  Intracavity second harmonic generation is one of the simplest of the quantum
optical processes and is well within the expertise of most optical
laboratories. It is well understood and characterised, both theoretically and
experimentally. We show that it can be a source of continuous variable
asymmetric Gaussian harmonic steering with fields which have a coherent
excitation, hence combining the important effects of harmonic entanglement and
asymmetric steering in one easily controllable device, adjustable by the simple
means of tuning the cavity loss rates at the fundamental and harmonic
frequencies. We find that whether quantum steering is available via the
standard measurements of the Einstein-Podolsky-Rosen correlations can depend on
which quadrature measurements are inferred from output spectral measurements of
the fundamental and the harmonic. Altering the ratios of the cavity loss rates
can be used to tune the regions where symmetric steering is available, with the
results becoming asymmetric over all frequencies as the cavity damping at the
fundamental frequency becomes significantly greater than at the harmonic.
  This asymmetry and its functional dependence on frequency is a potential new
tool for experimental quantum information science, with possible utility for
quantum key distribution. Although we show the effect here for Gaussian
measurements of the quadratures, and cannot rule out a return of the steering
symmetry for some class of non-Gaussian measurements, we note here that the
system obeys Gaussian statistics in the operating regime investigated and
Gaussian inference is at least as accurate as any other method for calculating
the necessary correlations. Perhaps most importantly, this system is simpler
than any other methods we are aware of which have been used or proposed to
create asymmetric steering.
