Cmd/Ctrl-click your logo layer thumbnail, making an active selection. Activate the Marquee tool, taping down and right, one to three times on the keyboard arrow keys. Press Cmd/Ctrl+Shift+I to invert your selection, next creating a new layer called ‘Logo Shadow’.
Paint to the active selection on this layer, using a dark grey tone, or a much darker value of your backdrop colour, with a soft brush, at 50%. Cmd/Ctrl-click your logo layer thumbnail once more, applying a layer mask to your Logo Shadow layer.
Cmd/Ctrl-click your logo thumbnail, activate your layer mask and go to Filter>Blur>Gaussian Blur. Apply a low-pixel Radius. Cmd/Ctrl-click the logo thumbnail again and invert, creating a new Outline layer. Select a 2px white hard brush, applying to the right outer edges.