Time-Energy Entangled Photon Pairs from Doppler-Broadened Atomic Ensemble via Collective Two-Photon Coherence Jiho Park, Taek Jeong, Heonoh Kim, and Han Seb Moon * Department of Physics, Pusan National University, Geumjeong-Gu, Busan 46241, Korea (Received 24 August 2018; published 26 December 2018) We experimentally demonstrate two-photon interference of a time-energy entangled photon pair generated via collective two-photon coherence in Doppler-broadened cascade-type 87 Rb atoms. The two photons originally proposed by J. D. Franson are realized as a photon pair due to collective effects, which are generated from the cascade atomic system with a relatively long lifetime of the initial state and a considerably shorter lifetime of the intermediate state. The achievement of two-photon interference with photon-pair sources generated from inhomogeneous atomic ensembles constitutes an important result for time-energy entanglement based on an atom-photon interaction. DOI: 10.1103/PhysRevLett.121.263601 Quantum entanglement first attracted attention as the heart of the Einstein-Podolsky-Rosen paradox and one of the most counterintuitive phenomena in the view of classical physics [1]. The generation of entangled photons has since become a key technology in the areas of quantum communication, quantum simulation, quantum computing, and quantum metrology [2–8]. In quantum optics, the physical properties of photons, such as polarization [9], position momentum [10], orbital angular momentum [11], and time frequency [12,13], have been used for realizing quantum entanglement. Recently, quantum optics experiments based on atomic ensembles [14] or artificial atoms such as quantum dots [15], impurity centers [16], and nanophotonics chips [17] have been applied to topics of special interest in quantum optics based on photon pairs produced via spontaneous parametric down-conversion in nonlinear crystals [18–21]. In particular, the photon pairs emitted from atomic ensem- bles have attracted considerable interest with respect to the field of quantum-information science and technology because of their very narrow spectral bandwidth, which is essential for the realization of atom-photon interfaces for quantum memory [22–24]. In the cases of cold [25–30] and Doppler-broadened [31–36] atomic ensembles, corre- lated photon pairs with narrow spectral width have been generated via spontaneous four-wave mixing (SFWM). The coherence time of the photons generated via SFWM is longer than the time resolution of a single-photon detector (SPD). Therefore, this time-energy entanglement source has the advantage of providing continuous and temporally pure photons without the need for supplemental filters [37,38]. As is well known, the Hong-Ou-Mandel (HOM) [18] and Franson interferences [20,21] are regarded as important evidence of the nonclassical nature of photon sources. Since a two-photon interference experiment with time- energy entangled photons was proposed by Franson [12], the fourth-order interferences beyond the one-photon coherence length have attracted considerable attention as important and interesting quantum phenomena in quantum optics [20,21]. Surprisingly, Franson interference has not been experimentally demonstrated by use of two-photon pairs emitted from a cascade-type atomic system with continuous wave (cw) pumping, as originally proposed by Franson [12]. Here, we experimentally demonstrate two-photon inter- ference between a time-energy entangled photon pair generated from Doppler-broadened cascade-type 87 Rb atoms using an unbalanced Michelson interferometer. In our system, the cw-mode time-energy entangled photon- pair sources are generated via the SFWM process and the collective two-photon coherence effect of a Doppler- broadened cascade-type atomic ensemble. The coherence time of the two-photon state from the Doppler-broadened atomic ensemble is more than 100 times longer than that of the single-photon state. We investigate two-photon interference (TPI) by means of highly time-resolved coincidence detection and determine the two-photon coher- ence length of a photon pair from the Doppler-broadened atomic ensemble. The two photons for the large-path-difference interfer- ometry originally proposed by Franson are emitted from a cascade atomic system, as shown in Fig. 1(a) [12]. However, it is difficult to experimentally demonstrate single-photon-interference-free TPI with photon pairs emit- ted from a cascade atomic system. The reasons are as follows: It is difficult to find a real atomic system with a relatively long lifetime (τ 1 ) of the initial state and a considerably shorter lifetime (τ 2 ) of the intermediate state, as shown in Fig. 1(a). Here, τ 1 and τ 2 are related to the PHYSICAL REVIEW LETTERS 121, 263601 (2018) 0031-9007=18=121(26)=263601(6) 263601-1 © 2018 American Physical Society