Which protocol is responsible for converting the logical address to a physical address?

(ARP) or Address Resolution Protocol does the Job , The RARP (Reverse ARP) does the contrary

Address Resolution Protocol (ARP) ARP is mostly generally used to translate IP

ARP...The address resolution protocol (arp) is a protocolused by the Internet Protocol (IP) [RFC826], specifically IPv4, to map IP network addresses to the hardware addresses used by a data link protocol

ARP... Address Resolution Protocol 

Before answering, I'd like to highlight that the assumption here on logical/physical addressing is that of the networking domain, specifically in the Ethernet implementation.

So the question should read: what protocol is used to map IP addresses to MAC addresses.

In which case, the answer, like others have stated, is Address Resolution Protocol (ARP).

To be precise, this answer only applies to mapping IP addresses to MAC addresses in a TCP/IP network, running on Ethernet media.  Other forms of logical addresses, e.g. Fully Qualified Domain Names (FQDN), for example, use higher layer protocols (DNS in this case) to map a fully qualified hostname to an IP address notation, which is yet another form of logical address.

Sorry to be pedantic, but in order to get a correct and valid answer, one must be precise.

Hope this helps ..

 ETHERNET IPV4 L2  networks use "ARP"  to obtain Mac address of an IP address with in their segment.IPV6  has a similar Neighbor Discovery protocol .

Address Resolution Protocol (ARP) does this job.