plotting - How to plot a figure like this

I saw a beautiful figure illustrating the optical lattice clock, and would like to make a similar one.

This is the figure (taken from here)

Is it possible to make a similar one using Mathematica?

Here is my try:

Show[
 Plot3D[0.05 (Cos[3 x] Cos[
       3 y])^4, {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}, 
  PlotRange -> {All, All, {-0.1, 0.1}}, PlotPoints -> 200, Mesh -> 60,
   MeshStyle -> Gray, 
  ColorFunction -> (ColorData["GreenPinkTones"][0.5 #3 + 0.5] &)],
 Graphics3D[{Darker[Green], 
   Scale[Sphere[{0, 0, -0.5}], 

    0.25 {\[Pi]/3, \[Pi]/3, .1}, {0, 0, 0}]}, Lighting -> "Neutral"],
 ImageSize -> {651.1743427005708`, 484.8`}, Lighting -> "Neutral", 
 Method -> {"RotationControl" -> "Globe", 
   "RotationControl" -> "Globe"}, 
 PlotRange -> {All, All, {-0.1`, 0.1`}}, 
 PlotRangePadding -> {Automatic, Automatic, Automatic}, 
 ViewAngle -> 0.13079882249358044`, 
 ViewCenter -> {{0.5`, 0.5`, 0.5`}, {0.5218420229698426`, 
    0.6543497570242808`}}, 
 ViewPoint -> {-2.144844931539977`, 

   1.84186142553857`, -1.8593511526229505`}, 
 ViewVertical -> {0.`, 0.`, -1.`}]

Answer

My pc is rather old so there was not much I could do. Maybe no as pretty as in the link but I'm happy because of the result:

r = 35;
p = Show[
     Plot3D[-Sum[2 Exp[-((x - xo)^2 + (y - yo)^2)], {xo, -24, 8, 4}, {yo, -28, 8, 4}],
            {x, -r, r - 4}, {y, -r, r - 4}, Evaluated -> True, 

            PlotRange -> All, PlotPoints -> 200, Mesh -> 300, ImageSize -> 800,
            ColorFunction -> (Blend[{White, White, White, Purple}, -#3] &), 
            ColorFunctionScaling -> False, MeshStyle -> Directive[Thick, GrayLevel@.4]
           ],
     Graphics3D[{Specularity[White, 15], Green, Sphere[{{-4, -4, .2}, {4, 4, .2},
                                                        {0, 8, .2}}, 1]}
           ],
     BoxRatios -> Automatic, Boxed -> False, Axes -> False, Lighting -> "Neutral",     
     ViewVector -> {{10, 20, 11}, {0, 0, 0}}, ViewAngle -> .5];


p = ImageResize[Rasterize[p, "Image", ImageResolution -> 3 72], Scaled[1/3]]

manual blurring :)

Table[ImageTake[p, {799 - i, 800 - i}, All] ~ Blur ~ (i/100),
      {i, 0, 798,2}] // Reverse // Transpose[{#}] & // ImageAssemble

I decided to not play with shadows because there is no easy way and my pc nearly died :)