M ,(2)R(m; N ) = N k+m[(m + 1)]2 ( N – k
M ,(2)R(m; N ) = N k+m[(m + 1)]2 ( N – k – m + 1) . ( N + 1) ( m + k + 1)(3)Symmetry 2021, 13,3 ofwhere (.) would be the Gamma function, k could be the quantity of added photons to the Safranin Purity coherent state of MP and [ N/2] is the greatest integer, which is less than or equal to N. The 3LA-field system is evaluated applying the time-dependent kind Schr inger equation, presented as d ^ i | AF (t) = H I | AF (t) . (four) dt The bipartite method wave function at t = 0 is assumed to take the kind| AF (0) =| A (0) | F (0) =|u |z; [ N/2]The final 3LA-field state at any time is formulated as(five)| AF (t) =[ N/2]n =0 j =Xj (n, t)|n + k + j – 1, j.(six)Under the Hamiltonian system (1) and substituting inside the Schr inger UCB-5307 Apoptosis Equation (4), we are able to get a three-coupled ODEidX2 (n,t) dt= -i X1 (n, t) + 1 f (n) nX2 (n – 2, t), 2 = 1 f (n + two) n + 2X1 (n + 2, t)+ 2 f (n + 1) n + 1X3 (n – two, t), dX (n,t) i 3dt = 2 f (n + 2) n + 2X2 (n + 2, t).idX1 (n,t) dt(7)The reduced density operator 3LA (t), primarily based on 3LA-field state, is written as 11 3LA (t) = TrF [(t)] = TrF AF (t) AF (t) = 21 31 12 22 32 13 23 , 33 (8)in which the diagonal elements with the reduced density matrix 3LA (t) describe the probabilities with the atomic occupation at the levels of l, m, and u. Because the lowered atomic density (8) was obtained, the other quantities related to the dynamical functionality from the degree of entanglement, the quantum Fisher info, along with the photon statistics of the field might be investigated [35]. To quantify the entanglement amongst 3LA along with the field inside the PACSMP, we examine the entanglement primarily based on the evolution of von Neumann entropy [36] S3LA = -Tr3LA 3LA ln 3LA , Therefore, the entanglement volume of the 3LA-field state takes the kind S3LA = – wherej 3 j ln j,(9)(ten)j =denotes the density operator’s eigenvalues (8) to satisfy the 3rd-order equation-+ Y+ Y2 =(11)exactly where Y1 = 33 22 + 22 11 + 11 33 – 12 two – 23 two – 31 two , Y2 = -33 22 11 – 12 23 31 – 13 21 32 + 11 23 2 + 22 13 2 + 33 12 2 . (12)Equation (11) is thought to contain three dissimilar real roots introduced throughj=1 2 + cos( j ) 31 – 3Y1 ,(13)Symmetry 2021, 13,four ofwhere3 j = cos–9Y1 – 27Y2 +(1 – 3Y1 )+ ( j – 1)two , with j = 1, two, 3.(14)3. The Atomic Population and Symmetry 2021, 13, x FOR PEER Assessment In this section, the discovery of periods of revival and collapse is explored. The collapse revival periods are characterized working with their association with the entanglement of five of ten field and qubits [379]. Additionally, the impact with the function of deformation and also the parameter of decay on the collapse and revival periods are examined.Figure 1. The time evolution on the atomic population probability 11 of a 3LA interaction together with the Figure 1. The time evolution from the atomic population probability of a 3LA interaction using the field of radiation within PACSMP (photon-added coherent state of Morse prospective) where MP field of radiation inside PACSMP (photon-added coherent state of Morse prospective) where thethe MP parameter = 20.20. The 11 is plotted, with and without thecoupling and based on the intenparameter N = The is plotted, with and without the coupling and depending on the intensity, ^ ^ ^ as f n) ) 1 1 for Figure f (n) = n for (b,d) for Figs. (b,d) respectively. (c,d), precisely the same conditions sity, as ((== for (a,c) and (a,c) and () = respectively. Furthermore, inIn addition, in (c,d), exactly the same circumstances as (a,b) apply but for thefive photons towards the CSMP (i.e., CSMP (i.e., k = 5).(red)blue as (a,b) apply b.
