Entangled states interferometer

The projectors (Iq ogz) correspond to dg in the 1-way basis. The entangled state of the QDS that emerges from the interferometer is expressed in the which-way basis through the analogs ofEq. (24) ... 

Quantum entanglement between matter-sustained quantum states and those presenting EM quantum states is one basic ingredient in discussing, for example, Eq. (31) in Scully et al. atom interferometer analysis. Also, in Section 4.2, a quantized EM field was used. Some key issues were not examined there below focus is on one issue concerning laboratory (real)/Fock space [5] connection. 

We use the same near-field interferometer as in the previous section and introduce various gases at low, controllable pressure (between 5.10-8 mbar and 2.5 x 10-6 mbar) into the vacuum chamber. Each collision between a fullerene molecule and a gas particle entangles their motional states. In order to obtain the properties of the isolated quantum system one has to trace over the state of the scattered molecule. We assume that the mass of the fullerene molecule is much greater than the mass mg of the gas particle and find that the density operator for the fullerene molecule alone, po(r f1), is modified by a multiplicative factor because of the collision... 

Fig. 1. Schematic two-way interferometer setup. The beam splitter BS distributes the input among the two-ways, that becomes entangled with the state of a quantum which-way detector WWD. A phase shifter PS induces a state-dependent phase shift phi 2 = 0/2 at the central stage of the interferometer. Finally the beam merger BM recombines the contributions into the final state of the quantum. Measurements of the output can build a fringe pattern versus variation of (p in the case the duality principle allows for it.

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