Time-Energy Entangled Photon Pairs from Doppler-Broadened Atomic Ensemble via Collective Two-Photon Coherence

Quantum interference of multidimensional quantum states via space-division multiplexing of a long-coherent single photon from a warm 87Rb atomic ensemble

The high-dimensional encoding of single photons can offer various possibilities for enhancing quantum information processing. This work experimentally demonstrates the quantum interference of an engineered multidimensional quantum state through the space-division multiplexing of a heralded single-photon state with a spatial light modulator (SLM) and spatial-mode mixing of a single photon through a long multimode fiber (MMF). In our experiment, the heralded single photon generated from a warm ⁸⁷Rb atomic ensemble was bright, robust, and long-coherent. The multidimensional spatial quantum state of the long-coherent single photon was transported through a 4-m-long MMF and arbitrarily controlled using the SLM. We observed the quantum interference of a single-photon multidimensional spatial quantum state with a visibility of >95%. These results may have potential applications in quantum information processing, for example, in photonic variational quantum eigensolve with high-dimensional single photons and realizing high information capacity per photon for quantum communication.

Photon-pair generation from a chip-scale Cs atomic vapor cell

The realization of a narrowband photonic quantum source based on an atomic device is considered essential in the practical development of photonic quantum information science and technology. In this study, we present the first step toward the development of a photon-pair source based on a microfabricated Cs atomic vapor cell. Time-correlated photon pairs from the millimeter-scale Cs vapor cell are emitted via the spontaneous four-wave mixing process of the cascade-type 6S_1/2-6P_3/2-8S_1/2 transition of ¹³³Cs. The maximum normalized cross-correlation value between the signal and idler photons is measured as 622(8) under a weak pump power of 10 µ;W. Our photon source violates the Cauchy-Schwartz inequality by a factor of >10⁵. We believe that our approach has very important applications in the context of realizing practical scalable quantum networks based on atom-photon interactions.

Experimental realization of efficient nondegenerate four-wave mixing in cesium atoms

Nondegenerate four-wave mixing (FWM) in diamond-type atomic systems has important applications in a wide range of fields, including quantum entanglement generation, frequency conversion, and optical information processing. Although the efficient self-seeded nondegenerate FWM with amplified spontaneous emission (ASE) has been realized extensively, the seeded nondegenerate FWM without ASE is inefficient in reported experiments so far. Here we present the experimental realization of the seeded nondegenerate FWM in cesium atoms with a significantly improved efficiency. Specifically, with two pump lasers at 852 and 921 nm and a seed laser at 895 nm, a continuous-wave laser at 876 nm is efficiently generated via FWM in a cesium vapor cell with a power up to 1.2 mW, three orders of magnitude larger than what has been achieved in previous experiments. The improvement of the efficiency benefits from the exact satisfaction of the phase-matching condition realized by an elaborately designed setup. Our results may find applications in the generation of squeezing and entanglement of light via nondegenerate FWM.

Indistinguishability of temporally separated pairwise two-photon state of thermal photons in Franson-type interferometry

The phenomenon of Franson interference with time–energy entangled photon pairs beyond the single-photon coherence length observed upon nonlocal measurement at two space-like separated locations is of particular research interest. Herein, we determine the coherence length of temporally separated pairwise two-photon (TSPT) states of thermal photons emitted from a warm atomic ensemble in Franson-type interferometry, with the setup consisting of two spatially separated unbalanced Michelson interferometers beyond the coherence length of a thermal photon. Using a novel method of square-modulated thermal photons, we show that the sinusoidal Franson-type interference fringe of thermal photons is determined by the presence or absence of TSPT states (corresponding to the time delay between the long and short paths in Franson-type interferometry). We find that the indistinguishability of the TSPT state in the Franson-type interference is independent of the temporal separation of the thermal photons in the TSPT states.

Four-wave mixing in a ladder configuration of warm 87Rb atoms: a theoretical study

We present a theoretical study of the four-wave mixing (FWM) spectra of 5S_1/2 - 5P_3/2 - 5D_5/2 ladder-type transitions of ⁸⁷Rb atoms. The density matrix equations are solved by considering all the magnetic sublevels to calculate the FWM signals in the atomic vapor cell. These results are subsequently compared with the experimental results. We observe that the FWM signal propagating exactly opposite to the driving field is measured experimentally. Additionally, we demonstrate the effects of optical depth, laser linewidths, and the coupling field power on the FWM spectra. Finally, the origin of the dispersive-like FWM signal is investigated by intentionally varying the intrinsic atomic properties.

Spectral-temporal biphoton waveform of photon pairs from cascade-type warm atoms

We investigate the spectral–temporal biphoton waveforms of the photon pairs emitted from cascade-type two-photon-coherent warm ⁸⁷Rb atoms via the spontaneous four-wave mixing process in the 5S_1/2–5P_3/2–5D_5/2 transition, under the condition of the different detuning frequencies (symmetric detuning conditions of ± 1 GHz) of the pump and coupling lasers relative to the 5P_3/2 state. In both detuning cases corresponding to ± 1 GHz, the biphoton temporal waveforms and biphoton spectral waveforms of the photon pairs are measured by means of time-resolved coincidence photon counting and stimulated measurements, respectively. Although photon-pairs were generated using opposite detunings, we confirm that the spectral–temporal biphoton waveforms of the photon pairs are very similar. Furthermore, we observe Hong–Ou–Mandel interference with 82% visibility with the two independent heralded single photons.

Joint spectral intensity of entangled photon pairs from a warm atomic ensemble via stimulated emission beat interferometry

Photonic quantum states generated from atomic systems play prominent roles in long-distance quantum networks and scalable quantum communication, because entangled photon pairs from atomic ensembles possess a universal identity and narrow spectral bandwidth for quantum repeaters. In this study, we propose and demonstrate a novel, to the best of our knowledge, method for the joint spectral intensity measurement of narrowband continuous wave (CW)-mode photon pairs from a warm atomic ensemble using stimulated emission and beat interferometry for the first time. Our approach offers the advantage of sub-megahertz resolution, absolute optical frequency measurements with megahertz-level accuracy, fast collection time, and high signal-to-noise ratio; thus, our method can find important applications in the characterization of narrowband photon pairs generated from sources including atoms and artificially structured material.

Entanglement swapping with autonomous polarization-entangled photon pairs from a warm atomic ensemble

Entanglement swapping forms a key concept in the realization of scalable quantum networks and large-scale quantum communication. For the practical implementation of entanglement swapping, completely autonomous entanglement sources and a joint Bell-state measurement (BSM) between two independent photons are essential. Here, we experimentally demonstrate entanglement swapping between two independent polarization-entangled photon-pair sources obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of ${^{87}}{\rm Rb}$⁸⁷Rb atoms. From the joint BSM, we estimate the ${\rm S}$S parameter in the Clauser-Horne-Shimony-Holt (CHSH) form of Bell's inequality and confirm the violation of the Bell-CHSH inequality by ${\rm S}={2.32} \pm {0.07}$S=2.32±0.07 with 4.5 standard deviations. We believe that this work is an important step toward realizing practical scalable quantum networks.

Generation of hyper-entangled photons in a hot atomic vapor

A source of hyper-entangled photons plays a vital role in quantum information processing, owing to its high information capacity. In this Letter, we demonstrate a convenient method to generate polarization and orbital angular momentum (OAM) hyper-entangled photon pairs via spontaneous four-wave mixing (SFWM) in a hot $ ^{87}{\rm Rb} $⁸⁷Rb atomic vapor. The polarization entanglement is achieved by coherently combining two SFWM paths with the aid of two beam displacers that constitute a phase self-stabilized interferometer, and OAM entanglement is realized by taking advantage of the OAM conservation condition during the SFWM process. Our hyper-entangled biphoton source possesses high brightness and high nonclassicality and may have broad applications in atom-photon-interaction-based quantum networks.

High-quality versatile photonic sources for multiple quantum optical experiments

Entangled sources are important components for quantum information science and technology (QIST). The ability to generate high-quality entangled sources will determine the extent of progress in this field. Unlike previous schemes, a thin quasi-phase matching nonlinear crystal and a dense-wave-division-multiplexing device are used here to build high-quality versatile photonic sources with a simple configuration that can be used to perform Hong-Ou-Mandel interference, time-energy entanglement and multi-channel polarization entanglement experiments. The measurement results from various quantum optical experiments show the high quality of these photonic sources. These multi-functional photonic sources will be very useful in a variety of QIST applications.

Temporal- and spectral-property measurements of narrowband photon pairs from warm double-Λ-type atomic ensemble

We investigate the temporal and spectral properties of narrowband photon pairs from a double-Λ-type atomic system of a warm ⁸⁷Rb atomic ensemble. The temporal properties of the narrowband photons are investigated by measuring their auto-correlation and cross-correlation functions. The spectral measurement of the photon pair is obtained by applying the stimulated emission method. We show that the biphoton spectral waveform with a spectral width of ∼6 MHz corresponds to the biphoton temporal waveform with a temporal width of ∼26 ns. We believe that our results can contribute to the characterization of narrowband photons generated from atomic ensembles and aid in the development of new photonic quantum states generated from atomic systems.

Temporal dynamics of zero-delay second order correlation function and spectral entanglement of two photons emitted from ladder-type atomic three-level systems

We theoretically investigate temporal dynamics of the second order cross correlation function at zero delay time (G12(2)(t)) and spectral entanglement of two photons emitted from an atomic three-level cascade. In Heisenberg's picture, a closed set of quantum kinetic equations of motion for G12(2)(t) is derived within density matrix formalism with cluster expansion rule. G12(2)(t) shows qualitatively distinctive features depending on the spectral entanglement of two photons. Although incoherent photon pairs generated from spontaneous radiation of the excited electron are not entangled, their correlation and anti-correlation properties can be found in G12(2)(t) depending on the radiative decay rates. In the coherent excitation regime where the light emitter is located in a high Q-cavity, and its atomic polarizations are predominantly initialized, spectral entanglement between two coherent photons is established. We show that G12(2)(t) is well fitted by the entanglement criterion by Duan-Giedke-Cirac-Zoller and explain the close relationship between them by means of the optically forbidden transition in the three-level cascade.

Generation and characterization of position-momentum entangled photon pairs in a hot atomic gas cell

Continuous-variable position-momentum entanglement (or Einstein-Podolsky-Rosen entanglement) of two particles has played important roles in the fundamental study of quantum physics as well as in the progress of quantum information. In this paper, we propose a scheme to generate Einstein-Podolsky-Rosen (EPR) position-momentum entangled photon pairs efficiently via spontaneous four-wave mixing (SFWM) process in a hot rubidium gas cell. The EPR entanglement between the photon pair is measured and characterized by using the ghost interference and the ghost imaging method. Due to the simplicity of the experimental setup and the high photon pair generation rate, our EPR entangled photon source may has potential applications in quantum imaging, hyperentanglement preparation and atomic ensemble based quantum information processing and quantum communication protocols.

High-visibility Franson interference of time-energy entangled photon pairs from warm atomic ensemble

We experimentally demonstrate Franson interference of a time-energy entangled photon pair generated via collective two-photon coherence in the 5S_1/2-5P_3/2-5D_5/2 transition of warm Rb87 atoms. The two unbalanced Michelson interferometers used in our setup are spatially separated in order to understand entanglement as a nonlocal property of the photon pairs from the warm atomic ensemble. We observe a Franson interference fringe with a high visibility of 99.1±1.3% with continuous-wave-mode photon pairs from the cascade-type atomic ensemble. To the best of our knowledge, this work is the first demonstration of the nonlocal two-photon interference experiment in separated photon channels by use of two-photon pairs emitted from a cascade-type atomic system as originally proposed by Franson [Phys. Rev. Lett.62, 2205 (1989)PRLTAO0031-900710.1103/PhysRevLett.62.2205].

Polarization-Entangled Photons from a Warm Atomic Ensemble Using a Sagnac Interferometer

We report a polarization-entangled photon-pair source obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of ^{87}Rb atoms using a Sagnac interferometer. Collective two-photon coherence occurs in the Doppler-broadened ladder-type atomic system with bidirectional counterpropagating two-photon resonant pump and coupling fields; hence, polarization-entangled photon pairs are collectively radiated in the phase-matched direction. Without phase stabilization of the interferometry for polarization entanglement, we robustly produce all four Bell states via a polarization Sagnac configuration. The brightness, stability, and temporal purity advantages provided by our polarization-entangled SFWM photon-pair source have very important applications in the context of a practical scalable quantum network.