Signatures of nonclassical effects in optical tomograms

Abstract

Abstract. Several nonclassical effects displayed by wave packets subject to generic nonlinear Hamiltonians can be identified and assessed directly from tomograms without attempting to reconstruct the Wigner function or the density matrix explicitly. We have demonstrated this for both single-mode and bipartite systems. We have shown that a wide spectrum of effects such as the revival phenomena, quadrature squeezing and Hong-Mandel and Hillery type higherorder squeezing in both the single-mode system and the double-well Bose-Einstein condensate can be obtained from appropriate tomograms in a straightforward manner. We have investigated entropic squeezing of the subsystem state of a bipartite system as it evolves in time, solely from tomograms. Further we have identified a quantifier of the extent of entanglement between subsystems which can be readily obtained from the tomogram and which mirrors the qualitative behavior of other measures of entanglement such as the subsystem von Neumann entropy and the subsystem linear entropy. The procedures that we have demonstrated can be readily adapted to multimode systems.

Estimation of entanglement in bipartite systems directly from tomograms

“…In contrast, the tomogram only provides information about the diagonal elements, although in several complete bases. Even though the tomographic indicator mentioned earlier mimics quite closely the qualitative features of the SVNE and SLE [9], it does not qualify to be a measure. It is therefore necessary to carry out a detailed comparative study between the tomographic indicator, on the one hand, and the SLE and SVNE, on the other hand, in order to assess its efficacy and limitations vis-à-vis standard entanglement measures.…”

“…is obtained by averaging the mutual information over an ideally very large number of values of θ A and θ B over the interval [0, π). In practice (as shown explicitly [9] in the case of the double-well BEC system), however, even as few as 25 values of S(θ A : θ B ) for θ A and θ B chosen at equally-spaced intervals in the range [0, π) suffice to yield a ξ tei that compares well with standard entanglement measures such as the SVNE.…”

“…and λ 1 = (λ 2 + ω 2 1 ) 1/2 . It can then be shown [9] that the state vector at time t is given by |ψ m1,m2 (t) = M m1,m2 (t) |ψ 00 (t) ,…”

Tomographic entanglement indicators in multipartite systems

“…It may be noted that choosing three orthogonal n j 's is equivalent to choosing three mutually unbiased basis sets for the subsystem concerned. Likewise, the measure ξ (AB) tei of the entanglement between the fields A and B is obtained [10] by averaging the corresponding mutual information over a sufficient number of basis sets in the ranges 0 θ a < π and 0 θ b < π.…”

“…In earlier work [10], we identified a tomographic entanglement indicator ξ tei that quantifies the extent of entanglement directly from the relevant tomograms, and assessed its performance vis-à-vis ξ svne and ξ sle in a double-well BEC system with inherent nonlinearities. We also carried out a comparative study between ξ tei and an entanglement indicator ξ ipr obtained from the inverse participation ratio both in the BEC system and in a nonlinear model of a multi-level atom interacting with a radiation field.…”