a cavity has been released by controlling the output coupling rate of the cavity using four-wave mixing in the qubit [@Pfaff2017a]. To the best of our knowledge, only this experiment has demonstrated *on-demand* generation of *traveling* cat states.

In this paper, we propose a simple alternative method for on-demand generation of traveling cat states. Our method is based on a recent theoretical result that a Kerr-nonlinear parametric oscillator (KPO) can generate intracavity cat states deterministically via quantum adiabatic evolution [@Goto2016a; @Puri2017a]. (The KPO has recently attracted attention for its application to quantum computing [@Goto2016a; @Puri2017a; @Goto2016b; @Nigg2017a; @Puri2017b].) In the previous work, the KPO is assumed to be lossless in ideal cases, and therefore the cat states are confined inside the KPO. In the present work, we theoretically investigate a coupled system of a KPO and a one-dimensional system (output mode). It turns out that the cat states generated inside a KPO can be released into the output mode by controlling the parametric pump amplitude dynamically, while the output coupling rate is constant. Hence by using a KPO, we can generate *traveling* cat states *on demand* without controlling the output coupling rate.

Model
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![Coupled system of a KPO and 