Optimal focusing conditions for bright spontaneous parametric down-conversion sources

Abstract

Optimizing the brightness of a spontaneous parametric down conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wavefunction, generalizing previous known results, by considering collinear and non-collinear emission. We present analytical expressions for our results in the thin crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is $1/\sqrt{2}$ for collinear degenerate emission and approaches $1/2$ for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\beta$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin crystal regime.

arXiv commentv1: 13 pages, 7 figures; v2, equivalent to the published version: minor changes to the discussion, added Figure 1, addes Section V-D, no changes to the results

References in corpus (16)

• Experimental quantum teleportation
• The Security of Practical Quantum Key Distribution
• Advances in Quantum Cryptography
• Optical Quantum Computing
• Photonic Boson Sampling in a Tunable Circuit
• A wavelength-tunable fiber-coupled source of narrowband entangled photons
• High efficiency entangled photon pair collection in type II parametric fluorescence
• Optimal Co-linear Gaussian Beams for Spontaneous Parametric Down-Conversion
• Effective fiber-coupling of entangled photons for quantum communication
• Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers
• Introduction to the Absolute Brightness and Number Statistics in Spontaneous Parametric Down-Conversion
• Absolute emission rates of Spontaneous Parametric Down Conversion into single transverse Gaussian modes
• Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion
• Why you should not use the electric field to quantize in nonlinear optics
• Efficient fiber coupling of down-conversion photon pairs
• Optimal coupling of entangled photons into single-mode optical fibers

Cited by in corpus (3)

• Energy-time and time-bin entanglement: past, present and future
• Engineering of maximally entangled orbital angular momentum states via path identity
• Spectrally Resolved Higher Order Photon Statistics of Spontaneous Parametric Down Conversion