1. Some general remarks about the significance of this period to our understanding of the rise of Jerusalem as a religious symbol
The Babylonian exile of the Jews has become proverbial. Thus when, for example, Protestant reformer of the 16th century Martin Luther speaks of a "Babylonian captivity of the Church" he does not refer to an actual exile but of a period of spiritual enslavement of the Church to the pontiff in Rome, a period now coming to its end in Luther’s own reform. Luther and others assume the posture of a prophet or a messianic king, i.e., an "anointed one," who brings about some sort of redemption. This messianic connotation of the end of exile (or captivity) is based on the oracles of the anonymous prophet known as Deutero-Isaiah (Isa 40-55), esp. Isa 45, where the prophet calls King Cyrus of Persia "the anointed of YHWH."
How did the Babylonian exile of the Jews grow "larger than life" and take on symbolic value beyond the actual historical circumstances? The reason why the Judahite exile in Babylon became proverbial is because, during and after the exile, the exiled Judahites developed an unprecedented creative energy that resulted in the final editing of the Pentateuch, of the deuteronomistic work of history (the Books of Samuel and Kings), of many of the prophetic books and also in the composition of new literature (such as the Chronistic works of history, i.e., Ezra, Nehemiah, and Chronicles) that reflects the concerns of the returnees from Babylone often more directly than the older literature. In other words, whether in form of careful reverential editing or in form of the composition of new works, the priests and scribes of the exilic community decisively shaped what we simply consider the biblical world view.
Since the exilic and postexilic redactors and authors often hide their own contribution to the sacred literature of Israel in subtle additions to older works rather than openly stating their authorship, since they furthermore prefer anonymity or attribution of their works to the great figures of the golden age before the destruction of Judah, Jerusalem, and the Solomonic temple, since they therefore create the literary fiction that the result of their deliberation was already available to the personages representing the golden age, we must deconstruct their fiction to get a sense of their real achievements. To this day, fundamentalist and naïve readers habituated to taking biblical stories as the literal truth have trouble imagining that the story framing the Mosaic legislation (from the creation of the world to the appearance of the LORD at Sinai, and from forty years of migration in the desert to the conquest under Joshua) may reflect the concerns of exilic or postexilic authors/editors rather than actual events truthfully (and passively) recorded.
If the above is even vaguely accurate, it follows that the role of Jerusalem in biblical literature is decisively shaped by the experience of loss and destruction reflected in exilic and early post-exilic literature (and in the editorial processes older texts and traditions underwent at this time). For the evident reason of the political dimension of loss and of all hopes for reconstruction, Jerusalem, in fact, is henceforth one of the three central religio-political symbols of Jewish (as subsequently of Christian and Islamic) eschatology, i.e., of any monotheistic teaching about the ultimate things to come, about the end of history, the final condition of the world, and the like.
2. Some notes on the changes from pre-exilic Israelite/Judahite culture to the early Jewish culture of the exile and of early post-exilic times
Pre-exilic
Before the exile, Judah was a monarchy that had taken on the traditions of "Israel," the tribal community once united under King David. It absorbed many of the pan-Israelite traditions but it still was a commonwealth, a political entity with no other purpose than to exist, survive, and thrive as a political entity.
Among the major institutions of pre-exilic Judah are:
Post-exilic
After the exile, Judah was politically rebuilt as a Persian satrapy, a semi-autonomous administrative province, ruled by a priestly elite that remigrated from Babylonia and whose views and attitudes were shaped by the religious blue-prints for reconstruction drafted in the exile. They were at odds with the local population, rigorously enforced separation from the mixed multitude of inhabitants of Judah, and ruled on the basis of the Torah. This code of law was promulgated by Ezra in the early 4th century BCE and it served as the legal ideal of a theocratic state (ruled by priests rather than kings). According to the later rabbis, the institution of the Torah as the basic law (in addition to which there must have been oral law traditions of various kinds) brought the earlier institution of prophecy to an end.
Religious practices now included the keeping of the Sabbath as a strictly enforced day of rest on every seventh day (roughly conforming to quarters of the lunar month but without real parallel in any other ancient culture). Persian influence is noticeable in Jewish apocalyptic literature (symbolism of good vs. evil, angelology, figure of Satan as "fallen angel" and personified evil). The administrative language of Judah is now Aramaic, the language of the Persian empire, rather than Hebrew. Important new institution are the Levites as auxilliary priests (cf. the emphasis in the Books of Chronicles on this institution with the virtual absence thereof in Samuel and Kings!).
The emerging Jewish religion is not just the cult of a state (in fact, it is no longer a state cult at all) but a religion with a sacred center in Jerusalem practiced and adhered to by an extended diasporah. This means, for example, that Jerusalem becomes the focus of elaborate pilgrimages and it is the recipient of lavish gifts and of taxes due to the sanctuary and its officials.
In comparison to its predecessors (Josiah’s monolatrism, the commandment in the Pentateuch to worship YWHW alone), this early Judaism is a monotheistic religion (see Isaiah 45!).
It should be noted that when the returnees (Armstrong: the "Golah") established this religion in Jerusalem, a Egyptian diaspora (dating back presumably to the time of the destruction of Jerusalem in 586) practiced Yahwism at a temple of their own located on the island of Elephantine (upper Nile). In other words, "Judaism" was not a monolithic practice and the Babylonian diaspora was not the only form in which Judah- and Israel-related traditions were continued after the destruction of the states of Israel and Judah. Of the temple in Elephantine we know futher that it was destroyed in 410 and rebuilt in 402. It was the temple of a Jewish military colony near the southern border of Egypt (the latter having lost independence to the Persians) and it continued to function in Second Temple times. The community of Elephantine was on friendly terms with the priestly establishment in Jerusalem despite the fact that it initially practiced syncretistic forms of worship (very much like the practices in Jerusalem before the destruction of 586) that were only gradually abandoned in consultation with the Second Temple priesthood in Jerusalem. What little we know about the history of early Second Temple Judaism from other sources is augmented from fragments of letters written on papyrus found by modern archeologists at Elephantine (excavated when the Assuan dam was built in the 1960s).
627-c. 585 Prophet Jeremiah
597/6 First deportation from Judah to Babylonia
593-571 Prophet Ezekiel
586 Destruction of the Kingdom of Judah, of Jerusalem, and of the Solomonic temple. Mass deportation to Babylonia and flight to Egypt.
539 Cyrus of Persia conquers Babylonia
538 Edict of Cyrus: release of people subjugated by the Babylonians, among them the Judahites
After 538 Sheshbazzar (davidic lineage) governor (pekhah) of satrapy (Persian province) of Yehud (Judah). Immediately tries to lay the foundations of a new temple. This act and similar ones undertaken by his successors is looked at with suspicion by the administration of the larger province of Samerina (the erstwhile Samaria/Israel).
Between 538 and 522 Arrival of the next pekhah, Zerubbavel (note the Babylonian theophoric name!). Z. was also of the davidic lineage. Under his governance, the high priesthood was reestablished. The lineage of the new high priest, Jehoshua ben Jehozadak, is Zadokite, i.e., it goes back to the Jebusite elite of Jerusalem that continued to serve under King David.
522-486 Persian King Darius I
c. 520 Prophets Haggai and Zecharias: strong messsianic expectations, hope for reconstruction, encourage Judahites to rebuild the temple.
520-515 Second temple built, altar of sacrifice rededicated in 515.
465/4-424 Persian king Artaxerxes I (Time of Ezra?)
445 Arrival of Nehemiah. Samarians (Sanballat), Ammonites (located near the city of Damascus, Syria), and various groups of Arabs living in and around Jerusalem oppose this attempt of Yehud/Judah at reasserting itself as a politically autonomous commonwealth. Nehemiah nevertheless completes the walls of Jerusalem and attempts to repopulate the city.
403-359 Persian king Artaxerxes II: Ezra the Scribe was presumably active during his time. (Others think he was active during the reign of Artaxerxes I which would make him a contemporary of Nehemiah).
332 Alexander the Great (Macedonian king) conquers Persian and Egyptian empires. This ends the time of Persian rule and ushers in the Hellenization of the entire Middle East. Note that Jews continue to speak Aramaic and practice the religion adopted during Persian times. This will lead to violent cultural and political conflicts during the Hellenistic period, ultimately leading to the war of defiance against the Roman empire during which Judah, Jerusalem, and the Temple (symbol of politico-religious independence) was to be destroyed for the second time.
For further reading: Lawrence H. Schiffman, From Text to Tradition. A History of Second Temple Rabbinic Judaism (Hoboken: Ktav, 1991), Martin S. Jaffee, Early Judaism (Upper Saddle River/NJ: Prentice Hall, 1997).