M ,(two)R(m; N ) = N k+m[(m + 1)]2 ( N - kM ,(two)R(m; N

M ,(two)R(m; N ) = N k+m[(m + 1)]2 ( N – k
M ,(two)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 would be the variety of added photons to the coherent state of MP and [ N/2] could be the greatest integer, that is significantly less than or equal to N. The 3LA-field method is evaluated making use of the time-dependent kind Schr inger equation, presented as d ^ i | AF (t) = H I | AF (t) . (four) dt The bipartite program wave function at t = 0 is assumed to take the type| AF (0) =| A (0) | F (0) =|u |z; [ N/2]The final 3LA-field state at any time is formulated as(5)| AF (t) =[ N/2]n =0 j =Xj (n, t)|n + k + j – 1, j.(6)Under the Hamiltonian method (1) and substituting in the Schr inger Equation (four), we can get a three-coupled ODEidX2 (n,t) dt= -i X1 (n, t) + 1 f (n) nX2 (n – 2, t), two = 1 f (n + 2) n + 2X1 (n + 2, t)+ 2 f (n + 1) n + 1X3 (n – 2, t), dX (n,t) i 3dt = two f (n + 2) n + 2X2 (n + two, t).idX1 (n,t) dt(7)The decreased density operator 3LA (t), based on 3LA-field state, is written as 11 3LA (t) = TrF [(t)] = TrF = 21 31 12 22 32 13 23 , 33 (eight)in which the diagonal components from the decreased density matrix 3LA (t) describe the probabilities with the atomic occupation at the levels of l, m, and u. As the UCB-5307 web reduced atomic density (eight) was PHA-543613 Autophagy obtained, the other quantities associated for the dynamical performance from the degree of entanglement, the quantum Fisher information and facts, and also the photon statistics of your field can be investigated [35]. To quantify the entanglement among 3LA and also the field in the PACSMP, we examine the entanglement based around the evolution of von Neumann entropy [36] S3LA = -Tr3LA 3LA ln 3LA , Therefore, the entanglement quantity of the 3LA-field state requires the kind S3LA = – wherej three j ln j,(9)(10)j =denotes the density operator’s eigenvalues (8) to satisfy the 3rd-order equation-+ Y+ Y2 =(11)where Y1 = 33 22 + 22 11 + 11 33 – 12 two – 23 two – 31 2 , Y2 = -33 22 11 – 12 23 31 – 13 21 32 + 11 23 2 + 22 13 2 + 33 12 two . (12)Equation (11) is believed to contain 3 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)2 , with j = 1, two, three.(14)three. The Atomic Population and Symmetry 2021, 13, x FOR PEER Overview In this section, the discovery of periods of revival and collapse is explored. The collapse revival periods are characterized utilizing their association using the entanglement of five of 10 field and qubits [379]. In addition, the influence on the function of deformation along with the parameter of decay on the collapse and revival periods are examined.Figure 1. The time evolution of your atomic population probability 11 of a 3LA interaction with the Figure 1. The time evolution of the atomic population probability of a 3LA interaction together with the field of radiation within PACSMP (photon-added coherent state of Morse possible) exactly where MP field of radiation within PACSMP (photon-added coherent state of Morse possible) exactly where thethe MP parameter = 20.20. The 11 is plotted, with and without the need of thecoupling and based on the intenparameter N = The is plotted, with and with no the coupling and based on the intensity, ^ ^ ^ as f n) ) 1 1 for Figure f (n) = n for (b,d) for Figs. (b,d) respectively. (c,d), the same circumstances sity, as ((== for (a,c) and (a,c) and () = respectively. In addition, inIn addition, in (c,d), the same circumstances as (a,b) apply but for thefive photons to the CSMP (i.e., CSMP (i.e., k = five).(red)blue as (a,b) apply b.