Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrowband photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrowband photons is expected to play an essential role in spatially-multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyper-entangled photons, etc.Entanglement, initially explored experimentally with the polarization states of a pair of photons [1, 2], has now been demonstrated in a variety of physical systems, e.g., two spontaneous parametric down-conversion (SPDC) photons [3, 4], two-mode squeezed states of optical fields [5, 6], trapped ions [7, 8], neutral atoms [9, 10], and artificial quantum systems [11, 12]. The gedankenexperiment proposed by Einstein-Podolsky-Rosen (EPR) in 1935, on the other hand, involves a pair of particles that are entangled in their positions and momenta [13][14][15]. In addition to fundamental interests, EPR entanglement is essential in quantum imaging and quantum metrology [16][17][18][19]. Here we report EPR position-momentum entanglement of narrowband (∼ MHz) photon pairs generated from χ (3) spontaneous four-wave mixing (SFWM) in a cold atomic ensemble. By using two-photon quantum ghost imaging and interference [20,21], we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR positionmomentum entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons [22][23][24][25][26][27][28]. To the best of our knowledge, this is the first experimental demonstration of EPR entanglement and EPR steering of position-momentum degrees of freedom of narrowband photon pairs, well suited for spatially-multiplexed quantum information processing, storage of quantum images, quantum interface involving hyper-entangled photons, etc [29][30][31][32][33][34].The position-momentum-like continuous variable feature of EPR entanglement has been explored initially by using quadrature-phase amplitudes of two-mode squeezed states [5, 6]. Genuine EPR position-momentum entanglement of photon pairs became available later by the SPDC process in a bulk crystal [14,15] and is thought to be essential in quantum imaging and quantum metrology [16][17][18][19]. The EPR-entangled SPDC photons, however, are inherently broadband, typically on the order of several THz in bandwidth. This large bandwidth makes the source unsuitable for interfacing with quantum memory based on atom-photon coherent interaction, which typically has the working bandwidth of a ...
Interferometric signals are degraded by decoherence, which encompasses dephasing, mixing and any distinguishing which-path information. These three paradigmatic processes are fundamentally different, but, for coherent, single-photon and N N 00 -states, they degrade interferometric visibility in the very same way, which impedes the diagnosis of the cause for reduced visibility in a single experiment. We introduce a versatile formalism for many-boson interferometry based on double-sided Feynman diagrams, which we apply to a protocol for differential decoherence diagnosis: twin-Fock states | 〉 N N , with ⩾ N 2 reveal to what extent decoherence is due to path distinguishability or to mixing, while double-Fock superpositions|( , , ) 2 with > > N M 0 additionally witness the degree of dephasing. Hence, double-Fock superposition interferometry permits the differential diagnosis of decoherence processes in a single experiment, indispensable for the assessment of interferometers.
We demonstrate a coherent and dynamic beam splitter based on light storage in cold atoms. An input weak laser pulse is first stored in a cold atom ensemble via electromagnetically-induced transparency (EIT). A set of counter-propagating control fields, applied at a later time, retrieves the stored pulse into two output spatial modes. The high visibility interference between the two output pulses clearly demonstrates that the beam splitting process is coherent. Furthermore, by manipulating the control lasers, it is possible to dynamically control the storage time, the power splitting ratio, the relative phase, and the optical frequencies of the output pulses. With further improvements, the active beam splitter demonstrated in this work might have applications in photonic photonic quantum information and in all-optical information processing.
Interferometric signals are degraded by decoherence, which encompasses dephasing, mixing and any distinguishing which-path information. These three paradigmatic processes are fundamentally different, but, for coherent, single-photon and N N 00 -states, they degrade interferometric visibility in the very same way, which impedes the diagnosis of the cause for reduced visibility in a single experiment. We introduce a versatile formalism for many-boson interferometry based on double-sided Feynman diagrams, which we apply to a protocol for differential decoherence diagnosis: twin-Fock states | 〉 N N , with ⩾ N 2 reveal to what extent decoherence is due to path distinguishability or to mixing, while double-Fock superpositions|( , , ) 2 with > > N M 0 additionally witness the degree of dephasing. Hence, double-Fock superposition interferometry permits the differential diagnosis of decoherence processes in a single experiment, indispensable for the assessment of interferometers.
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