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.
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.
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.
All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described.
A proposal for an experimental realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment is described. Two 199Hg atoms, each with nuclear spin 1/2, are produced in an entangled state with total nuclear spin zero. Such a state is obtained by dissociation of dimers of the 199Hg2 isotopomer using a spectroscopically selective stimulated Raman process. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two-photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition.
An experimental test of Bell’s inequalities using two-level atoms is proposed. The test is analogous to that proposed by Bohm but, instead of using spins and Stern-Gerlach magnets, two-level atoms and resonant pulses are used. Two atoms excited to a common Rydberg state, but traveling in different directions, are introduced into a microwave cavity. The microwave field resonantly couples two Rydberg states and excites the atoms into a correlated state. The atoms then pass out of the cavity and into separate interaction regions where resonant microwave fields rotate their Bloch vectors through angles directly corresponding to the angles of orientation of the Stern-Gerlach magnets in the spin experiment. State selective ionization is then used to determine whether each atom is in the upper or lower Rydberg state. State selective ionization of Rydberg states has been demonstrated with an efficiency approaching 100% so that tests of Bell’s inequalities which are even more stringent than those using cascade photon polarization may be possible.
Let us imagine an experimentalist, who has maximally entangled photons and wants to violate Bell’s inequality in his laboratory. Among many obstacles he has to overcome, two of them are the most significant. Firstly, he has to avoid exchanging information about the measurement settings between the particles. Secondly, he has to detect particles with a high enough probability, because if the detection efficiency is too low, one can reproduce quantum correlations using a LHV (Local Hidden Variables) model. These two problems are known in the literature, respectively, as the locality loophole [1] and the detection loophole [2, 3]. Fortunately, it is possible to close the locality loophole using photons in the experiment [4, 5, 6, 7, 8]. However, closing the detection loophole is still an object of study. The authors of [9] showed that for the CHSH inequality, the lower bound for detector efficiency needed to close the loophole is 82.8% for maximally entangled states. This bound was lowered to 66.7% by Eberhard [10]. Furthermore, the detector efficiency has been studied for other Bell inequalities [11, 12, 13, 14, 15, 16]. In our research, we are trying to answer the following question: If we prepare a Bell experiment and we have two detectors, having different efficiencies both smaller than 100%, which detector should each party receive? And also: Which representation of the chosen Bell inequality should we consider? These are very crucial questions, which arise in laboratories. Hence, we hope that our results will be useful for experimentalists. We focus on the I3322 inequality [17], which is a natural candidate for testing, because of its asymmetry [14, 18]. We consider the case of a post-selection strategy, which consists in rejecting all the rounds in the Bell experiment when one of the detectors does not click. We used numerical optimisation methods to find both the best classical strategy for Alice and Bob and the best detector clicking strategy. Thus, we have found minimal efficiencies of the detectors of Alice and Bob needed to violate I3322. We made the same studies also for symmetric representations of I3322 [19]. Our results show that the minimal efficiencies of Alice and Bob’s detectors of the asymmetric representation of I3322 is lower than in case of the symmetric one [20]. It is work in progress, and we are examining other post-selection methods as well as other Bell inequalities. We want to consider also the case when non-maximally entangled states are used in Bell experiments.