How to set java path for elasticsearch

I have java-11 i want to add JAVA_HOME path in elasticsearch how can i do this i edit this in /etc/default/elasticsearch but when do GET /_cluster/stats/ it give me output

"jvm" : {
      "max_uptime_in_millis" : 105897,
      "versions" : [
        {
          "version" : "15.0.1",
          "vm_name" : "OpenJDK 64-Bit Server VM",
          "vm_version" : "15.0.1+9",
          "vm_vendor" : "AdoptOpenJDK",
          "bundled_jdk" : true,
          "using_bundled_jdk" : true,
          "count" : 1
        }
      ],

in /etc/environment file
export JAVA_HOME=/usr/lib/jvm/java-11-openjdk/

place this export JAVA_HOME=/usr/lib/jvm/java-11-openjdk/ in elasticsearch-env file

Out of curiosity, why not using the provided one as you are using the "same" distribution "openjdk"?