechanical
misalignment.
in which only the probe beam is sent to the SUT while
red areas refer to the case in which the system is fed
also with a pump beam of 5 mW power. In such weak
pumping regime, we already observe photorefractive ef-
fect. The pump irradiation changes the effective refrac-
tive index seen by the probe at 1550 nm and, in turn, its
transmitted power through the FPI [27]. This is clearly
visible between 25 s and 85 s when regular dips appear in
the transmission trace, due to refractive index variation
associated with mode hopping of the pump beam. These
mode fluctuations spontaneously reduce until the system
stabilizes on a given mode as witnessed by the probe
transmission after 85 s. At 140 s the pump laser is turned
off with little impact on the space-charge field. This is
related to the long lifetime of the trapped electrons. At
165 s we illuminate the sample with a high-intensity halo-
gen bulb (1.4 W) to accelerate the redistribution rate of
the trapped electrons so as to restore the initial material
conditions and beam transmission.
C. Model of the waveguide cavity
The large variety of phenomena shown in Fig. 2 sug-
gests why photorefractivity is generally hard to predict
and control. The usual countermeasure consists in in-
creasing the SUT temperature around 100°C. However,
this only shifts the occuring of photorefractive effect to-
wards higher pump powers, without completely suppress-
ing it. We illustrate this behavior in Fig. 3a, where we
show the transmission traces for the probe beam at differ-
ent heating temperatures with a pump injection starting
at t=10 s. At low temperatures, the pump power was
adjusted so as to avoid mode hopping. For all cases,
the final transmission for stabilized waveguide is differ-
ent from the original one. Before reaching this point, a
transient oscillatory behaviour might be observed.
To better understand the interplay between cavity and
photorefractive effect, we recall the transmission of the
Fabry-Perot waveguide resonator [28]:
T(t) = 1
1 + Fsin22πL·(nef f +∆n(t))
λ,(1)
with F=4R
(1−R)2is the finesse of the cavity, λthe probe
wavelength, L=15 mm the length of the chip, neff the
effective index of the mode without photorefraction,
and ∆n(t) the pump-induced photorefractive index
modification. Since photorefractive effect barely changes
Fresnel’s coefficients, we can consider Fconstant.
From the sin2term, we see that for weak variation of
∆nover time, the transmitted power can show an oscil-
latory behaviour, half a period corresponding to an index
variation ∆n∼2.6×10−5. This kind of variation can
be observed in the T= 30°C curve of Fig. 3a between 10
and 15 s, giving an overall index change ∆n∼8×10−5;
for higher temperatures, ∆nis weaker and oscillations
disappear. We note that transmission is affected by pho-
torefractivity even at 130°C. At such high temperature,
a small, time-independent, refractive index shift can be
observed [29]. This constant shift slightly modifies the
cavity optical resonance condition and, as a consequence,
the transmitted power at the probe wavelength. Beside
the use of anti-reflection coatings, the most pertinent way
to suppress parasitic FPI is to polish the chip end-facets

4
FIG. 3. Transmitted power at 1550 nm versus time measured in a channel waveguide in a resonant (a), and non-resonant (b)
configuration. Grey-dashed line indicates the onset of the pump beam. Insets show a simple schematics of the chip.
with an angle in order to prevent guiding of light reflected
at the interface. We confirm this concept by employing
as a SUT a chip with output facets polished with a 7°an-
gle [30]. The corresponding transmissions are shown in
Fig. 3b: all measurements are taken at a maximum pump
power of 20 mW. The signature of photorefraction is re-
moved or negligible for all working temperatures. Resid-
ual effects are due to the photorefractive inducted ∆n,
that changes the fiber-to-waveguide coupling at the input
of the non-resonant device, thus affecting the measured
transmitted power.
Eventually, we note that, in CV quantum optics, beside
modifying the sample transmission, the detuning from
perfect cavity resonance (∆) induced by ∆n(t) can af-
fect the dynamics of squeezing generation [23]. For ex-
ample, Fig. 4 a shows the quantum noise spectrum of
single-mode squeezed light at the output of a resonant
PPLN waveguide [15]. The detuning is normalized to
the cavity linewidth. The squeezing spectrum (dashed
lines) exhibits a minimum at a frequency that depends
on the detuning and shows a noise reduction less impor-
tant than the one expected in the perfectly resonant case
(∆ = 0). This effect is more obvious when ∆increases.
This is represented in Fig. 4b where the best squeezing
(antisqueezing) is represented as functions of the detun-
ing. As for a numerical example, for a cavity of 15 mm,
with mirror reflectivity of 0.77 and 0.99 as in [15], a varia-
tion of ∆n= 2.6×10−5would correspond to a normalized
detuning of ∆ =1.5 and lead to a degradation of squeez-
ing, from an initial value of -5dB, to only -2 dB. Similar
calculations show that the same detuning would reduce
an initial squeezing of -10 dB to only ≈-5 dB.
FIG. 4. (a) Squeezing (dashed) and anti-squeezing (solid line)
spectra emitted by SPDC in a resonant nonlinear waveguide
cavity and (b) corresponding optimal squeezing and anti-
squeezing as functions of the detuning. In the simulations,
∆ represents the detuning normalized to the cavity linewidth.
We assume no active feedback system ensuring the cavity res-
onance condition.

5
IV. DIRECTIONAL COUPLERS AND
HOMODYNE DETECTION
Directional couplers are basic building blocks for any
photonic integrated circuit as they permit to design light
routing, (de)multiplexing and interference stages. We
consider here devices exploiting evanescent-wave cou-
pling to obtain a periodic transfer of light intensity from a
waveguide to another: when two single-mode waveguides
are close enough, their evanescent fields spatially overlap
and give rise to a coupling between the two structures,
as sketched in Fig.5.
FIG. 5. Schematics of evanescent-wave coupling balanced
beam splitter, here with a total length of 3/2 Lc. The two
output ports are Rreflected (i.e. the same in which injection
is made), and Ttransmitted. LCstands for coupling length,
i.e. the propagation length after which all the optical power
is in the transmitted arm.
The fraction of optical power transferred to the adja-
cent waveguide is generally said to be transmitted, while
the rest is reflected; by extension we will call the two
waveguides reflecting (R) and transmitting (T), with
propagation constants βR=2πnR
λand βT=2πnT
λ, re-
spectively. If ∆β= 0, light will periodically undergo
a perfect transfer from a waveguide to the other during
its propagation. All optical power is found in the trans-
mitting arm after a distance referred to as the coupling
length, Lc=π
2kwhere kis the coupling constant that
depends on the effective refractive indices of the modes
and on the distance separating the waveguides.
In the context of CV integrated circuits, directional
couplers are needed for multiple applications. On the
one hand, strongly unbalanced couplers are used to pick
up a fraction of a non-classical state and send it to a
single photon detector for the heralded preparation of
non-Gaussian states [31]. On the other hand, perfectly
balanced couplers are mandatory for homodyne detec-
tion, in which the properties of a state under scrutiny
are retrieved by making it interfere with a local oscil-
lator [7]. Refractive index change induced by photore-
fractivity can affect the symmetry of directional couplers
(∆β= 0) and shift their working point. This effect is
detrimental in most of practical situations.
We investigate the influence of photorefractivity
thanks to a passive directional coupler (sketched in the
inset of Fig. 6a) consisting in a 15 mm long chip with its
output facet angle-polished to prevent parasitic FPI. It
comprises two waveguides of 6 µm width with 14 µm sep-
aration, corresponding to a coupling k=0.46 mm−1,i.e.
Lc= 3.43 mm at T= 30°C for λprobe = 1550 nm. The
coupler length is 4.3 mm long. At the pump wavelength,
the coupling between the waveguides is negligible. This
geometry, although made of only one output (the reflec-
tion waveguide), is perfectly suitable to study the device
sensitivity to photorefractivity.
As shown in Fig. 6a, both pump and probe beams
are injected in the coupler and the probe beam exit-
ing the chip is analyzed. When the pump beam is in
the reflection waveguide, it modifies its refractive index
nR→nR+ ∆n, changing the propagation constant to
∆β=2π∆n
λ. Correspondingly, the fraction of reflected
probe power is:
Rprobe =PR
P0
= 1 −4k2
4k2+ ∆β2·sin2 L·p4k2+ ∆β2
2!,(2)
with P0(PR) the input (reflected) probe power. Mea-
sured coupler reflectivity at 1550 nm is plotted in
Fig. 6a as a function of the pump power Ppat 775 nm.
Experimental data have been fitted using Eq. (2) in
order to infer ∆n. We assume a dependence of ∆nupon
the pump power of the form ∆n=−aPp
b+cPpwhere a,b
and care constants determined by the material [32, 33].
Obtained ∆nvalues are shown in Fig. 6b. We note that,
for studied pump powers, the dependence of ∆nwith
Ppis linear and does not saturate. The experimental
values are consistent with Fig. 3b and compatible with
results published in the literature [32]. As for an
example, a pump power of 10 mW induces a ∆n∼10−4,
close to the value of 8 ·10−5as found from the FPI
analysis. The difference between the two measured ∆n
values can be explained by a combination of sample
geometrical variations, due to the fabrication process,
and measurement uncertainties (of the order of ≤10%).
Note that, as expected, higher temperatures reduce the
photorefractivity; above 90°C, photorefractivity impact
on the coupler is negligible.
We can apply these findings to the discussion on per-
formances of an integrated homodyne detector as the one
implemented in [7]. As sketched in Fig.7a, in CV quan-
tum optics, information on an optical beam is obtained
by mixing it on a 50/50 coupler with a reference beam
called local oscillator (LO) and then by detecting the in-
tensities of the two outputs beams. Single-mode squeez-
ing level can be obtained from the noise variance of the

6
FIG. 6. (a) Coupler reflectivity, R, at 1550 nm as a function of the pump power coupled in the waveguide at 30°C (red dots),
60°C (blue squares), 90°C (black diamonds); solid lines represent the fits. (b) Refractive index variation of the integrated
coupler, ∆n, at 1550 nm as a function of the pump power. Inset: coupler chip schematics, the two waveguides are separated
by 14 µm (center-to-center), the coupling length Lcat 1550 nm is 3.43 mm at 30°C, 3.27 mm at 60°C and 2.96 mm at 90°C.
photocurrent difference, ∆i2
diff (R). For a generic coupler of reflectivity R and transmissivity T = 1 −R, the mea-
sured quantum noise is:
∆i2
diff (R) = |α|2(T −R)2+ 4R ·T·(e2ssin2φ+e−2scos2φ)+O(|α|3),(3)
where sis the squeezing parameter, |α|is the LO field
amplitude, and φis the relative phase between LO and
the squeezed beam. In the previous expression, we con-
sider a perfect coherent local oscillator without classical
noise. The noise of the squeezed observable (typically
the electromagnetic field phase quadrature [4]) is e−2s,
while the anti-squeezing on its conjugate observable (the
amplitude quadrature) is e2s. In the following we assume
φ= 0 for simplicity and focus only on squeezing detec-
tion. For a balanced coupler, i.e. T=R=1/2, the
terms from unbalanced LO disappear and residual clas-
sical noise contributions are fully suppressed. In this op-
timal condition, ∆i2
diff (1/2) = |α|2e−2s. In experiments,
to quantify the noise reduction with respect to a refer-
ence noise, squeezed light before the coupler is blocked
so as to measure the vacuum noise (shot noise level) |α|2
used to normalize ∆i2
diff . In integrated realizations, resid-
ual pump beam from the squeezing stage can circulate
in the homodyne coupler and induce photorefractivity:
this can change the splitting ratio either in the measure-
ment or in the calibration step. From the ∆nvalues of
Fig. 6b, we can evaluate the impact of photorefractivity
on squeezing homodyne measurement. Fig. 7b shows the
measured squeezing level as a function of the residual
pump power circulating in the homodyne optical cou-
pler. The estimation is made for a coupler with 14 µm-
waveguide separation, working at 30°C and designed to
have a perfectly balanced splitting in absence of optical
pumping at 775 nm. Fig. 7b shows that the splitting ratio
alteration induced by photorefractivity can significantly
reduce the measured squeezing level; this underestima-
tion can easily remain unnoticed without a preliminary
proper characterization of the photorefractivity.
Empirically, we find that a temperature of 90°C is suffi-
cient to suppress photorefractivity when the pump power
is below 15 mW. However, the total effect is strongly re-
lated to the exact configuration (coupling constant, cou-
pling length, substrate, pump power). To conclude this
section we note that integrated wavelength division mul-
tiplexer (WDM) have already been integrated on LiNbO3
photonic chips [6]. Provided they are added before the
homodyne detection stage, this kind of devices could be
a solution to suppress residual pump power and, in turns,
photorefractivity in the integrated coupler. However,
such a realization would come at the cost of an increased
complexity and additional losses in the circuit.

7
FIG. 7. (a) Schematics of a generic integrated homodyne detection setup; LO: Local oscillator; Sq beam: squeezed beam; idiff :
photo-current difference between the detectors. (b) Calculated maximal measurable squeezing ∆i2
diff when the splitting ratio
of the homodyne coupler is altered by pump-induced photorefractivity for 3 different initial squeezing levels. We assume the
coupler working at 30°C. We consider a perfect coherent local oscillator without classical noise.
V. SPONTANEOUS PARAMETRIC DOWN
CONVERSION
We investigate the impact of photorefractivity on the
nonlinear properties of a periodically poled lithium nio-
bate waveguide (PPLN/w). In particular, due to its role
in squeezing generation, we discuss the evolution of spon-
taneous parametric down conversion (SPDC) at different
pump regimes and temperatures. The SPDC spectrum is
determined by energy conservation and phase matching
conditions that rule the conversion of pump photons (p)
at 775 nm, into pairs of signal (s) and idler (i) photons at
telecom wavelength (≈1550 nm). These can be written,
in a PPLN medium, as:
1
λp
=1
λi
+1
λs
,np
λp
−ni
λs
−ns
λs
=1
2Λ,(4)
where λjis the wavelength of the beam (j=p, s, i), nj
the corresponding refractive index, and Λ the poling pe-
riod [3]. We note that the generation of single mode
squeezing is achieved when signal and idler are fully de-
generate [5], in the general case two mode squeezing is
obtained [34]. As the quasi-phase matching condition de-
pends on the material refractive indices, photorefractive
effect can considerably modify the SPDC working point.
The experimental setup used to investigate the impact
of photorefractivity on SPDC is depicted in Fig. 8. A
tunable pump laser delivering a wavelength of 770.73 nm
(774.63 nm) is injected through a fiber into a in-house
15 mm long PPLN SPE waveguide working at 30°C
(90°C), designed to have its SPDC degeneracy around
1550 nm. The waveguide is polished so that incident
beams are orthogonal to end-facets (0°-cut). To com-
ply with cavity effects, before acquiring the spectrum,
we wait for the resonant system stabilization (see Fig.3).
At the output of the sample, the generated photon
pairs are coupled to an optical fiber, spectrally scanned
by using a tunable filter, and measured by a single-
photon detector. This characterisation method is typical
FIG. 8. SPDC experiment schematics; Pump: tunable laser
(Coherent Mira); PC: polarization controller; PPLN/w: in-
house 15 mm long PPLN soft-proton-exchanged waveguide;
∆λ: tunable spectral bandpass filter (Yenista XTM-50);
SPAD: InGaAs/InP single-photon avalanche diode (ID Quan-
tique Id220), with efficiency set to 10% and dead time to 15 µs;
s: signal, i: idler.
for the analysis of SPDC in quantum optics [35]. The
dark count rate is on the order of ∼1 kcounts/s. Note
that, for all of the investigated powers, the sample
works in a non-stimulated regime. As the photon pair
emission rate is proportional to the pump power [36],
an in-line fiber attenuator (not represented in Fig. 8) is
used downstream the sample, in order to keep the count
rate below 20 kHz to avoid detector saturation.
The normalized resulting SPDC spectra for different
pump powers (Pp) and temperatures are shown in
Fig. 9a (30°C) and Fig. 9b (90°C). The pump wavelength
is adjusted for each temperature in order to be out of
degeneracy when Pp=0.25 mW. At low temperature, as
expected, the photorefractive effect due to the pump
power, changes the phase-matching condition. When Pp
increases, the emission reaches the degeneracy such that
idler and signal emission spectra to overlap. Similar
results have been found in [9] for second-harmonic
generation where a blue shift of the phase-matching
wavelength has been observed. We note that, as found
for the directional coupler, phase matching is insensitive
to the pump beam influence when the device is set to a
temperature of 90°C.
In this context, photorefractivity affects directly the

8
FIG. 9. SPDC normalized spectra for different pump powers coupled in the PPLN waveguide at (a) 30°C and (b) 90°C.
squeezing generation. Indeed, the squeezing parameter,
sis equal to µpPp[5], where µis the nonlinear efficiency,
often considered as constant in PPLN waveguides. How-
ever, we have seen that photorefractivity modifies the
phase matching conditions, and µthen depends on Pp
via the refractive indices in Eq. (4).
Let us compare an ideal PPNL waveguide, i.e. not af-
fected by photorefractivity (constant nonlinearity), to a
realistic one (submitted to photorefractivity). In the
first case, we take µ= 0.101 mW−1/2as reported in
the literature [5]. In the second case, we take into ac-
count the degradation of the quasi-phase matching due
to photorefractivity from the SPDC spectra depicted in
Fig. 9a. Both reachable squeezing levels are shown in
Fig. 10. The shifted-QPM, photorefractive PPLN (red
dotted line) is strongly degraded compared to the ideal,
photorefraction-free PPLN (black dashed line). There-
fore, to optimize the squeezing level, proper and care-
ful characterisations must thus be realized on the device
working conditions in order to comply with photorefrac-
tivity and to compensate for the unwanted spectral shift,
by fine adjustement of the temperature and pump wave-
length.
VI. CONCLUSIONS
Integrated photonics enable a continuous increase of
optical function complexity. This is extremely advanta-
geous for quantum information technology and in par-
ticular in CV quantum photonics where losses and sta-
bility need to be carefully controlled. In this paper
we have focused on LiNbO3-based integrated photonic
circuits which represent one among the most reliable
platforms for CV-quantum regime and squeezing exper-
iments. However, LiNbO3notoriously suffers from pho-
torefractivity and this is particularly crucial for squeezing
as it requires strong pump beams at short wavelengths.
Here, we have derived a framework to analyze the im-
pact of photorefractive effect on integrated cavities, di-
FIG. 10. Squeezing for an ideal PPLN (dashed line) and for
a PPLN that suffers from photorefraction (red circles), calcu-
lated using the SPDC efficiency spectra reported in Fig. 9 a.
rectional couplers, and nonlinear waveguides which are
building blocks for any CV integrated photonic circuits.
We have demonstrated that photorefractivity might com-
promise the success of an experiment even in conditions
far from mode hopping. A temperature increase is a vi-
able solution to reduce photorefractivity. For the specific
case-studies investigated in this work, an operating tem-
perature of at least 90°C is sufficient to suppress the im-
pact of photorefractivity on waveguide coupling or SPDC
process. Nevertheless, this strategy, even above 120°C,
doesn’t apply for resonators and cavities which are ex-
tremely sensitive to refractive-index variations. There-
fore, particular attention should be taken to avoid para-
sitic cavities. If cavity is needed, the use of metal doped-
LiNbO3becomes mandatory above a certain pump power
that depends on the specific waveguide technology. We
believe this work might be a useful guideline to effi-
ciently characterize LiNbO3integrated photonic chips for
squeezing experiments.

9
FUNDING
This work was conducted within the framework of
the project OPTIMAL granted through the European
Regional Development Fund (Fond Europeen de de-
veloppement regional, FEDER). The authors acknowl-
edge financial support from the Agence Nationale de
la Recherche (HyLight ANR-17-CE30-0006-01, SPOCQ
ANR-14-CE32-0019-03, Q@UCA ANR-15-IDEX-01).
DISCLOSURES
The authors declare no conflicts of interest.
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