  The ability to produce nonclassical wave in a system is essential for
advances in quantum communication and computation. Here, we propose a scheme to
generate highly nonclassical phonon emission statistics -- antibunched wave in
a quantum van der Pol (vdP) oscillator subject to an external driving, both
single- and two-phonon losses. It is found that phonon antibunching depends
significantly on the nonlinear two-phonon loss of the vdP oscillator, where the
degree of the antibunching increases monotonically with the two-phonon loss and
the distinguished parameter regimes with optimal antibunching and single-phonon
emission are identified clearly. In addition, we give an in-depth insight into
strong antibunching in the emitted phonon statistics by analytical calculations
using a three-oscillator-level model, which agree well with the full numerical
simulations employing a master-equation approach and a Schrodinger-equation
approach at weak driving. In turn, the fluorescence phonon emission spectra of
the vdP oscillator, given by the power spectral density, are also evaluated. We
further show that high phonon emission amplitudes, simultaneously accompanied
by strong phonon antibunching, are attainable in the vdP system, which are
beneficial to the correlation measurement in practical experiments. Our
approach only requires a single vdP oscillator, without the need for
reconfiguring the two coupled nonlinear resonators or the complex nanophotonic
structures as compared to the previous unconventional blockade schemes. The
present scheme could inspire methods to achieve antibunching in other systems.
