This dataset contains the source files of the research paper

"Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological 
stochastic background of spacetime"
Diego A. Quinones, Teodora Oniga, Benjamin T. H. Varcoe, Charles H.-T. Wang
arXiv:1702.03905 [gr-qc]
(see related ressources)

The file SGW.tex is the source file and the files SWG_fig1a.eps, SWG_fig1b.eps, SWG_fig2a.eps, SWG_fig2b.eps, 
SWG_fig3a.eps, SWG_fig3b.eps and SWG_fig4.eps figures necessaries to generate the paper in file SGW.pdf.

The files SWG_fig1a.png and SWG_fig1b.png are Simulations with N atoms using the master equation
(1) in the file SWG.pdf with the quantum dissipator (35) in the same file for the correlated 
2-level atoms and negligible matter interaction Hint.From Eq. (43) the relaxation time is approximately given
by tN = (NG0)-1. The initial state of the forms (30) and (31) at t = 0 is given by |0, Ni = |p = N + 1i 
with all N atoms occupying the excited atomic level. During the dynamical evolution, 
the density matrix remains diagonal of the form (37) and relaxes into an inverse exponential profile 
represented by Eq. (46), yielding the asymptotic height of ?p=1 =[Ngw(?0)(1 - e-N/Ngw(?0))]-1. 
The stochastic gravitational wave distribution function evaluated at the atomic transitionfrequency ?0 
is chosen to be Ngw(?0) = 1. Accordingly, inplot SWG_fig1a.png with N = 100 atoms, the initial 
state corresponding to the spike of height one at (p,G0t) = (101, 0) relaxes into an inverse exponential
profile peaked at (p,G0t) = (1, 0.1) on time scale of tN = 0.01/G0. 
Similarly, in plot SWG_fig1b.png with N = 200 atoms, the initial state corresponding to the spike
of height one at (p,G0t) = (201, 0) relaxes into an inverse exponential profile similarly peaked 
at (p,G0t) = (1, 0.1) but on a halved time scale of tN = 0.005/G0.


The files SWG_fig2a.png and SWG_fig2b.png are simulations of short-time collective spontaneous delays
due to vacuum fluctuations of spacetime without additional stochastic gravitational waves so 
that Ngw(?0) = 0. In plot SWG_fig2a.png with N = 100 atoms, the initial state corresponds
to the spike of height one at (p, t) = (50, 0). As shown, in file SGW.pdf it delays into adjacent 
lower states with a relaxation time tvac = 4/(N 2G0) = 0.0004/G0 according to Eqs. (61) and (62) in the file.
In plot SWG_fig2b.png with N = 200 atoms, the initial state corresponds to the spike of 
height one at (p, t) = (100, 0). For a doubled N, this state delays into adjacent lower states with a quarter
of the preceding relaxation time with tvac = 4/(N 2G0) = 0.0001/G0.


The files SWG_fig3a.png and SWG_fig3b.png are simulations of short-time collective transitions due
to vacuum fluctuations of spacetime and additional stochastic gravitational waves with a 
chosen Ngw(?0) = 1. In plot SWG_fig3a.png with N = 100 atoms, the initial state corresponds to the
spike of height one at (p, t) = (50, 0). While this state delays similar to the descriptions for 
files SWG_fig2a.png and SWG_fig2b.png, its adjacent higher state with p = 51 is excited with an initial time 
scale of tgw = 4/(N 2G0Ngw(?0)) = 0.0004/G0 according to Eqs. (60) and (62) in file SGW.pdf. 
In plot SWG_fig3b.png with N = 200 atoms, the initial state corresponds to the spike of height one 
at (p, t) = (100, 0). For a doubled N, its adjacent higher state with p = 101 is excited
with a quarter of the preceding initial time scale with tgw = 4/(N 2G0Ngw(?0)) = 0.0001/G0.


The file SWG_fig4.png is the theoretical lower bounds for the spectral functions of gravitational 
waves ?(f) determined by Eq. (66) in file SGW.pdf that could be detected using an ensemble of 
correleted 2-level Rydberglike atoms given their total atom number N, excitation principal
quantum number n, and measurement time t . For conventional stochastic gravitational waves, 
we have ?(f) = ?gw(f) with t = tgw, whereas for zero-point, i.e. vacuum, meric fluctuations,
we have ?(f) = ?vac(f) with t = tvac introduced in this work by Eqs. (62) and (64). In both cases, 
we choose t = 1 sec as a physically reasonable overall transition time scale for Rydberg atoms in 
generating the above diagram. As shown in file SGW.pdf, the atomic transition frequency f is related to the
quantum number n by Eq. (65). The lower bounds for ?(f) given by Eq. (66) for five selected total atom 
numbers N are plotted with inclined solid lines. It suggests, for example, measuring the zero-point 
fluctuations of spacetime would require 1028 atoms with n = 50 at f = 100 GHz approximatly.
For comparison, we have superimposed the expected spectral functions of stochastic gravitational waves from 
various sources such as inflation and that may be detected by different
methods such as LIGO from Ref. [20] in file SGW.pdf.