  We develop a theoretical framework to describe how zero-photon detection may
be utilized to enhance laser cooling via the anti-Stokes interaction and,
somewhat surprisingly, enable cooling via the Stokes interaction commonly
associated with heating. Our description includes both pulsed and continuous
measurements as well as optical detection efficiency and open-system dynamics.
For both cases, we discuss how the cooling depends on the system parameters
such as detection efficiency and optomechanical cooperativity, and we study the
continuous-measurement-induced dynamics, contrasting to single-photon detection
events. For the Stokes case, we explore the interplay between cooling and
heating via optomechanical parametric amplification, and we find the efficiency
required to cool a mechanical oscillator via zero-photon detection. This work
serves as a companion article to the recent experiment [E. A. Cryer-Jenkins, K.
D. Major, et al., arXiv:2408.01734 (2024)], which demonstrated enhanced laser
cooling of a mechanical oscillator via zero-photon detection on the anti-Stokes
signal. The framework developed here provides new approaches for cooling
mechanical resonators that can be applied to a wide range of areas including
nonclassical state preparation, quantum thermodynamics, and avoiding the often
unwanted heating effects of parametric amplification.
