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We develop a dissipative quantum state preparation scheme for the creation ofphase- and number-squeezed states. It utilizes ultracold atoms in a double-wellconfiguration immersed in a background Bose-Einstein condensate, with thelatter consisting of an atom species different from the atoms in the doublewell and acting as a dissipative quantum reservoir. We derive a master equationfor this system starting from microscopic physics, and show that squeezingdevelops on a time scale proportional to $1/N$, where $N$ is the number ofparticles in the double well. This scaling, caused by bosonic enhancement,allows us to make the time scale for the creation of squeezed states veryshort. The lifetime of squeezed states is limited by dephasing arising from theintrinsic structure of the setup. However, the dephasing can be avoided bystroboscopically switching the driving off and on. We show that this approachleads to robust stationary squeezed states. Finally, we provide the necessaryingredients for a potential experimental implementation by specifying aparameter regime for rubidium atoms that leads to squeezed states.

Dissipative preparation of phase- and number-squeezed states with ultracold atoms