Recent advances in high-intensity laser-produced plasmas have demonstrated their potential as compact charge particle accelerators. Unlike conventional accelerators, transient quasi-static charge separation acceleration fields in laser produced plasmas are highly localized and orders of magnitude larger. Manipulating these ion accelerators, to convert the fast ions to neutral atoms with little change in momentum, transform these to a bright source of MeV atoms. The emittance of the neutral atom beam would be similar to that expected for an ion beam. Since intense laser-produced plasmas have been demonstrated to produce high-brightness-low-emittance beams, it is possible to envisage generation of high-flux, low-emittance, high energy neutral atom beams in length scales of less than a millimeter. Here, we show a scheme where more than 80% of the fast ions are reduced to energetic neutral atoms and demonstrate the feasibility of a high energy neutral atom accelerator that could significantly impact applications in neutral atom lithography and diagnostics.