Counter-propagating spontaneous four wave mixing: photon-pair factorability and ultra-narrowband single photons

Abstract

We introduce a new kind of spontaneous four wave mixing process for the generation of photon pairs, in which the four waves involved counter-propagate in a guided-wave c ( ) 3 medium; we refer to this process as counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for the simplest CP-SFWM source, in which all waves propagate in the same polarization and transverse mode and in which self-and cross-phase modulation effects are negligible, phasematching is attained automatically regardless of dispersion in the fiber or waveguide. Furthermore, we show that in two distinct versions of this source (both pumps pulsed, or one pump pulsed and the remaining one monochromatic), the two-photon state is automatically factorable provided that the length of the nonlinear medium exceeds a certain threshold, easily achievable in practice since this threshold length tends to be in the range of mm to cm. We also show that if one of the pumps approaches the monochromatic limit, and for a sufficient nonlinear medium length, the bandwidth of one of the two photons in a given pair may be reduced to the level of MHz, compatible with electronic transitions for the implementation of atom-photon interfaces, without the use of optical cavities.

Heralding pure single photons: A comparison between counterpropagating and copropagating twin photons

“…In the spontaneus regime, twin-photons may be naturally generated in either spectrally entangled or decorrelated states by simply modifying the pump pulse duration (or crystal length), without the need of special tuning conditions [1]. Similar features have recently been described in counterpropagating FWM [24].…”

“…Clearly, the first mechanism dominates for T p |τ s |, as shown by Eqs. (24) and (26), the second mechanism for T p |τ s | [see Eq. (25)].…”

“…According to the previous results, when T p |τ ± i | ≥ |τ s | the two-photon state state is highly entangled in any configuration. We can for example use the asymptotic form (24) of the joint temporal amplitude (20), and insert it into formulas (53,54). The coherence functions of the signal and the idler obtained in this way are identical (a part from negligible offsets), and have the form…”

Frequency and polarization emission properties of a photon-pair source based on a photonic crystal fiber

“…single-mode 9 , weakly-guiding birefringent 10 , dispersion-shifted 11 , few-mode 12 , and photonic crystal fibers, (PCF) 13 , as well as in integrated waveguides 2 , 14 . In part due to this breadth of possible source types, the SFWM process is remarkably versatile, permitting a number of source characteristics, including: (1) single- or multi-mode operation (the latter permitting intra-mode phasematching) 2 , 8 , (22) counter- or co-propagating 4 , 15 , as well as cross- or co-polarized 7 , 16 geometries, (3) the use of degenerate or non-degenerate pumps 2 , 16 , 17 , and (4) the presence of quantum correlations or entanglement in polarization 6 , 18 , frequency, transverse mode 8 , 19 , 20 , or time-bin 21 degrees of freedom. Among the above optical fiber alternatives, it is well known that PCFs exhibit unique characteristics that make them an attractive medium for photon-pair source implementations 13 , 22 , 23 , exhibiting engineered dispersion properties leading to spectrally or temporally tailored two-photon state generation, and high effective nonlinear coefficients permitting large emission rates.…”

Dual-pump approach to photon-pair generation: demonstration of enhanced characterization and engineering capabilities

“…1(a)); this additional degree of freedom is beneficial for photon-pair source design, with experimental uses including degenerate photon-pair generation [11][12][13][14] and avoiding single-pump SFWM background [15]. In addition, it has been shown theoretically that dualpump SFWM leads to improved capabilities in tailoring the inter-correlations of the photon pairs [16,17], including a proposed method that relies on the group-velocity difference between pump pulses [18].…”