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arXiv:1607.06012

Heralding pure single photons: a comparision between counter-propagating and co-propagating twin photons

E. Brambilla, T. Corti, A. Gatti

Published Jul 20, 2016• 0 citations
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Abstract

We investigate the possibility of generating pure heralded single photons through spontaneous parametric down-conversion comparing the counter-propagating geometry studied in [1] with more conventional co-propagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. We estimate the Schmidt number associated to the temporal modes as a function of the pump pulse duration for three particular configurations, showing how the different phase-matching conditions influences the degree of separability that can be achieved.

DOI
10.48550/arxiv.1607.06012

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We investigate the possibility of generating pure heralded single photons through spontaneous parametric down-conversion comparing the counter-propagating geometry studied in [1] with more conventional co-propagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. We estimate the Schmidt number associated to the temporal modes as a function of the pump pulse duration for three particular configurations, showing how the different phase-matching conditions influences the degree of separability that can be achieved.
We investigate different strategies suitable to generate pure heralded single photons through spontaneous parametric down-conversion, comparing the counterpropagating geometry with more conventional copropagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. We derive general results for the Schmidt number associated to the temporal modes, which provide a quantitative estimate of the purity. An analysis of the correlation of twin photons in the temporal domain provides a more physical view of the mechanisms that permit to eliminate the temporal entanglement of the state and to generate high-purity heralded photons. The efficiency of the various strategies and the individual properties of the heralded photons thereby generated are then compared.
Twin photon pairs generated through parametric downconversion (PDC) in a χ 2 medium is one of the most widely used source of entanglement. We focus here on a non-conventional geometry in which one of the twin photons propagates in the opposite direction with respect to the pump beam, exploiting quasi-phase-matching in a periodically poled crystal. Through predicted almost 50 years ago, this new PDC configuration has been realized experimentally only recently [1] thanks to new fabrication techniques achieving the required sub-micrometer poling period. Because of the presence of distributed feedback, the optical system has been shown to behave as a Mirrorless Optical Parametric Oscillator (MOPO) and exhibits peculiar spectral properties which strongly differ from those found in more common geometries involving co-propagating beams. In this work we provide a detailed analysis of the correlation and coherence properties of counter-propagating twin beams both in the purely spontaneous regime and in the neighborhood of the MOPO threshold. We consider on the on side the regime of spontaneous pair production where the characteristic narrow band of the counter-propagating twin beams offers the unique opportunity of generating heralded single photon states with a high degree of purity, a relevant property for applications in quantum communication. In this context, we investigate how the degree of separability of the twin photon state varies with the pump pulse duration τp. We find that two well separated time scales characterize the system dynamics: a short time scale τgvm, in the picoseconds range, corresponding to the typical temporal delay of co-propagating waves due to group-velocity mismatch, and a much longer time scale τgvs associated with the temporal separation of counter-propagating waves. Such a difference of time scales occurs naturally in the counterpropagating configuration, for basically any kind of material and tuning condition. Because of this same feature, counter-propagating twin photons in a pure state can in principle be heralded at any wavelength by choosing the appropriate poling period. We show that a high degree of separability can be achieved when the pump pulse duration satisfy the condition τgvm ≪ τp ≪ τgvs, as put in evidence from the evaluation of Schmidt number as a function of the pump pulse duration which reaches a minimum close to unity in this region. The separability is lost in the nearly monochromatic limit ( τp ≫ τgvs ) as well as for ultra-short pulses ( τp ≪ τgvm ), where the entanglement between the signal and idler frequencies can be inferred by the non factorable shape of the spectral biphoton amplitude. We offer a physical interpretation of such a behaviour, and a detailed analysis of the Schmidt number characterizing the entanglement of the state. We also considered a completely different regime of operation, close to the MOPO threshold, where the combined effect of stimulated PDC and distributed feedback affects dramatically the property of coherence of the field. Our analysis put in evidence a progressive narrowing of both the spectral twin beam correlation and the intensity spectra as the pump field intensity approaches its threshold value. This translates into a drastic increase of the correlation and coherence times in the temporal domain, a feature which can be attributed to the critical slowing down of the fluctuation dynamics characterizing the transition toward coherent emission occurring at the MOPO threshold. Furthermore, we investigate the potentiality of the source to generate squeezing and EPR type correlations in the threshold vicinity. In this regards, the obtained results shows that the system displays a behaviour which is very similar to that found in standard optical parametric oscillators enclosed in a resonant cavity. In the last part of the work, we present some preliminary results from numerical simulations illustrating the transition above the MOPO thresholds. We also take into account non collinear PDC emission, showing explicitely that the spatial and the temporal degrees of freedoms of the emitted twin photons are almost uncoupled. This feature strongly distinguish the counter-propagating configuration from standard co-propagating geometries where the phase-matching mechanism usually leads to strong angular dispersion.
Sources of single photons in pure quantum states are essential to many quantum optics applications. We explore a technique, known as group-velocity matching, that enables the heralded generation of pure single photons through nonlinear optical processes. It reduces or eliminates the requirement of spectral filtering that conventional sources rely on to achieve high purity, therefore increasing both heralding efficiency and photon flux. Implementation in both spontaneous parametric downconversion and spontaneous four-wave mixing is studied as we discuss several recent experimental realizations demonstrating purity of more than 0.84 for the heralded photons.
This work analyzes the temporal coherence and correlation of counterpropagating twin photons generated in a quasiphase matched nonlinear crystal by spontaneous parametric down-conversion. We find out different pictures depending on the pump pulse duration relative to two characteristic temporal scales, determined, respectively, by the temporal separation between the counterpropagating and the co-propagating wave packets. When the pump duration is intermediate between the two scales, we show a transition from a highly entangled state to an almost separable state, with strongly asymmetric spectral properties of the photons.
We explore a promising method of generating pure heralded single photons. Our approach is based on parametric down-conversion in a periodically-poled waveguide. However, unlike conventional downconversion sources, the photon pairs are counter-propagating: one travels with the pump beam in the forward direction while the other is backpropagating towards the laser source. Our calculations reveal that these downconverted two-photon states carry minimal spectral correlations within each photon-pair. This approach offers the possibility to employ a new range of downconversion processes and materials like PPLN (previously considered unsuitable due to its unfavorable phasematching properties) to produce heralded pure single photons over a broad frequency range.