[[Edit]] Oracle Java 13 is no longer supported / updated by Oracle, and its latest version is no longer available for download. Please switch to either Oracle Java SE 11 (which is a long term release) or the latest Oracle Java SE 14.
Oracle Java 13 was released earlier this month. Debian, Ubuntu, Linux Mint, Pop!_OS and other Debian / Ubuntu-based Linux distribution users can now install it from the Linux Uprising Java PPA. JDK 13 will receive a minimum of two updates, and it will be followed by Oracle JDK 14 in March 2020.
To check out the enhancements in Java 13, visit the release announcement and the release notes.
It's worth reminding you that Oracle Java uses a commercial license (starting wit Oracle Java 11) that allows downloading and using it with no cost for development and testing only, but it requires paying a fee to use it in production! So I recommend using open source JDK builds, like the Zulu OpenJDK or AdoptOpenJDK builds (as a side note, back when I wrote about Zulu OpenJDK, it was the only open source OpenJDK that had repositories for various Linux distributions but since then, AdoptOpenJDK has also added repositories for DEB and RPM based Linux distributions).
The Oracle Java 13 installer is based on the Web Upd8 Java package (so credits go to the original creators) with minor modifications, and it only works on 64bit, since Oracle only offers 64bit downloads.
This installer automatically downloads Oracle JDK 13, runs update-alternatives for the Java binaries and man pages, and it optionally sets Oracle Java 13 as the default Java version (setting JAVA_HOME, etc.). Once Oracle will stop providing public Oracle Java 13 downloads (when it will require users to login to download Oracle Java 13), I will create a new package, like I did for Oracle Java 11 (as long as it's still available, and there are new versions), which will allow you to download the Oracle Java 13 .tar.gz yourself and place it in a folder on your system, then the installer will use that to set everything up.
Also see: How To Install Oracle Java 12 (JDK 12) In Ubuntu, Linux Mint Or Debian (Using PPA).
As a reminder, Oracle java 12 and 10 have reached the end of public updates, therefore they are longer available for download, so no installers are provided for these versions.