Experimental Test of the Bell Inequalities

Generation of Entangled State

Rather than being based on the polarization correlation of photons it is based on entangled states between atoms. The entangled singlet state of two 199Hg atoms, each with nuclear spin 1/2, is produced by two-photon induced dissociation of the mercury dimer, 199Hg2. The measurement of the spin correlations between the two spatially separated Hg atoms is based on the use of polarized laser beams, which selectively ionize only one spin state.

199Hg was selected, since it has no angular momentum, no electron spin, but nuclear spin of F=1/2. This simplifies the analysis of the spin states. Furthermore, the nuclear spin is relatively immune to environmental conditions, i.e. magnetic fields etc., making it easier to preserve the entanglement. The Hg dimer is produced in a supersonic jet expansion. The preparation of the entangled state is based on a two-photon dissociation scheme. First, a Opens internal link in current windowlaser pulse at 266 nm excites the dimers in an excited electronic state. A Opens internal link in current windowsecond laser pulse (355 nm) pumps them back down onto a dissociative part of the potential energy surface. The dimer falls apart and the two fragments start moving towards their respective detectors. The ability to only dissociate dimers in a singlet state is based on the symmetry properties of the molecular wave function. Briefly, the two Hg atoms are Fermions. Hence the overall wavefunction has to conform to the Pauli exclusion principle. Considering the symmetries of the different parts of the overall wavefunction (electronic, vibrational, rotational and nuclear (singlet wavefunction)), the excitation has to be restricted to dimers in even rotational state. This can be achieved through spectroscopic selection (for more details see this paper).

Potential energy surfaces relevant to the generation of the entangled state.
Experimental setup of the experiment.

Measurement of Spin Correlation

After their dissociation the two particles move towards their respective detectors in which they are analyzed for their spin direction. Since the nuclear moment is too weak, a Stern-Gerlach analyzer cannot be used for the analysis. Instead, we use a two photon ionization step that makes use of the selection rules for Zeeman sublevels.

Specifically, the Hg atom has nuclear spin 1/2, i.e. two Zeeman sublevels m=-1/2 and m=+1/2 corresponding to spin up and down, respectively. Suppose the first laser is left hand circular polarized. Therefore we require for dipole allowed transitions, Deltam=-1. Hence, a Hg atom in state m=1/2 will be excited into the m=-1/2 state of level 2 (see fig. below). A particle in the m=-1/2 state will not be excited, since their is no appropriate level in the intermediate state. In the second step the ionizing laser takes the atom to an autoionizing state, where it decays into a positively charged ion and an electron. Simulations show that the efficiency achievable is larger than 99%! Atoms in the m=-1/2 state can only be ionized through a much less efficient route, i.e. the F=3/2 component of the 6s6p state. It is detuned by 22 GHz. Requirement of the efficiency is a very well defined Opens internal link in current windowtiming of the two lasers involved. The quantization axis, with respect to which the spin analysis is conducted, is represented by the propagation direction of the first circular polarized laser beam (only in that direction, the polarization is circular.) The experiment therefore involves rotation of the 253.7 nm laser beams at the two detectors.

Spin analysis scheme
Detector setup

After their ionization the Hg ion or the electron has to be detected. The required high detection efficiencies are reached by secondary electron production from both the ion and the associated photo electron, followed by detection in channeltrons. Our detection scheme includes detection of the electron and ion in order to increase the efficiency and to accurately measure the detection efficiencies at all times during the experiment.

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Prof. Dr. Thomas Walther

Laser und Quantenoptik
Institut für Angewandte Physik
Fachbereich 05 - Physik
Technische Universität Darmstadt
Schlossgartenstr. 7
D-64289 Darmstadt

+49 6151 16-20831 (Sekretariat)

+49 6151 16-20834 (Fax)




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