# Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion.

**ABSTRACT** Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.

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**ABSTRACT:**It is shown that spatial correlation functions measured for correlated photon pairs at the single-photon level correspond to speckle patterns visible at high intensities. This correspondence is observed for the first time in one experimental setup by using different acquisition modes of an intensified CCD camera in low and high intensity regimes. The behavior of intensity auto- and cross-correlation functions in dependence on pump-beam parameters including power and transverse profile is investigated.Optics express. 04/2014; 22(11). - SourceAvailable from: Alice Meda[Show abstract] [Hide abstract]

**ABSTRACT:**Sub shot noise imaging of weak object by exploiting Parametric Down Converted light represents a very interesting technological development. A precise characterization of PDC speckle structure in dependence of pump beam parameters is a fundamental tool for this application. In this paper we present a first set of data addressed to this purpose.International Journal of Quantum Information 11/2011; 07(supp01). · 0.99 Impact Factor - SourceAvailable from: Ivan Agafonov[Show abstract] [Hide abstract]

**ABSTRACT:**We realize and test in experiment a method recently proposed for measuring absolute quantum efficiency of analog photodetectors. Similar to the traditional (Klyshko) method of absolute calibration, the new one is based on the direct detection of two-mode squeezed vacuum at the output of a traveling wave OPA. However, in the new method, one measures the difference-photocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for high-gain OPA. In this work we test the new method versus the traditional one for the case of photon-counting detectors where both techniques are valid.International Journal of Quantum Information 11/2011; 09(supp01). · 0.99 Impact Factor

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arXiv:quant-ph/0407211v1 27 Jul 2004

Detection of sub-shot-noise spatial correlation in high-gain parametric

down-conversion

O. Jedrkiewicz1, Y.-K Jiang2, E. Brambilla1, A. Gatti1, M. Bache1, L. A. Lugiato1, and P. Di Trapani1

1INFM, Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Via Valleggio 11, 22100 Como, Italy

2Department of Electronic Science and Applied Physics, Fuzhou University, 350002 Fuzhou, China

(Dated: February 1, 2008)

Using a 1GW-1ps pump laser pulse in high gain parametric down-conversion allows us to detect

sub-shot-noise spatial quantum correlation with up to one hundred photoelectrons per mode, by

means of a high efficiency CCD. The statistics is performed in single-shot over independent spatial

replica of the system. The paper highlights the evidence of quantum correlation between symmetrical

signal and idler spatial areas in the far field, in the high gain regime. In accordance with the

predictions of numerical calculations the observed transition from the quantum to the classical

regime is interpreted as a consequence of the narrowing of the down-converted beams in the very

high gain regime.

PACS numbers:

Spatial quantum optical fluctuations are studied be-

cause of new potential applications of quantum optical

procedures in parallel processing and multi-channel op-

eration. Examples are quantum holography [1], the quan-

tum teleportation of optical images [2], and the measure-

ments of small displacements beyond the Rayleigh limit

[3]. There is now a large literature on spatial effects in

the spontaneous regime of parametric down-conversion

(PDC) where photons are created one pair at a time [4].

The process of PDC is in fact particularly suitable for the

study of spatial correlations because of its large emission

bandwidth in the spatial frequency domain [5]. Never-

theless to date most spatial correlation measurements in

PDC have been performed in single photon counts regime

[6, 7] without evidencing any relevant quantum effects.

The quantum twin beam character of the PDC emission

has been evidenced in [8] by using low-to-medium pump-

power lasers (≤ 1 MW) and relying on statistical ensem-

bles from different temporal replicas of the system. With

increasing gain a transition from the quantum to the clas-

sical regime has been observed [9]. However, recent the-

oretical investigations predict multi-mode spatial quan-

tum correlations (sub-shot-noise photon-number correla-

tion between symmetrical portions of the signal and idler

angular distributions) also for arbitrarily high gains, pro-

vided that the detection area exceeds the typical size of

the mode (coherence area) [10, 11].

Here we report on the first quantum spatial mea-

surements of PDC radiation performed by using a low-

repetition rate (2 Hz) pulsed high-power laser (1GW-

1ps). This enables us to tune the PDC to the high-gain

regime while keeping a large pump beam size (∼ 1mm).

The huge number of transverse modes (roughly given by

the ratio between: (i) the area of the near-field gain pro-

file and (ii) the inverse of the angular bandwidth of the

PDC process) allows us to identify regions of the sig-

nal and idler beams where symmetrical signal-idler pixel

pairs correspond to independent spatial replica of the

quantum system. We concentrate on a portion of the

parametric fluorescence emitted close to the collinear di-

rection and within a narrow frequency bandwidth around

degeneracy. The generated pairs of signal and idler

phase-conjugate modes propagate at symmetrical angles

with respect to the pump direction in order to fulfil the

phase-matching constraints, and each pair of symmetri-

cal spots characterizing the far field represents a spatial

replica. Thanks to the very large number of these, the

statistical ensemble averaging necessary for the quantum

measurement can be solely done over the spatial replicas

for each, single, pump-laser pulse. A characterization of

the system over several shots was only made in our case

in order to verify that the selected spatial replicas are

indeed statistically identical, as required for the suitable

definition of the ensemble. The single-shot measurements

reveal sub-shot-noise spatial correlations for a PDC gain

G (intensity amplification factor) leading to the detec-

tion of up to ≃ 100 photoelectrons per mode. Finally, by

numerically solving the three-waves coupled equations in

the framework of a 3D+1 quantum model, we are able to

attribute the observed transition from quantum to classi-

cal regime to the near-field gain narrowing that occurs in

presence of a bell-shaped pump beam, at very-high gain.

The experimental setup is sketched in Fig. 1.

third harmonic (352 nm) of a 1ps, chirped-pulse ampli-

fied Nd:glass laser (TWINKLE, Light Conversion Ltd.)

is used to pump a type II 5x7x4mm3β-barium borate

(BBO) non-linear crystal, operated in the regime of para-

metric amplification of the vacuum-state fluctuations.

The input and output facets of the crystal are anti-

reflection coated at 352 nm and 704 nm, respectively.

The pump beam is spatially filtered and collimated to a

beam waist of approximately 1 mm (FWHM) at the crys-

tal input facet. The energy of the 352nm pump pulse can

be continuously tuned in the range 0.1-0.4 mJ by means

of suitable attenuating filters and by changing the en-

ergy of the 1055nm pump laser pulse, allowing to have

The

Page 2

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a gain in the range 10 ≤ G ≤ 103.

fluorescence at the horizontally polarized signal and ver-

tically polarized idler modes is emitted over two cones,

whose apertures depend on the specific wavelengths (see,

e.g., [13, 14]). The BBO crystal (θ = 49.05◦, φ = 0) is

oriented in order to generate signal and idler radiation

cones tangent in the collinear direction at the degener-

ate wavelength ωs= ωi= ωp/2 (s, i and p referring to

signal, idler and pump respectively). The fluorescence

around the collinear direction is selected by means of a

5mm x 8mm aperture, placed 15 cm from the output

facet of the BBO. The aperture turned out to be nec-

essary in order to prevent beam clipping by the PBS,

otherwise giving rise to substantial scattered radiation.

The selected portion of the beam is transmitted through

a polarizing beam splitter (PBS), which separates the

signal and idler beams. The latter are finally sent onto

two separate regions of a deep-depletion back illuminated

charged coupled device (CCD) camera [15] (Roper Scien-

tific NTE/CCD-400EHRBG1, 16 bits dynamical range,

quantum efficiency η≈ 89% at 704 nm at -40◦C, dark cur-

rent and read out noise < 1e/pixel/s and < 3e/pixel/s

respectively), placed in the common focal plane of the

two lenses (f =10 cm) used to image the signal and idler

far fields. The detection array has 1340x400 pixels, with

a pixel size of 20µmx20µm. Prior to the experiment the

CCD was calibrated with a coherent source allowing the

retrieval of spatial shot-noise statistics in its full dynamic

range [16]. In our setup the correlation measurements are

performed without using any narrow-band interferential

filters (IFs), in contrast to the case of photon-counting

experiments (coincidence measurements), since IFs un-

avoidably introduce relevant transmission losses reducing

the visibility of sub-shot noise correlations. The pump-

frequency contribution is removed by using normal in-

cidence (M5) and at 45 deg (M4) high-reflectivity (HR)

mirrors coated for 352 nm placed before and after the

PBS, respectively, and a low-band pass color filter (90%

transmission around 704 nm) placed in front of the CCD.

A further HR@352nm mirror (M′

the two arms at a suitable angle in order to balance the

unequal transmission of the PBS in the two arms. All

the optical components (except the color filter) have an-

tireflection coatings at 704 nm.

tum efficiency of each detection line, which accounts for

both the transmission losses and the detector efficiency,

is ηtot≃75%.

Fig. 2a shows a typical far field image recorded in a

single shot, where a fairly broadband radiation (i.e. the

one transmitted by the rectangular aperture) is acquired

in the signal (left) and idler (right) branches. The se-

lection of the desired temporal and angular bandwidth

around degeneracy is made by temporarily inserting in

front of the CCD a 10nm wide IF around 704 nm, allow-

ing us to locate the collinear degeneracy point (see Fig.

2b). The data analysis is limited within two rectangu-

The parametric

4) is placed in one of

The estimated quan-

Teflon pinhole

(200 µm diameter)

(352nm, 1ps)

Filter

PBS

Rectangular

aperture

Pump pulses

CCD

f=10cm

f=10cm

Type II BBO

M5

M4

M4

M’4

M1

M2

M3

FIG. 1: Scheme of the experimental set-up used for the spatial

correlation measurements (see text).

lar boxes (black frames in Fig.2a) corresponding to an

angular bandwidth of 20 mrad x 8 mrad and to a tempo-

ral bandwidth smaller than 10 nm. The selected regions

contain 4000 pixels each. In this work we investigate

pixel pair correlation, and since the size of the CCD pixel

approximately corresponds to the physical size of the

replica, the ensemble is large enough to perform the de-

sired statistics. We have observed that much larger boxes

worsen the level of the correlation; this is attributed to

residual scattering owing to diffraction from the borders

of the aperture but also to the contribution of other fre-

quency components (far from degeneracy) characterized

by a lower angular symmetry between signal and idler

cones. A zoom of the selected areas is presented in Fig.2c,

where the rather spectacular symmetry of the intensity

distribution in the signal and idler branches shows the

twin-beam character of the phase-conjugate modes.

The aim of the experiment is to quantify the sym-

metrical pixel pair correlation.

suring the variance σ2

s−iof the PDC photoelectron-

number difference ns− ni of the signal/idler pixel pair

versus the mean total number of down-converted pho-

toelectrons (pe) of the pixel pair.

σ2

spatial averages performed over all the symmetrical pixel

pairs contained in the chosen regions. Each single shot

of the laser provides a different ensemble, characterized

by its pixel pair average pe number ?ns+ ni?, in turn

related to the parametric gain. In the experiment, en-

sembles corresponding to different gains are obtained by

varying the pump-pulse energy. We note that the read-

out noise of the detector, its dark current, and some un-

avoidable light scattered from the pump, signal and idler

fields contribute with a non-negligible background noise

to the process. This is taken into account by applying a

This is done by mea-

This variance is

s−i= ?(ns− ni)2? − ?ns− ni?2where the averages are

Page 3

3

(a)

(b)

(c)

FIG. 2: (a) Single-shot far field image recorded by the CCD

for a pump beam waist w0 ≃ 1mm and pump energy εp ≃

0.3mJ. The spatial areas for statistics are delimited by the

white boxes selected within the degenerate signal and idler

modes, spatially localized from the single shot image recorded

with the 10nm-broad IF (b). (c) Zoom of two symmetrical

areas of the signal and idler far fields.

standard correction procedure (see for example [18]), by

subtracting the background fluctuations σ2

fectively measured variance σ2

sity difference (signal+background)-(idler+background)

obtaining σ2

noise, having a standard deviation of 7 counts (±0.1 from

shot to shot, estimated by repeating the measurement

with the same pump-pulse energy) is measured in pres-

ence of pulse illumination over an area of the same size

of the acquisition area and suitably displaced from the

directly illuminated region. The validity of the data cor-

rection procedure is tested by sending in the setup (with

no crystal) through the PBS a coherent circularly polar-

ized pulsed beam (@704nm), and verifying for different

laser energies that the intensity difference fluctuations

from the two coherent portions of beams recorded on the

CCD lie at the shot noise level.

Fig. 3 shows the experimental results where each point

is associated with a different laser shot. The data are

normalized to the shot noise level (SNL), and their statis-

tical spread accounts for the background correction. Al-

bfrom the ef-

(s+b)−(i+b)of the total inten-

s−i= σ2

(s+b)−(i+b)− 2σ2

b. This background

0.4

-0.2

-10

x shift (pixels)

20

SNL

10 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

σ

2

s-i/<ns+ni>

<ns+ni> (pe)

FWHM

~2 pixels

-200 10

-0.6

-0.4

0.0

0.2

0.6

0.8

1.0

1.2

Correlation γ

γ@0.99

FIG. 3: Intensity difference variance σ2

SNL ?ns+ ni?. Each point (white circle) corresponds to a

single shot measurement where the spatial ensemble statis-

tics has been performed over a 100 x 40 pixels region. The

triangles (each one obtained by averaging the experimental

points corresponding to a certain gain) and their linear fit il-

lustrate the trend of the data in the region between ?ns+ ni?

=8 and 20. Inset: Typical correlation degree profile in the

regime where ?ns+ ni? ≃ 8 (see text).

s−inormalized to the

though the noise on the individual signal and idler beams

is found to be very high and much greater than the stan-

dard quantum limit (=?ns? and ?ni? respectively), we

observe an evident sub-shot noise pixel pair correlation

up to gains characterized by ?ns+ ni?≈ 15 − 18. Since

in that regime the observed transverse size of the co-

herence areas (i.e. of the modes) is about 2-4 pixels,

this approximately corresponds to 100 pe per mode. We

can have an idea of the transverse size of the mode by

looking at the standard two-dimensional cross-correlation

degree γ = (?nsni? − ?ns??ni?)/?σ2

angularly symmetrical signal and idler pixels contained

within the black boxes (see Fig. 2a). This can be plotted

for instance as a function of the horizontal and vertical

shifts of the recorded image on the CCD, keeping fixed

the position of the boxes. In general | γ |≤ 1 with γ = 1

for perfect correlation. A transverse section of the corre-

lation function obtained from a single-shot image char-

acterized by ?ns+ ni?≈ 8 is plotted in the inset of Fig.

3 as a function of the horizontal shift x (in pixels units).

As expected, virtually perfect correlation (in our case the

peak value is ≃ 0.99) is obtained for perfect determina-

tion (i.e. within one pixel) of the center of symmetry

between the signal and the idler regions.

In order to interpret the observed transition from quan-

tum to classical regime we present in Fig. 4 the results of

the numerical calculations. The full quantum model ac-

counts for the two transverse and the temporal degrees

of freedom with propagation along the crystal, for the

sσ2

i, between all the

Page 4

4

0246810

0.0

0.5

1.0

1.5

2.0

<ns+ni> ~ 10 pe

<ns+ni> ~ 40 pe

<ns+ni> ~ 210 pe

<ns+ni> ~ 1140 pe

<ns+ni> ~ 1830 pe

σ2

s-i/<ns+ni>

N (pixels)

Pixel/pixel correlation

FIG. 4: Numerical calculation of σ2

between symmetrical portions of signal and idler plotted as a

function of the detection area represented by N x N binned

pixels. Different curves correspond to different values of the

gain characterized by the mean number of down-converted pe

per pixel pair ?ns+ ni?.

s−i(normalized to SNL)

angular and chromatic material dispersion up to the sec-

ond order, and for the finite spatial and temporal widths

of the Gaussian pump pulse.

pulse parameters are those relative to the experiment.

The figure presents σ2

s−i, normalized to the SNL, vs the

size of the detection area for different gains. Each point

is the result of a statistics performed over one single

laser-shot. The case N=1 corresponds to the experiment.

The simulations (data not shown) outline that, in spite

of the fixed pump-beam diameter, the signal and idler

beam diameters at the crystal output strongly depend

on the gain and decrease when the latter increases. This

can be easily interpreted when considering that the sig-

nal and idler beam size maps not the pump-beam pro-

file but the actual parametric amplification gain profile

G(r) ∼ cosh2[σA(r)L] [19] (L being the crystal length, A

the pump field amplitude and σ a parameter proportional

to the setting characteristics), as long as filtering due to

the limited spatial bandwidth does not take place [20].

On narrowing the size of the PDC beams, the coherence

areas in the far field (i.e. the modes) increase their size,

as straightforward consequence of the convolution theo-

rem in Fourier analysis [13]. Since revealingquantum cor-

relations requires detection areas larger (or comparable)

to the mode size (as also discussed in [10]), it is necessary

when increasing the gain to have larger detectors in or-

der to obtain below-shot-noise variance as shown in Fig.

4. Note that Fig. 4 evidences the transition from quan-

tum to classical regime in case of single-pixel detection

(N=1) for a gain that is higher than in the experiment.

Instead, in the experiment, excess noise is observed for

?ns+ ni? >20, which we attribute first to the effect of

residual scattered light whose contribution grows linearly

The crystal and input-

with the radiation fluence and is thus expected to over-

come the shot noise at large pumping, and second to the

uncertainty in the determination of the symmetry center

of the signal and idler image portions. In fact simulations

have shown that an uncertainty as small as a few microns

(i.e. a fraction of the pixel size, unavoidable experimen-

tally), prevents to observe sub-shot-noise correlation as

soon as ?ns+ ni? exceeds some tens of pe, while still pre-

serving sub-shot-noise correlation for smaller gain values.

Finally, the maximum level of noise reduction observed

experimentally agrees with the theoretical limit (dotted

line in Fig. 3) determined by the total losses of the system

(∼ 1 − ηtot[10]), in accordance with the result of Fig. 4.

In conclusion, we have shown that twin beams of light

generated in parametric down-conversion exhibit sub-

shot noise spatial correlation by measuring an evident

quantum noise reduction on the signal/idler intensity dif-

ference. A transition to above shot-noise correlation is

observed as the gain increases. This quantum-to-classical

transition, in agreement with numerical simulations, is

explained as a narrowing of the signal/idler beams with

increased gain. This leads in turn to a larger mode size

and therefore also to the need of larger pixels to observe

below shot-noise correlation [10]. This will be the aim of

a future work. To our knowledge, this is the first exper-

imental investigation of quantum spatial correlations in

the high gain regime, where the huge number of trans-

verse spatial modes is detected in single shot by means

of a high-quantum-efficiency CCD.

This work has been supported by the European Union

(QUANTIM contract IST-2000-26019). M. B. acknowl-

edges support from the Carlsberg foundation.

[1] A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and

M. C. Teich, Opt. Express 9, 498 (2001).

[2] I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato,

Opt. Commun. 193, 175 (2001).

[3] N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre,

H.-A Bachor, and C. Fabre, Phys. Rev. Lett. 88, 203601

(2002).

[4] L. A. Lugiato, A. Gatti, and E. Brambilla, J. Opt. B:

Quantum Semiclassical Opt. 4, S176 (2002), and refer-

ences therein.

[5] F. Devaux and E. Lantz, Eur. Phys. J. D 8, 117 (2000).

[6] B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A.

Saleh, and M. C. Teich, Opt. Express 81, 3 (1998).

[7] S. S. R. Oemrawsingh, W. J. van Drunen, E. R. Eliel, and

J. P. Woerdman, J. Opt. Soc. Am. B 19, 2391 (2002).

[8] O. Aytur and P. Kumar, Phys. Rev. Lett. 65, 1551

(1990).

[9] M. L. Marable, S.-K. Choi, and P. Kumar, Opt. Express

2, 84 (1998).

[10] E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato,

Phys. Rev. A 69, 023802 (2004).

[11] A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev.

Lett. 83, 1763 (1999).

Page 5

5

[12] A. Yariv, Quantum electronics (John Wiley and Sons,

New York, 1989).

[13] A. Berzanskis, W. Chinaglia, L. A. Lugiato, K.-H. Feller,

and P. Di Trapani, Phys. Rev. A 60, 1626 (1999).

[14] M. H. Rubin, Phys. Rev. A 54, 5349 (1996).

[15] J.R. Janesick, Scientific Charge-Coupled Devices (SPIE

Press Bellingham, Washington, 2001), pp. 204-205; see

also http://www.roperscientific.de/theory.html.

[16] Y.-K. Jiang, O. Jedrkiewicz, S. Minardi, P. Di Trapani,

A. Mosset, E. Lantz, and F. Devaux, Eur. Phys. J. D 22,

521 (2003).

[17] K. Koch, E. Cheung, G. T. Moore, S. H. Chakmakjian,

and J. M. Liu, IEEE J. of quant. electron. 31, 769 (1995).

[18] A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur.

Phys. J. D 28, 447 (2004).

[19] S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Op-

tics of Femtosecond Laser Pulses (American Institute of

Physics, New York, 1992), p.151.

[20] P. Di Trapani, G. Valiulis, W. Chinaglia and A. An-

dreoni, Phys. Rev. Lett. 80, 265 (1998).

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