Can you name a ccc forcing with the following properties?

1. Atomless

2. The least size of a dense set is large, say at least $\aleph_3$, hopefully as big as you like.

3. Existence is consistent with CH.

4. Preserves CH.

If you can think of any, please list as many as you can.

Can you name a ccc forcing with the following properties?

1. Atomless and separative

2. The least size of a dense set is large, say at least $\aleph_3$, hopefully as big as you like.

3. Existence is consistent with CH.

4. Preserves CH.

If you can think of any, please list as many as you can.