Multidimensional transporter device

From Memory Alpha, the free Star Trek reference.

The multidimensional transporter device is a device from the mirror universe capable of transporting a person from one universe into another.

In 2371, Miles 'Smiley' O'Brien used the device to take Benjamin Sisko back to the mirror universe. (DS9: "Through the Looking Glass")

The mirror Jennifer Sisko visited the primary universe a year later using another device. She brought a device for Benjamin Sisko to join her and Jake Sisko in the mirror universe. It was programmed to only allow Sisko to use it. (DS9: "Shattered Mirror")

In 2374 the mirror Bareil Antos used the device to transport to the primary universe to steal an orb. (DS9: "Resurrection")

Miles O'Brien somehow obtained schematics for this device which he gave to Rom to study. In 2375, Rom left a PADD out containing the schematics; Grand Nagus Zek found the PADD and duplicated the interdimensional transporting process, entering the mirror universe in hopes of establishing commercial relations. Ezri Tigan used the device to cross over and recruit Quark in a plan to rescue Zek. (DS9: "The Emperor's New Cloak")