Effective fiber-coupling of entangled photons for quantum communication

Abstract

We report on theoretical and experimental demonstration of high-efficiency coupling of two-photon entangled states produced in the nonlinear process of spontaneous parametric down conversion into a single-mode fiber. We determine constraints for the optimal coupling parameters. This result is crucial for practical implementation of quantum key distribution protocols with entangled states.c 2008 Optical Society of America OCIS codes: 000.1600, 220.4830.Entangled-photon pairs generated in the nonlinear process of spontaneous parametric down conversion (SPDC) are proven to be a highly desirable means 1 for practical quantum cryptography 2 . The main difficulty of practical utilization of such system usually stems from a relatively low photon collection efficiency because of the complex spatial distribution of SPDC radiation and due to the broad spectral width of entangled-photon wave packets.The problem of coupling entangled photons into a fiber has been considered before by Kurtsiefer et al.3 . Assuming the pump to be a plane wave the emission angle of the SPDC has been calculated as a function of the wavelength. The waist of the focused pump beam has been chosen to maximally overlap the "impression" of the Gaussian mode of a single-mode fiber on the crystal 3 . It has been pointed out that the coupling efficiency may be significantly affected by transverse walk-off.In this letter we present a significantly modified approach allowing us to achieve a high-efficiency coupling of the SPDC pairs into single mode fibers. In particular, we demonstrate how the pump beam waist, crystal length, optical system magnification and the fiber mode field diameter (MFD) must obey a precise joint relation in order to ensure high coupling efficiency. We describe a The function Φ(q o , ω o ; q e , ω e ) = E p (q o + q e , ω o + ω e ) χ (2) (q o , ω o ; q e , ω e ) accounts for the phase matching conditions. E p (·) represents the amplitude of the plane-wave expansion of the pump field andInside the crystal the zcomponent of the wave-vector is defined as k z (q, ω) = [ω n(q, ω)/c] 2 − |q| 2 . All the information on the state is given by the amplitude A 1,2 (x 1 , t 1 ; x 2 , t 2 ) 5,6 of detecting the SPDC two-photons in space-time events at (x 1 , t 1 ) and (x 2 , t 2 ). The Fourier transform with respect to t 1 and t 2 of the two-photon amplitude A 1,2 (x 1 , t 1 ; x 2 , t 2 ) is given by A 1,2 (x 1 , ω o ; x 2 , ω e ) = dq o dq e Φ(q o , ω o ; q e , ω e ) · ·H 1 (x 1 ; q o , ω o ) H 2 (x 2 ; q e , ω e ) (2)

Direct Measurement of Nonlinear Properties of Bipartite Quantum States

“…Subsequently the photons are sent to the beam-splitters BS1 and BS2, so that each beam-splitter receives two photons, one photon from each entangled pair. The photons are coupled in Single-Mode (SM) Fibers [13] and detected by the silicon-based single-photon counting modules (Perkin-Elmer SPCM-AQR-14). Once the correct position of the two beam splitters is established the fourfold coincidence interference patterns are measured.…”

Shaping the Waveform of Entangled Photons

“…For instance, gaussian modes when the downconverted photons are collected with an imaging system followed by single mode optical fibers [20,21]. Projection into large area modes is equivalent to projection into q s = q i ≃ 0, i.e., …”

Heralded single photon sources: a route towards quantum communication technology and photon standards

“…The main result was to observe a higher matching/collection efficiency when the single collected mode waists were about the same as the pump waist, for a short crystal; the effect of the transverse spatial distribution of the pump was not observed. A more rigorous study of the coupling efficiency of SMFs with PDC was done in reference [39], which included crystal parameters as well as optical propagation parameters. In particular, it was demonstrated how the pump beam waist, crystal length, optical system magnification and the fiber mode waist must obey a precise joint relation in order to ensure high coupling efficiency.…”

“…femtosecond-pumped Type II PDC in nonlinear crystals of variable thickness [39]. A more complete theory of the mode matching efficiency for the general case in CW pump operation was then provided [40].…”

“…In Section 3 we review the theory of PDC state decomposition in multi and single modes, considering the inseparability between spatial and spectral degrees of freedom of the states. In Section 4, a review of production of heralded photon sources in bulk nonlinear crystal is provided, discussing various experiments [38][39][40][41][42][43][44][45], both with CW and pulsed pump configurations. In Section 5 we will review attempts to generate heralded single photons in periodically poled crystals [46][47][48][49][50].…”