Analysis:
This quatrain from Saadi Shirazi beautifully encapsulates the unique nature of heartache caused by love. Let's break down each line:

Line 1: آن درد ندارم که طبیبان دانند

"I don’t have a pain that physicians know,"
The speaker is asserting that their pain is of a different kind, a pain that is beyond the realm of physical ailments that doctors can diagnose and treat.

Line 2: دردیست محبت که حبیبان دانند

"It’s a pain of love that only lovers understand."
Here, Saadi emphasizes that the pain he is experiencing is unique to those who have loved and lost. It's a pain that only those who have felt the depths of love can truly comprehend.

Line 3: ما را غم روی آشنایی کشتست

"The sorrow of a familiar face has killed us,"
The speaker suggests that the pain is so intense, it feels like a death. The "familiar face" refers to a loved one, and the sorrow associated with them has caused emotional devastation.

Line 4: این حال نباید که غریبان دانند

"This state should not be known to strangers."
The speaker wishes to keep their pain private. They believe that those who have not experienced love's sorrow cannot fully understand or empathize with their suffering.

Deeper Meaning:
This quatrain explores the profound and often isolating nature of heartbreak. It suggests that:

Love is a unique experience: The pain of love is distinct from physical pain and can only be understood by those who have experienced it.
Heartbreak is a form of death: The intensity of emotional pain is likened to physical death, signifying the end of a part of oneself.
Love and loss are intertwined: The speaker suggests that the joy of love and the pain of loss are inseparable.

This quatrain captures the universal human experience of heartbreak and offers a poignant reminder of the depth of emotion that love can inspire.