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arXiv:1303.6261 · New Journal of Physics

Heralded mapping of photonic entanglement into single atoms in free space: proposal for a loophole-free Bell test

Nicolas Sangouard, Jean-Daniel Bancal, Philipp Müller, Joyee Ghosh, Jürgen Eschner

Published Aug 8, 2013• 17 citations
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Abstract

An obvious way to entangle two atoms located at remote locations is to produce a pair of entangled photons half-way between the two atoms, to send one photon to each location and to subsequently map the photonic entanglement into the atoms. The efficiency of this process is, however, fundamentally limited due to overall transmission losses. We propose a method to herald the success of the mapping operation in free space without destroying nor revealing the stored quantum state. Interestingly for a Bell test, the heralding signal does not open the detection loophole provided the measurement choice is performed once the heralding is obtained only. We show through a detailed feasibility study that this approach could provide an attractive alternative to Bell tests where the atom–atom entanglement is created from atom–photon entanglement using an entanglement swapping operation.

DOI
10.1088/1367-2630/15/8/085004

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An obvious way to entangle two atoms located at remote locations is to produce a pair of entangled photons half-way between the two atoms, to send one photon to each location and to subsequently map the photonic entanglement into the atoms. The efficiency of this process is, however, fundamentally limited due to overall transmission losses. We propose a method to herald the success of the mapping operation in free space without destroying nor revealing the stored quantum state. Interestingly for a Bell test, the heralding signal does not open the detection loophole provided the measurement choice is performed once the heralding is obtained only. We show through a detailed feasibility study that this approach could provide an attractive alternative to Bell tests where the atom–atom entanglement is created from atom–photon entanglement using an entanglement swapping operation.
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Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Quantum communication attempts to harness the unique rules of quantum mechanics to perform communication tasks that are difficult or impossible using classical rules. To realize these benefits, information must be carried on quantum systems. Photons make excellent carriers because they interact very little with the environment, move quickly, and can naturally store quantum information in their polarization. However, it is notoriously difficult to detect a single photon without destroying it. Standard detectors simply absorb the photon, losing the quantum information. This is a critical outstanding problem in quantum communication, as advanced protocols need to know exactly when a photon has arrived at a receiver after transmission through the atmosphere or an optical fibre before performing further quantum-information-processing tasks. Certifying a photon’s presence is of particular interest in tests of Bell’s inequalities, which have only recently been performed without loopholes arising from photon loss, and in device-independent quantum cryptography, which relies on such Bell tests for security. \n \nIn this thesis, I first present work on directly reducing losses in a successful loophole-free Bell test. This is an extremely difficult task that cannot be extended for long-distance communication. Therefore I then focus on ways to circumvent loss by detecting photons without destroying them while preserving their quantum information. First I analyze theoretically a way to herald photons using only linear-optical elements (beam splitters and phase shifters) and extra ancilla photons. Similar but older methods have been demonstrated experimentally by other groups, and my improvements will help future advanced quantum communication protocols. \n \nThe main experiment in this thesis certifies the presence of a photon in a rather simple way: split the photon into two using a nonlinear optical crystal, then detect one of the pair to herald the other. I show in this first proof-of-principle experiment that photonic qubit precertification indeed preserves qubit states, with up to (92.3 ± 0.6)% fidelity and rates of 1100 events per hour. With reductions in detector dark counts, precertification could outperform direct transmission, even with extremely lossy fibre links. \n \nFinally, I present two sources of photons based on nonlinearities in optical fibres. One of the limitations of the photon splitting scheme for heralding is the low success probability due to the very low likelihood of splitting a photon in two. In these fibre photon sources I investigate increasing the splitting likelihood in four-wave mixing through advanced materials and fibre designs. I use polarization-maintaining fibres to generate entangled photon pairs as a prerequisite to precertification, with (92.2 ± 0.2)% fidelity to a maximally-entangled state. Then I show that one type of highly nonlinear chalcogenide glass, never before used for photon pair generation, could outperform standard nonlinear crystals by two orders of magnitude, with calculated conversion efficiency up to 10^-3. To approach the single photon regime, I generate photon pairs in chalcogenide microwires with pump powers as low as 480 nW and verify their timing correlations. \n \nThese advances demonstrate the capability of nondestructive precertification of photons to allow advanced quantum communications protocols even over long distance, and could lead to the first implementations of fully device-independent quantum cryptography.
Certifying genuine nonclassical correlations over long distances is essential for device-independent quantum information. In photonic platforms, however, this remains challenging due to photon loss, which opens the detection loophole, rendering violations increasingly difficult for less-efficient detectors. Eberhard showed that using nonmaximally entangled states lowers the detection-efficiency threshold to 66.7%, but existing photonic approaches are restricted to short distances with linear transmittance scaling. Conversely, single-photon event-ready schemes extend the distance with favorable square-root scaling with channel transmittance, yet still demand detection efficiencies above 82.6%. Here, we propose the first all-photonic, heralded entanglement distribution protocol that unifies these two advances: It achieves a postselection-free violation at the Eberhard limit while preserving twin-field-like scaling. We identify the loss independent of the vacuum component amplitude of the prepared state as the source of this enhancement. Our approach addresses both resilience to loss and scalability, providing a practical route toward long-distance, loophole-free Bell tests and device-independent applications with current technology.
Summary form only given. Here we present our experiment using heralded entanglement between two 87Rb-atoms separated by 400 m violating Bell's inequality [1]. First each atom is entangled with a photon, which is coupled into single-mode fiber. The interference of the two photons at a beam splitter enables one to project the state onto a Bell state, which leaves the atoms in an entangled state [2]. For space-like separation, the state measurements on the two atoms together with the random choice of the measurement basis, have to be performed in a time shorter than 1.33μs. The atomic state readout itself is based on a highly efficient state-selective ionization and subsequent detection of the ionization fragments by channel-electron-multipliers (CEM) [3]. Altogether the time for the state readout is below 1μs and the locality condition is fulfilled. Evaluation of 5000 events for each of two entangled atom-atom states shows a significant violation of Bell's inequality with S-parameters of 2.240 ± 0.047 and 2.204 ± 0.047.