After setting
actionBar.setHomeButtonEnabled(true);
You have to configure the parent activity in your AndroidManifest.xml
<activity
android:name="com.example.MainActivity"
android:label="@string/app_name"
android:theme="@style/Theme.AppCompat" />
<activity
android:name="com.example.SecondActivity"
android:theme="@style/Theme.AppCompat" >
<meta-data
android:name="android.support.PARENT_ACTIVITY"
android:value="com.example.MainActivity" />
</activity>
Look here for more information http://developer.android.com/training/implementing-navigation/ancestral.html