Entangled photon-number states

As shown in Fig. 16.11, two pairs of entangled photons are produced by sources A and B, which are actually realized by passing a UV pulse twice through the same BBO crystal. Source A emits photons numbers 1 and 2, while source B emits photons numbers 3 and 4. The state of the four-photon system at this point can be represented as... 

For our first measurement we act on the photon-number entangled states in mode 3. Since the NS operation is an interference effect, it only proceeds when the entangled photons and the ancilla photon arrive at BS2 within their coherence time rcoh- In this case, the operation performs the following ... 

From the birth-paired photons, so-called path-entangled states can be constructed by overlapping them on a non-polarizing 50/50 beamsplitter (the numbers denote transmission and reflection coefficients of the beamsplitter). Two photons having the same polarization and coupled into different input ports of the beamsplitter will interfere and produce a new state that can be described as ... 

Similarly, Are momentum transfer associated with a collision of photons with atoms is used regularly to cool atoms [242], that is, to alter the translational energy of an atom. Indeed, the momentum of large numbers of photons (over 140-photon momenta) have been successfully transferred coherently to atoms [243], This suggests the possibility of preparing an initial superposition of internal states of a molecule, followed by tire state-specific absorption of photon momenta of one of the internal states in order to form the required entangled supeiposition of the translational and internal states. 

Quantum coherence is extremely sensitive to environmental interactions. This is a main stumbling block in the attempts to build quantum computers, and in spite of the fact that such devices are planned to be based on very weakly interacting systems (entanglement of photons or atoms well isolated in cavities) it is extremely difficult to preserve coherence over a sufficiently large number of basic operations steps. Coherent states in molecules are still more perturbed, as displayed for instance by the difference between the spectra of NHs and AsHs gases [Omnes 1994], Here, the H-atom in NH3 is delocalized in a quantum superposition, being on both sides of the //.rplane, while the spatial coherence of the heavier As-atom disappears during the time of observation which results in quite different optical properties. 

One of the major trends of current research is the study of transmission of information between the atom and photons in the process of emission and absorption. In particular, the conservation of angular momentum provides the transmission of the quantum phase information in the atom-held system. The atomic quantum phase can be constructed as the 57/(2) phase of the angular momentum of the excited atomic state (Section III). It is shown that this phase has very close connection with the EPR paradox and entangled states in general. Via the integrals of motion, it is mapped into the Hilbert space of multipole photons (Section IV.A). This mapping is adequately described by the dual representation of multipole photons, constructed in another study [46] (see also Section IV.B, below). Instead of the quantum number m, corresponding to the... 

Assume that photon A (number 1) from the entangled state belongs to Alice, and photon B (number 2) to Bob. Alice and Bob introduce a common fixed coordinate system. Both photons have identical polarizations in this coordinate system, but neither Alice nor Bob knows which. Alice may measure the polarization of her photon and send this information to Bob, who may prepare his photon in that state. This, however, does not amount to teleportation because the original state could be a linear combination of the 0) (parallel) and 1) (perpendicular) states. 

---