Preservation of energy-time entanglement in a slow light medium.

Temporal control of the properties of qubits is a significant challenge in the quest for practical quantum information processing (QIP). For photons, or ‘‘flying qubits’’, their temporary storage in a quantum memory can facilitate many applications (e.g., linear optics quantum computing [1]). Quantum memories have varying design requirements depending on the application. These range from the most stringent requirements of on-demand retrieval of stored qubits to simpler passive but tunable temporary qubit buffers. Here we investigate entanglement preservation of an energy-time entangled biphoton in a double resonance slow light medium. We show that it can be used as a passive, tunable qubit buffer. Different types of quantum memories for photons have been investigated, each with its own strengths. Cyclical free-space memories for photonic qubits using Pockel cells have been demonstrated experimentally [2,3]. Cyclical fiber-based memories have also been proposed [4]. Both are well suited to QIP applications with a master clock cycle. Memories using Raman transitions and dark-state polaritons [5] in atomic ensembles have been extensively studied [6 ‐10]. While extremely versatile, these types of memories often suffer from the difficulty of efficiently isolating and detecting single photons in the presence of strong coupling beams. In this Letter we report on the buffering of a single photon from an entangled pair in a slow light medium and show that entanglement is preserved. We use the fine structure resonances of Rubidium to delay the amplitude of a single photon with a correlation bandwidth of 1.5 THz by � 1:3 correlation lengths. We observe a post-selected fourth order correlation fringe visibility of 80:0 � 4:8% (reduced from 97:0 � 4:4%) for an energy-time entangled biphoton. This exceeds the value of 70.7% needed to violate a Bell inequality and demonstrates the preservation of entanglement. Additionally, we demonstrate that broadening is the primary mechanism responsible for the reduction of fringe visibility. The fourth order correlation fringes are created with a Franson interferometer, a useful tool in the analysis of energy-time entanglement [11‐13]. It consists of two Michelson interferometers with highly unbalanced arm lengths so that no single photon interference occurs (see Fig. 1). Inserting a photon from an energy-time entangled biphoton into each Michelson interferometer and then scanning one of the four arms results in interference fringes in the detected coincidences. The fringes arise due to spectral correlations between the entangled photons. The visibility of these interference fringes can be used to verify the presence of entanglement [14,15]. By inserting a slow light medium into one arm of one of the interferometers, we delay the photon probability amplitude traveling in that path. The delay can be measured by observing a shift in the location of the Franson fringes. Additionally, the reduction of entanglement can be observed via the reduction of fringe visibility and the elongation of the fringe envelope due to group velocity dispersion of the photons in the slow light medium. The energy-time entangled pair is generated with spontaneous parametric down-conversion (SPDC). The unnormalized SPDC quantum state for an extremely narrow band pump is given by