System mixedness as a contributor to entanglement in the Jaynes–Cummings model

Abstract

The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber-Lachs state were investigated in the framework of the Jaynes-Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.

Effect of thermal noise on atom-field interaction: Glauber-Lachs versus mixing

“…If λ k are the eigenvalues ofρ P T (t), then N (t) = k [|λ k | − λ k ] /2. In the case of atom-field evolution under Jaynes-Cummings interaction, the time-averaged entanglement depends on the initial mixedness of the bipartite state [14]. The mixedness of the DTS…”

Bound entanglement in the Jaynes–Cummings model

“…One reaches the same condition by finding an upper bound to the concurrence of the state projecting the qudit into the subspace spanned by two consecutive Fock states |n , |n + 1 [17]. Another way to arrive to the constraints given by (19) is by using the bound on the concurrence for a 2 × N dimensional system derived in [50] in which a set of N(N − 1)/2 quantities are proposed to bound the concurrence of the system. Of these only N − 1 turn out to be not trivial and they express the same bounds contained in (19).…”

“…Another way to arrive to the constraints given by (19) is by using the bound on the concurrence for a 2 × N dimensional system derived in [50] in which a set of N(N − 1)/2 quantities are proposed to bound the concurrence of the system. Of these only N − 1 turn out to be not trivial and they express the same bounds contained in (19). Using the results from [50] the following bound for the concurrence is found:…”

“…Local filtering operations map entangled states to entangled states and separable states to separable states and thus σ is still positive and is PPT. The positivity and PPT conditions equivalent to equations (12,19) are now…”

“…While some of the previous results concerned pure states [9][10][11], mixed state entanglement has been addressed using either entropic relations [12][13][14][15][16] or detection techniques drawn directly from the field of quantum information. In particular, projecting the Fock space of the EMF mode onto a two-dimensional subspace results in a combined Hilbert space that essentially reduces to a two-qubit system whose entanglement properties are well understood [17][18][19][20][21][22]. Also, the positive partial transpose (PPT) criterion introduced by Peres [23] has been used to this aim [24][25][26][27][28].…”