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Temporal properties of counter propagating twin photons

T. Corti

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

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.

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Scientific Reports•Jun 16, 2021•32 citations
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.
This work analyzes the temporal coherence and correlation of twin beams generated in a quasi-phase-matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the mirrorless optical parametric oscillator threshold. Here, we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible for the MOPO threshold.
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.
This work describes the continuous variable entanglement of the counter-propagating twin beams generated in a Mirrorless Optical Parametric Oscillator (MOPO) below threshold, encompassing both their quadrature and photon-number correlation. In the first case, a comparison with the single-pass co-propagating geometry outlines a completely different stability of the two sources with respect to the phase-angle. In the second case, stimulated by the critical divergence of the correlation time evidenced by Corti et al., we address the issue of the temporal bandwidth of the intensity squeezing.
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.
Counter-propagating parametric conversion processes in non-linear bulk crystals have been shown to feature unique properties for efficient narrowband frequency conversion. In quantum optics, the generation of photon pairs with a counter-propagating parametric down-conversion process (PDC) in a waveguide, where signal and idler photons propagate in opposite directions, offers unique material-independent engineering capabilities. However, realizing counter-propagating PDC necessitates quasi-phase-matching (QPM) with extremely short poling periods. Here, we report on the generation of counter-propagating single-photon pairs in a self-made periodically poled lithium niobate waveguide with a poling period on the same order of magnitude as the generated wavelength. The single photons of the biphoton state bridge GHz and THz bandwidths with a separable joint temporal-spectral behavior. Furthermore, they allow the direct observation of the temporal envelope of heralded single photons with state-of-the art photon counters.
We report the generation of frequency-uncorrelated photon pairs from counter-propagating spontaneous parametric down-conversion in a periodically-poled KTP waveguide. The joint spectral intensity of photon pairs is characterized by measuring the corresponding stimulated process, namely, the difference frequency generation process. The experimental result shows a clear uncorrelated joint spectrum, where the backward-propagating photon has a narrow bandwidth of 7.46 GHz and the forward-propagating one has a bandwidth of 0.23 THz like the pump light. The heralded single-photon purity estimated through Schmidt decomposition is as high as 0.996, showing a perspective for ultra-purity and narrow-band single-photon generation. Such unique feature results from the backward-wave quasi-phase-matching condition and does not has a strict limitation on the material and working wavelength, thus fascinating its application in photonic quantum technologies.