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State readout of single Rubidium-87 atoms for a loophole-free test of Bell’s inequality

Norbert Ortegel

Published Jan 1, 2016• 4 citations
Publisher

Abstract

In contrast to classical physical theories, quantum mechanics - the theory describing particles and waves in the microscopic world - has very peculiar properties: The most prominent of them are the Heisenberg uncertainty principle, that makes it impossible to determine certain pairs of variables of a system simultaneously, as well as the existence of entangled states, which allow to establish non-local correlations between two particles at arbitrary distances. This lead to the derivation of the famous paradox of Einstein, Podolsky and Rosen, from which the authors con cluded that quantum mechanics cannot be a complete theory. The possibility of the existence of the thereupon postulated complete local hidden variable theories (LHV) became testable with Bell’s inequality. This theorem limits the correlations between measurements on particles from a pair of two-level systems. Until recently experiments on Bell’s inequality suffered from loopholes that impeded a conclusive exclusion of LHVs. These are the locality loophole that requires spacelike separation of the measurements and the detection loophole that requires that a mini mum number of all created particle pairs is read out. This work contributes to a Bell-experiment with a pair of single Rubidium 87 atoms that are trapped at a distance of 400 meters. It focuses on the implementation of an atom trap setup that enables a fast, efficient and precise readout of the atomic state which shall allow to close both loopholes simultaneously in one experiment. The atomic two-level system consists of two Zeeman states of the ground state atoms. The readout is based on a Zeeman state selective ionization of the atoms and subsequent fast detection of the ionization fragments with charged particle detectors. The atoms can be analyzed in arbitrary measurement bases and the experimentally determined contrast to distinct between two orthogonal Zeeman states is in the range of 90%...93%. This is sufficient for demonstrating a violation of Bell’s inequality with two entangled atoms. For every readout attempt an answer about the atomic state is obtained which allows to close the detection loophole. Furthermore, including the setting of the measurement basis the overall duration of the readout is 820 nanoseconds. Given the inter-atomic distance of 400 meters, it hence becomes also possible to close the locality loophole in the same experiment. Rubidium atoms are a commonly used carrier of qubit states in quantum information science. In the realm of quantum cryptography the presented readout scheme could for example open the path to realizing device-independent quantum key distribution with single atoms.

DOI
10.5282/edoc.19972

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In contrast to classical physical theories, quantum mechanics - the theory describing particles and waves in the microscopic world - has very peculiar properties: The most prominent of them are the Heisenberg uncertainty principle, that makes it impossible to determine certain pairs of variables of a system simultaneously, as well as the existence of entangled states, which allow to establish non-local correlations between two particles at arbitrary distances. This lead to the derivation of the famous paradox of Einstein, Podolsky and Rosen, from which the authors con cluded that quantum mechanics cannot be a complete theory. The possibility of the existence of the thereupon postulated complete local hidden variable theories (LHV) became testable with Bell’s inequality. This theorem limits the correlations between measurements on particles from a pair of two-level systems. Until recently experiments on Bell’s inequality suffered from loopholes that impeded a conclusive exclusion of LHVs. These are the locality loophole that requires spacelike separation of the measurements and the detection loophole that requires that a mini mum number of all created particle pairs is read out. This work contributes to a Bell-experiment with a pair of single Rubidium 87 atoms that are trapped at a distance of 400 meters. It focuses on the implementation of an atom trap setup that enables a fast, efficient and precise readout of the atomic state which shall allow to close both loopholes simultaneously in one experiment. The atomic two-level system consists of two Zeeman states of the ground state atoms. The readout is based on a Zeeman state selective ionization of the atoms and subsequent fast detection of the ionization fragments with charged particle detectors. The atoms can be analyzed in arbitrary measurement bases and the experimentally determined contrast to distinct between two orthogonal Zeeman states is in the range of 90%...93%. This is sufficient for demonstrating a violation of Bell’s inequality with two entangled atoms. For every readout attempt an answer about the atomic state is obtained which allows to close the detection loophole. Furthermore, including the setting of the measurement basis the overall duration of the readout is 820 nanoseconds. Given the inter-atomic distance of 400 meters, it hence becomes also possible to close the locality loophole in the same experiment. Rubidium atoms are a commonly used carrier of qubit states in quantum information science. In the realm of quantum cryptography the presented readout scheme could for example open the path to realizing device-independent quantum key distribution with single atoms.
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.
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.
In 1935 Einstein, Podolsky and Rosen used the assumption of local realism to conclude in a Gedankenexperiment with two entangled particles that quantum mechanics is not complete. For this reason EPR motivated an extension of quantum mechanics by so-called local hidden variables. Based on this idea in 1964 Bell constructed a mathematical inequality whereby experimental tests could distinguish between quantum mechanics and local-realistic theories. Many experiments have since been done that are consistent with quantum mechanics, disproving the concept of local realism. But all these tests suffered from loopholes allowing a local-realistic explanation of the experimental observations by exploiting either the low detector efficiency or the fact that the detected particles were not observed space-like separated. In this context, of special interest is entanglement between different quantum objects like atoms and photons, because it allows one to entangle distant atoms by the interference of photons. The resulting space-like separation together with the almost perfect detection efficiency of the atoms allows a first loophole-free test of Bell's inequality. The primary goal of the present thesis is the experimental realization of entanglement between a single localized atom and a single spontaneously emitted photon at a wavelength suitable for the transport over long distances. In the experiment a single optically trapped Rb87 atom is excited to a state which has two selected decay channels. In the following spontaneous decay a photon is emitted coherently with equal probability into both decay channels. This accounts for perfect correlations between the polarization state of the emitted photon and the Zeeman state of the atom after spontaneous decay. Because these decay channels are spectrally and in all other degrees of freedom indistinguishable, the spin state of the atom is entangled with the polarization state of the photon. To verify entanglement, appropriate correlation measurements in complementary bases of the photon polarization and the internal quantum state of the atom are performed. It is shown, that the generated atom-photon state yields an entanglement fidelity of 0.82. The experimental results of this work mark an important step towards the generation of entanglement between space-like separated atoms for a first loophole-free test of Bell's inequality. Furthermore entanglement between a single atom and a single photon is an important tool for new quantum communication and information applications, e.g. the remote state preparation of a single atom over large distances.
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.
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by 398 m with fast and efficient measurements of the atomic spin states closing essential loopholes. We obtain a violation with S=2.221±0.033 (compared to the maximal value of 2 achievable with models based on local hidden variables) which allows us to refute the hypothesis of local realism with a significance level P<2.57×10^{-9}.
It is well known that Bell’s inequality may be violated for special quantum states, e.g., an entangled state for a pair of particles. The entangled state is generalized here into a polyentangled state. Specifically, instead of only two possible states for each individual particle of the pair, several states are possible in an entangled way. An experimental realization for the polyentangled state is presented. It is the state for a pair of atoms in their Zeeman sublevels, in which the atoms are produced from dissociation of a homonuclear (I = 1/2) paradimer that is initially in a J = even rotational state of the singlet electron state. The three possible angular momentum components (M2 = 0,±1) in a specific direction can be determined because the different Zeeman sublevels can be selectively excited by polarized lasers, and then subsequently detected by photoionization. Because of the high detection efficiency (>90%) and fast responsivity (<10 ns) for these processes, the two main loopholes in previous LHV experiments using optical photons can be blocked.