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Intracavity generation of broadband biphotons in a thin crystal

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IOP PUBLISHING Laser Phys. Lett. 10 (2013) 045203 (5pp)

LASER PHYSICS LETTERS

doi:10.1088/1612-2011/10/4/045203

LETTER

Intracavity generation of broadband biphotons in a thin crystal
K G Katamadze1 ,2 , N A Borshchevskaya1 , I V Dyakonov1 , A V Paterova and S P Kulik1
1 2

1

Faculty of Physics, Moscow M. V. Lomonosov State University, Moscow, Russia Institute of Physics and Technology, Russian Academy of Science, Moscow, Nakhimovsky prospect, 34, Russia E-mail: k.g.katamadze@gmail.com

Received 14 December 2012 Accepted for publication 17 December 2012 Published 27 February 2013 Online at stacks.iop.org/LPL/10/045203 Abstract We propose and realize a method of high intensity generation of broadband biphotons and achieve its value up to 150 THz. The source is based on a thin BBO crystal with a thickness of 100 microns, in which spontaneous parametric down-conversion takes place. To compensate for the intensity decrease of the down-conversion caused by the small thickness of the crystal, it is placed inside the cavity of an Ar+ laser. In general, this experiment relates to the widely discussed problem of two-photon shaping in the frequency and/or angular domain. (Some figures may appear in colour only in the online journal)

1. Introduction
Biphotons are light states consisting of pairs of correlated photons. The most widely used method for biphoton generation is spontaneous parametric down-conversion (SPDC). Phenomenologically, SPDC is described as the spontaneous decay of pump photons in a medium possessing quadratic susceptibility (2) into pairs of photons, traditionally called signal and idle [1]. In the stationary case the energy conservation and phase-matching conditions have to be held, s + i = p , kp - ks - ki kp - ks - ki = =


(1) (2) (3)

k 2 /L, k = 0,

where the indices p, s and i relate respectively to the pump, signal and idler photons, the indices and denote parallel and orthogonal components relative to the pump direction, k is the mismatch and L is the thickness of the nonlinear medium layer.
1612-2011/13/045203+05$33.00 1

Pairs of correlated photons generated by SPDC are very useful tools for various problems in quantum optics, quantum information and quantum communication. One of the most important properties of such pairs is their strong correlation in time. This property is used in problems of remote clock synchronization [2] and quantum optical coherence tomography (QOCT) [3] as well as in applications where efficient two-photon interaction with matter is necessary, such as quantum interferometric optical lithography [4]. The smaller the correlation time, the broader the spectrum of each photon forming a biphoton [1, 5], but the spectral properties of such individual photons are interesting for another reason as well--they determine the entanglement degree of the combined bipartite quantum system, i.e. biphoton. To assess the entanglement degree of a quantum system with continuous variables it is helpful to use the spectral Fedorov ratio R = is the spectral width of each photon [6], where pair (at fixed angle) and is the width of the so-called conditional spectral distribution, registered in correlation schemes when the frequency of one selected photon is fixed, while scanning the frequency of the second one. For cw and quasi-monochromatic pumps is determined by its spectral
c 2013 Astro Ltd Printed in the UK & the USA


Laser Phys. Lett. 10 (2013) 045203

K G Katamadze et al

width, whereas the properties of the nonlinear medium are responsible for . Obviously, a biphoton field with a broad spectrum has a greater entanglement degree and a smaller correlation time. Besides, it enables a higher effective dimension of the Hilbert space which can be used for quantum communication and quantum imaging applications. Another promising fundamental aspect of two-photon spectral engineering is its on-demand Schmidt mode filtering. Unlike spatial mode filtering, which has been demonstrated in a series of proof-of-principle experiments with two-photon light [7], on-demand Schmidt mode selection in the frequency domain has been neither performed experimentally nor even mentioned in the literature. At the same time, control of the frequency spectra has been performed (see below).

Figure 1. The experimental setup for measuring the spectrum of the biphoton field.

2. Generation of broadband biphotons
The spectral amplitude of the biphotons, f (s , i ), generated via the SPDC process with a quasi-monochromatic pump has the following form [1]: p p f s = + , i = - 2 2
2 p L

4

-

2 0

dz exp[i k( , z)z],

(4)

where is the frequency mismatch. In the case of a homogeneous nonlinear medium the integral (4) can be taken exactly, f( ) â
2 p

4

-

2

L exp -i

k( )L sinc 2 (5)

k ( )L . 2

2 It should be noted that the term p /4 - 2 covers a wide range and is usually skipped, but in the broadband phase-matching case we need to take it into account. In our experiment conditions, the pump wavelength is 351 nm, so this term contributes within a 2000 nm or 600 THz range. There are various methods for broadband SPDC generation. First of all we should notice that the SPDC spectrum has an X-shape in the coordinate angle frequency so collecting photons from all angles leads to a very wide range of frequencies, = /2 , up to 167 TGz [8­10]. However, such an experiment requires complicated aberration free and achromatic optical elements. Moreover, such a state of the biphoton field is difficult to pass at a great distance because it needs to be collimated. If one detects only a small fraction of the SPDC angular spectrum (up to 1 ), the typical width of the frequency spectrum does not exceed a few tens of terahertz. To increase the width of the biphoton spectrum registered inside a small angular range a number of methods have been developed. Some of them are based on the use of nonlinear inhomogeneous media, including chirped gratings [11­14], while some methods exploit the selection of terms for broadband matching in homogeneous media [15­19]. At the same time, as follows from (2) and (4),

the simplest (and most obvious) way to get the two-photon field with a broad spectrum is generation of SPDC in a thin nonlinear crystal [20]. However, this method has one major drawback: the smaller the length of the crystal, the lower the efficiency of the SPDC. In this article we discuss a method to remove this shortcoming. To obtain a two-photon field with a broad spectrum, we used a thin BBO crystal with a thickness of 0.1 mm. The experimental setup is shown in figure 1. Biphotons originate from the emission of an SPDC process in a 0.1 mm-thick -barium borate (BBO) crystal oriented for the collinear type I configuration. The crystal is pumped by cw radiation with a central wavelength of 351 nm and an average power of 100 mW obtained from an argon laser. The Glan­Thompson prism V only passes vertical polarization of the pump beam. The filter F cuts the pump beam and biphotons polarized along the horizontal direction pass through the second Glan­Thompson prism H crossed with the first one and enter the lens O, the focus of which coincides with the slit of the spectrograph ISP-51. Thus, the radiation falling on the lens at different angles is focused at the slit in different coordinates. The avalanche photodiode D operating in photon counting mode is mounted in the focal plane of the spectrograph. The optical scheme is chosen in such a way that the detector D accepts the part of the angular spectrum within 0.2 . Since the intensity of the SPDC radiation generated by the thin crystal is very low compared with the noise3 , we first measured the spectrum of the total radiation entering the spectrograph and then subtracted the noise spectrum measured in the same way, but without the crystal. The result is shown in figure 2 (dots). The width of the spectrum obtained was 217 nm, or 132 THz. The experimental data were slightly corrected by taking into account the overall spectral transmission of the Glan­Thompson prism and the lens as well as the wavelength dependence of the spectral window bandwidth (), which is covered by the detector area placed in the spectrograph's focal plane. Theoretical spectra were calculated according to equation (4) and also corrected by the factor 1/2 , which represents the number of modes passing through the pinhole [21]. The theoretical spectral
3 The source of this noise is mainly the luminescence of the optical elements

of the setup. 2


Laser Phys. Lett. 10 (2013) 045203

K G Katamadze et al

.

Figure 2. The SPDC spectrum for 0.1 mm BBO. Dots--experimental data, thin blue line--theoretical spectrum for exact collinear degenerate phase-matching, thick red line--theoretical spectrum for slightly non-collinear phase-matching with a BBO tilt angle of 0.2 . For comparison, the green dashed line shows the theoretical spectrum for 1 mm BBO.

bandwidth for 0.1 mm BBO at exact collinear degenerate phase-matching (thin blue line) is 251 nm (153 THz). We suppose that in the experiment the crystal was slightly tilted with respect to the optimal position. Therefore, we also present the theoretical spectrum for 0.1 mm BBO tilted by 0.2 (thick red line), which agrees better with the experimental data. For comparison we also give the theoretical spectrum for 1 mm BBO (green dashed line). One can clearly see that it is three times narrower: 90 nm or 55 THz.

3. Intracavity SPDC generation
As noted above, the main disadvantage of generating broadband biphotons in a thin crystal is the low efficiency of the process. Indeed, the integral intensity of SPDC is 2 proportional to L (2) Sp , while the spectral intensity is proportional to L2 (2) Sp , where Sp is the pump intensity [1]. The typical length of nonlinear crystals used for obtaining biphotons is a few millimeters, and the typical
2

power of the pump laser is hundreds of mW. Thus, to get a high spectral intensity of SPDC using a 0.1 mm crystal, one needs to either find a medium with (2) one order of magnitude higher than the typical one or increase the intensity of the pump by two orders of magnitude. Since the quantum efficiency of single-photon detectors has its maximum in the 650­800 nm range, it is necessary to use an ultraviolet laser operating in the range of 325­400 nm as a pump. As in the linear regime the average power of the SPDC is determined by the average pump power, the use of a pulsed laser does not solve the problem. Moreover, for short pulses it will lead to a broadening of the pump spectrum and as a consequence a reduction of the degree of entanglement [6]. However, effective increase of the pump power can be achieved by placing a nonlinear crystal inside the cavity4 , as shown in figure 3. The prism assembly at one end of the cavity selects only the lasing wavelength of 351 nm. Biphotons generated in the non-collinear regime are removed from the cavity by means of the additional mirrors M1,2 and focused by the lenses O1,2 on the apertures of the multimode fibers. Also, we used an additional detector D3 to control the pump power by monitoring the beam reflected from the output window of the laser tube. The main problem that arises in this scheme is a decrease of the pump power caused by the presence of the crystal inside the cavity. To minimize these losses, we used anti-reflective coating at a wavelength of 351 nm on both sides of the crystal (R < 1% on each side). In addition, replacement of the output mirror with one with a higher reflection (R351 = 99.9%, R700 = 2%) allowed us to increase the pump power inside the cavity. In the experiment, we measured the intensity of the radiation within the cavity as a function of the discharge current for two cases: (1) cavity with a passing end mirror (R351 = 98%) in the absence of the crystal, and (2) cavity with the crystal inside and a high-reflectance mirror (R351 =
4 In our experiments we used an argon laser.

Figure 3. The experimental setup for intracavity generation.
3


Laser Phys. Lett. 10 (2013) 045203

K G Katamadze et al

Figure 4. The intensity of the pump inside the cavity versus the current in the two schemes: (1) with a passing mirror in the absence of the crystal (black squares) and with a fully reflecting mirror in the presence of the crystal (red circles).

Figure 5. The ratio of the SPDC spectral width registered at an angle (with respect to the pump wavevector) within the angular range to the spectral width registered in the collinear regime.

99.9%). The results are shown in figure 4. It is evident that despite the increase in the laser threshold from 30 to 33 A with higher discharge current the intensities for the two cases are visually identical. Therefore, given that the transmittance through the mirrors is about T 2%, it can be argued that the intensity of the SPDC in the intracavity scheme will be about 50 times higher with respect to the usual mode, when the crystal is placed on the outside of the cavity.

4. Discussion
The scheme shown in figure 3 can serve as a source of a broadband biphoton field of high intensity. However, some experimental problems arise with this scheme. First of all, the signal-to-noise ratio decreases sharply due to the luminescence in the crystal. Therefore, it is important to keep its surface as high quality as possible as well as to improve its anti-reflection coating. Secondly, there is a large contribution to the noise created by the discharge in the active medium of the gas laser. This problem can be overcome in two ways: either by placing a dispersion prism between the crystal and the gas discharge tube or by registering SPDC radiation in the non-collinear regime. In both cases, the signal must be carefully collimated by inserting pinholes into the cavity. However, the use of the non-collinear regime causes significant narrowing of the spectral range [22], which can be compensated by an increase of the spatial coupling of biphotons. Figure 5 shows the ratio between the widths of the spectrum in the non-collinear and collinear regimes. Here, the orientation of the crystal corresponds to non-collinear phase-matching. Note that the spectrum of the 0.1 mm-thick BBO crystal is three times wider than the spectrum of 1 mm-thick BBO. Therefore, we are only interested in the parameter area above a curve of 0.3 (shown as a bold line). Thus, for photon detection at an angle of = 2 within the angular range of = 1 , the corresponding spectral width is about 87% of the maximum.
4

We also tested whether the regime of biphoton generation was spontaneous or induced. There are several arguments in favor of the fact that the regime is spontaneous. First, the laser pump cavity cannot serve as a cavity for SPDC since it is generated in the non-collinear regime and there is no feedback for biphotons. Moreover, if one passes to the collinear regime this feedback becomes negligible since both mirrors reflecting the UV pump transmit visible and near infrared radiation of SPDC. Finally, we have to check whether the pump intensity inside the cavity is not enough to pass to the superradiance regime. To obtain this regime one has to satisfy the condition 2 1, where is the parametric gain [1],
2

=

(2 ) c

5



(2)

L

2



s

Sp ,

(6)

where (2) is about 10-7 (CGS), L = 0.1 mm, s = 600­850 nm, c is the speed of light in vacuum and Sp is the intensity of the pump laser. The diameter of the pump beam is 2 mm, therefore the inequality (6) holds if the pump power exceeds 100 kW. However, in our case the pump power outside the cavity is 100 mW, so inside the cavity we estimate it as 5­10 W taking into account losses at the output mirror. Finally we estimate the entanglement degree for the biphoton quantum state that we obtain. Taking into account the typical bandwidth of the Ar+ laser as 5 GHz, the Schmidt mode number takes the value K R = / = 2.6 â 104 .

5. Conclusion
This article reports the intracavity generation of biphotons in a thin crystal of beta-barium borate. It leads to effective broadening of the two-photon emission's spectrum. This


Laser Phys. Lett. 10 (2013) 045203

K G Katamadze et al

method can be used in different quantum communication and quantum imaging applications, which require a significant amount of spectral entanglement. It is important to stress that in the experiments performed, the generation of biphotons occurred in the spontaneous regime since the intracavity pump intensity was about four orders of magnitude lower than the threshold level.

[9] [10]

[11]

Acknowledgments
[12]

This work was supported in part by the Russian Foundation of Basic Research (projects 10-02-00204a and 12-01-31274), the Federal Program of the Russian Ministry of Education and Science (grant 8393), the European Community's Seventh Framework Programme (308803 BRISQ2) and the ERA.Net RUS Project `NANOQUINT'. K G Katamadze is grateful to the Dynasty Foundation for financial support.

[13]

[14]

[15]

References
[1] Belinsky A V and Klyshko D N 1994 Two-photon wave-packets Laser Phys. 4 663­89 [2] Valencia A, Scarcelli G and Shih Y 2004 Distant clock synchronization using entangled photon pairs Appl. Phys. Lett. 85 2655 [3] Nasr M, Saleh B, Sergienko A and Teich M 2003 Demonstration of dispersion-canceled quantum-optical coherence tomography Phys. Rev. Lett. 91 083601 [4] Boto A, Kok P, Abrams D, Braunstein S, Williams C and Dowling J 2000 Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit Phys. Rev. Lett. 85 2733­6 [5] Chekhova M V 2002 Two-photon spectron JETP Lett. 75 225­6 [6] Mikhailova Y, Volkov P and Fedorov M 2008 Biphoton wave packets in parametric down-conversion: spectral and temporal structure and degree of entanglement Phys. Rev. A 78 062327 [7] Straupe S S, Ivanov D P, Kalinkin A A, Bobrov I B and Kulik S P 2011 Angular Schmidt modes in spontaneous parametric down-conversion Phys. Rev. A 83 060302R [8] Gatti A, Brambilla E, Caspani L, Jedrkiewicz O and Lugiato L 2009 X entanglement: the nonfactorable [16] [17] [18] [19] [20]

[21] [22]

spatiotemporal structure of biphoton correlation Phys. Rev. Lett. 102 223601 Caspani L, Brambilla E and Gatti A 2010 Tailoring the spatiotemporal structure of biphoton entanglement in type-I parametric down-conversion Phys. Rev. A 81 1­14 Jedrkiewicz O, Blanchet J-L, Brambilla E, Di Trapani P and Gatti A 2012 Detection of the ultranarrow temporal correlation of twin beams via sum-frequency generation Phys. Rev. Lett. 108 253904 Harris S 2007 Chirp and compress: toward single-cycle biphotons Phys. Rev. Lett. 98 1­4 Katamadze K G and Kulik S P 2011 Control of the spectrum of the biphoton field J. Exp. Theor. Phys. 112 20­37 Katamadze K G, Paterova A V, Yakimova E G, Balygin K A and Kulik S P 2011 Control of the frequency spectrum of a biphoton field due to the electro optical effect JETP Lett. 94 262­5 Okano M, Okamoto R, Tanaka A, Subashchandran S and Takeuchi S 2012 Generation of broadband spontaneous parametric fluorescence using multiple bulk nonlinear crystals Opt. Express 20 11 Nasr M, Giuseppe G, Saleh B, Sergienko A and Teich M 2005 Generation of high-flux ultra-broadband light by bandwidth amplification in spontaneous parametric down conversion Opt. Commun. 246 521­8 Pe'er A, Silberberg Y, Dayan B and Friesem A 2006 Design of a high-power continuous source of broadband down-converted light Phys. Rev. A 74 1­7 Carrasco S, Sergienko A, Saleh B, Teich M, Torres J and Torner L 2006 Spectral engineering of entangled two-photon states Phys. Rev. A 73 1­6 Hendrych M, Micuda M and Torres J P 2007 Tunable control of the frequency correlations of entangled photons Opt. Lett. 32 2339­41 O'Donnell K A and U'Ren A B 2007 Observation of ultrabroadband, beamlike parametric downconversion Opt. Lett. 32 817­9 Aktsipetrov O A, Kitaeva G K, Mishina E D and Penin A N 1979 The lineshape of spontaneous parametric light scattering in thinplates of lithium niobate Sov. Phys.--Solid State 21 1051­2 Spasibko K, Iskhakov T and Chekhova M 2012 Spectral properties of high-gain parametric down-conversion Opt. Express 20 7507­15 Baek S-Y and Kim Y-H 2009 Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion Phys. Rev. A 80 033814

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