import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class Text {

    public void startup() {
        final JFrame frame = new JFrame("Just a demo");
        final JButton north = new JButton("North");
        final JTextArea text = new JTextArea(15,20);
        final JScrollPane scroller = new JScrollPane(text);
        final JButton south = new JButton("South");
        frame.add(north, BorderLayout.PAGE_START);
        frame.add(scroller, BorderLayout.CENTER);
        frame.add(south, BorderLayout.PAGE_END);
        frame.pack();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setVisible(true);
        Action next = new AbstractAction("jumptonext"){
                @Override public void actionPerformed(ActionEvent e){
                    KeyboardFocusManager.getCurrentKeyboardFocusManager().focusNextComponent(text);
                }
            };
        text.getInputMap().put(KeyStroke.getKeyStroke(KeyEvent.VK_TAB,0), "jumpnext");
        text.getActionMap().put("jumpnext",next);
        frame.addWindowListener(new WindowAdapter(){
                @Override public void windowOpened(WindowEvent e){
                    text.requestFocusInWindow();
                }
            });
    }

    public static void main(final java.lang.String[] args) {
        EventQueue.invokeLater(new java.lang.Runnable(){
                @Override public void run(){
                    new Text().startup();
                }
            });
    }
}

------解决方案--------------------

楼上的方法可以借鉴下。
你给JTextArea添加Tab事件
当触发Tab的时候你就在TextArea2中获取焦点。