Lighting creates sharp shadows, doesn't gently fade

I'm making a voxel engine as a project, and I've hit a lighting snag.

Basically, when you punch out some blocks and walk in, the shadows from Unity's lighting system don't gently fade off. They just sharply appear.

Instead of a realistic "The deeper you go the darker it gets" type of system, you get a "Lit by sun or cast into shadow" is/isn't type of transition.

I tried messing with the directional lights lighting the scene, it did nothing.

How do I make smooth, drop-off shadows? Do I need to roll my own lighting solution?

 

This is generally handled with ambient occlusion or ambient obscuration, basically some type of "closer I am to a deep notch in geometry, the darker I make the pixel."

There are various runtime solutions to this, including screenspace techniques such as SSAO that approximate the effect for runtime use.

 

Alternately - make your ambient light color black.

 

I made it black to try, it did not go smoothly. It doesn't go from lit to shadowy to black.

It just goes from lit to pitch-darkness. Sunlight next to midnight-shadow.