Move logical volume to a new physical disk

I have three logical volumes in a single volume group using a single physical volume (the whole existing disk /dev/sda).

I now want to move one of those logical volumes to a new, faster disk, i.e., going from:

/dev/sda
    |-vg0-root → mounted to /
    |-vg0-foo  → mounted to /foo
    |-vg0-bar  → mounted to /bar

to:

/dev/sda
    |-vg0-root → mounted to /
    |-vg0-foo →  mounted to /foo

/dev/sdb
    |-vg1-bar  → mounted to /bar

From what I understand I cannot use pvmove or vgsplit because there's only one physical volume in the existing volume group.

What's a good approach to achieve this (preferably online)?