Recommended reading http://dailyzohar.com/daily-zohar-1712/
“עַל נַהֲרוֹת, בָּבֶל–שָׁם יָשַׁבְנוּ, גַּם-בָּכִינוּ: בְּזָכְרֵנוּ, אֶת-צִיּוֹן”
“By the rivers of Babylon, there we sat down, and wept, when we remembered Zion.”
The mourners of Zion weep over the destruction of the Holy Temple and the exile of the Shechinah.
Zion is the Yessod of Malchut it is the spiritual point that connects the Light to the Holy Temple in Jerusalem. With the destruction we lost the connection to Zion. The Shechina lost its proper dwelling place and the ability to create continuous flow of light to the world.
“עַל הַר-צִיּוֹן שֶׁשָּׁמֵם, שׁוּעָלִים הִלְּכוּ-בוֹ”
“for Mount Zion which lies desolate; jackals prowl over it.”
The ‘Mountain of Zion’ is where the Holy Temple existed. After the exile it became desolated and a place where negativity can freely roam.
The righteous people wake up after midnight when the light of Chassadim begins to reveal in the world and they mourn the exile of the Shechina. When they start reciting Psalms 137, the Holy One Blessed be He is awakened, roars and cries as it is said in Jeremiah 25:30
“יְהוָה מִמָּרוֹם יִשְׁאָג וּמִמְּעוֹן קָדְשׁוֹ יִתֵּן קוֹלוֹ”
“YHVH will roar from on high And utter His voice from His holy habitation;”
The Holy One Blessed be He then remembers that the Israelites are in exile and sheds two tears to the ‘large sea’, which is Binah, and the light of Chassadim spreads down. At that time the rooster crows and God enters the Garden of Eden to be with the righteous souls. They provide the support that we need when we are in exile.