  We conduct intensity mapping to probe for extended diffuse Ly$\alpha$
emission around Ly$\alpha$ emitters (LAEs) at $z\sim2-7$, exploiting very deep
($\sim26$ mag at $5\sigma$) and large-area ($\sim4.5$ deg$^2$) Subaru/Hyper
Suprime-Cam narrow-band (NB) images and large LAE catalogs consisting of a
total of 1781 LAEs at $z=2.2$, $3.3$, $5.7$, and $6.6$ obtained by the HSC-SSP
SILVERRUSH and CHORUS projects. We calculate the spatial correlations of these
LAEs with $\sim1-2$ billion pixel flux values of the NB images, deriving the
average Ly$\alpha$ surface brightness (${\rm SB_{Ly\alpha}}$) radial profiles
around the LAEs. By carefully estimating systematics such as fluctuations of
sky background and point spread functions, we detect diffuse Ly$\alpha$
emission ($\sim10^{-20}-10^{-19}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$) at
$100-1000$ comoving kpc around $z=3.3$ LAEs at the $4.1\sigma$ level and
tentatively ($\sim2\sigma$) at the other redshifts, beyond the virial radius of
a dark-matter halo with a mass of $10^{11}\ M_\odot$. While the observed ${\rm
SB_{Ly\alpha}}$ profiles have similar amplitudes at $z=2.2-6.6$ within the
uncertainties, the intrinsic ${\rm SB_{Ly\alpha}}$ profiles (corrected for the
cosmological dimming effect) increase toward high redshifts. This trend may be
explained by increasing hydrogen gas density due to the evolution of the cosmic
volume. Comparisons with theoretical models suggest that extended Ly$\alpha$
emission around a LAE is powered by resonantly scattered Ly$\alpha$ photons in
the CGM and IGM that originates from the inner part of the LAE, and/or
neighboring galaxies around the LAE.
