It is felt that:
-in the offer letter PSU must have given the date by which you have to join the PSU.
-you should inquire the formalities to be completed by you within this period, and which documents you need to submit on the date of joining. The PSU may indicate a date within which you need to submit all documents required by them failing which PSU can terminate the employment. This is a HR process, and concerned HR executive shall not hesitate to issue an email or letter to you on this subject. You can have a heart to heart discussion with HR and later you can minute it by email/letter as suitable to you.Based on the requirement of PSU, you can plan for smooth exit formalities with your current employer. You know both the employers better than any body else.
-from your side you can indicate that you shall resign on the close of office hours of a day before you join the duty, and on the date of joining you can produce copy of resignation, along with proof of dispatch ( redg. AD) and POD (if required, which you can obtain from concerned PO), and you shall be able to submit the work experience certificate/service certificate, relieving letter, NOC/NDC (if applicable, otherwise FNF, acknowledgment of company property) if and as and when received from your employer. If you resign with immediate effect you have to tender notice pay as applicable. You may mention to HR in confidence that if they want they can dispatch copy of your resignation to your current employer.
You can also submit notice of resignation with effective date of resignation ( as suitable to you) clearly mentioned in it, addressed to good offices of your appointing authority ,MD, Head-HR, and request the good offices to supply you the acknowledgment of resignation immediately and acceptance of resignation, settlement of your a/c and payment of dues by bank DD and thru redg post, work experience certificate/service certificate, relieving letter, FNF statement, form 16, PF withdrawal/transfer forms,PF accumulation reports, etc, and ensure completion of smooth handing over the charge and exit formalities, within and up to effective date of your resignation. You may request good offices to inform to whom you should handover the company property and the designated employee may be informed with a copy to you to handover the acknowledgment of company property on the spot, and also supply you the original forms/formats for this purpose.
If you tender notice of resignation you can withdraw it before effective date of resignation. If you are willing to pay the monetary penalty of breaking of bond you may mention it in your notice/resignation. Do you the copy of the bond? It shall be appropriate to show the bond to elders in the family, competent and experienced well wishers, lawyer/law firm as company might have incorporated many conditions, in additions to monetary compensation, and you shall need to handle that. Your line management and HR in current company can help you to get a waiver on the bond or exit from the bond, from good offices. This shall be quickest and easiest solution. If you wish you may erase the names and post the copy of bond in forum.