Bell-Type Inequalities for Cold Heteronuclear Molecules

Abstract

We introduce Bell-type inequalities allowing for non-locality and entanglement tests with two cold heteronuclear molecules. The proposed inequalities are based on correlations between each molecule spatial orientation, an observable which can be experimentally measured with present day technology. Orientation measurements are performed on each subsystem at different times. These times play the role of the polarizer angles in Bell tests realized with photons. We discuss the experimental implementations of the proposed tests, which could also be adapted to other high dimensional quantum angular momenta systems. [5]. Since entanglement and non-locality are related (non-locality implies entanglement but not all entangled states are non-local), such tests may equally serve as entanglement witnesses [6]. The interest of such approach also lies in the fact that for arbitrary high dimensional systems one does not dispose of necessary and sufficient conditions for entanglement characterization. However, detecting quantum properties of high dimensional systems is of clear interest in atomic, molecular and optical physics.A number of experimental proposals are aiming to throw some light to these questions by means of Belltype tests performed in different continuous or multidimensional systems: it was shown recently that correlated atoms originated from the dissociation of a molecular Bose-Einstein condensate can be used to test the Einstein-Podolski-Rosen paradox as originally formulated [3,7]. The dichotomization of measurement results performed in a continuous system can also lead to maximal violation of Bell-type inequalities in phase space [8]. Finally, discrete multi-dimensional systems also allow for non-locality tests [9], and recent experiments show the violation of Bell-type inequalities with two effective spin-1 particles [10]. In parallel, recent advances in single molecule manipulation and detection open the way to the controlled creation of molecular entanglement [11]. Moreover, cold polar molecules confined in optical or magnetic traps have been recognized as a promissing candidate for quantum information processing [12], especially when their rotational levels are used as qubits [13,14]. Rotational states are relatively long lived, allowing for short quantum gate implementation times: one can perform about 10 4 gate operations before decoherence takes place. This excellent performance, when compared to cold collision based quantum gates [15], originates from the strength of dipolar interactions.In the present paper, we propose realistic non-locality and entanglement tests for a system composed of two cold and trapped heteronuclear diatomic molecules. As in usual Bell tests scenarios, measurements are performed independently on each molecule by observers placed far apart, so that no comunication between them is possible during the realization of the protocol. We show in the following that inequalities built from local realism assumptions can be violated by a set of entangled states using measurements of corr...

Molecular orientation entanglement and temporal Bell-type inequalities

“…One can also easily understand the mirror symmetry about the t 1 = t 2 line with the help of the particle exchange symmetry of operator B 1 . We have shown in [22] that Eq. (8) can be violated by a number of pure states, and numerically studied the relative violation (10) with increasing dimension.…”

“…The inequalities studied in this paper are based on molecular spatial orientation correlations measurements [22] instead of spin-like observables. However, the same type of idea can be generalised to other continuous bounded observable.…”

Long-range string orders and topological quantum phase transitions in the one-dimensional quantum compass model

“…In this model, the pseudospin-1/2 operators characterize the orbital degrees of freedom, and the anisotropic couplings between these pseudospins simulate the competition between orbital orderings in different directions. Furthermore, such an idea has been implemented to describe some Mott insulators with orbital degeneracy 18,19 , polar molecules in optical lattices 20 and ion trap systems 21 , protected qubits for quantum computation in Josephson junction arrays 22 , and so on.…”

Bell inequalities with continuous angular variables

“…In order to show that, we calculate the spectra of B(φ a , φ a , φ b , φ b ) operators. Actually, such spectra depend only on the relative phases φ a − φ a and φ b − φ b [14,15]. We can define…”