Sorry I was late to respond. I was out of office.
Ok, to start with:
The baby is a US citizen no matter what. Only children of A visa (diplomats) do not have that previllage.
A mere fact that the baby was born here will not affect the L-1 of the father.
Once a child is born here, normally parents apply for a US passport for the child.
The child after attainment of age of 21 can sponser his/her immediate relatives.
Here's an insight to citizenship by birth:
Citizenship by birth (INA § 301, 8 USC § 1401)
The US law on citizenship by birth incorporates two traditional legal principles:
a. Jus soli ("right of the soil"), under which citizenship results from being born in the US, and b. ius sanguinis ("right of the blood"), under which citizenship results from having an American parent or parents.
Each of these principles is subject to certain restrictions. For example, children born in the US to foreign diplomats are not US citizens. Also, children born abroad to parents who have US citizenship but have never lived in the US are not US citizens (this rule being designed to prevent the proliferation of endless generations of foreign-born and -raised "Americans").
Many dual-citizenship situations result from the interaction of two countries' implementations of ius soli and/or ius sanguinis in their respective citizenship laws. For example, a child might acquire the citizenship of the country in which he was born (via ius soli), and also the citizenship of his parents' country (via ius sanguinis), and as a result start life as a dual citizen.
Section 301 of the INA [8 USC § 1401] defines the following classes of people as having US citizenship from the time of birth:
anyone born in the US and subject to its jurisdiction (basically meaning anyone other than a child of foreign government representatives with diplomatic immunity);
Indians and other aboriginal people born in the US;
anyone born outside the US, if at least one parent is a US citizen and certain residency or physical presence requirements were fulfilled by the citizen parent or parents prior to the child's birth;
anyone who is found in the US while under five years of age, whose parents cannot be identified, and who is not shown prior to his or her 21st birthday to have been born outside the US.
The only part of this section that is mandated by the 14th Amendment is the part giving citizenship to anyone born in the US and subject to its jurisdiction. The Supreme Court, in Rogers v. Bellei, held that the citizenship status of a person born outside the US to an American parent is not constitutionally protected.
Note that children born in the US to tourists -- or even to illegal aliens -- are US citizens by birth. Some politicians have proposed changing the law to deny citizenship to US-born children unless at least one parent is a US citizen or permanent resident alien ("green card" holder). However, since such children are guaranteed citizenship by the 14th Amendment to the Constitution (see the Supreme Court's rulings in U.S. v. Wong Kim Ark and Afroyim v. Rusk), it is unlikely that this part of the INA could be successfully changed without another amendment to the Constitution. Even attempts to deny citizenship to such children by redefining them as not being subject to US jurisdiction (as proposed, for instance, by various bills in the current Congress) would probably have a rough time in the courts on account of the Wong Kim Ark precedent.
Under certain conditions, children born outside the US may have US citizenship by birth. This depends on whether one or both parents have US citizenship, how long (if at all) the American parent(s) lived in the US prior to the child's birth, and whether the parents were married to each other or not. The rules have changed several times during the 20th century (mostly in a more liberal direction), so the exact date of one's birth can also be important when determining a claim to citizenship by descent.
Under the current law, if both parents are US citizens and are married, then the child is a US citizen if either parent had a "residence" in the US at any time in his or her life prior to the child's birth. It appears (based on my personal experience in registering my own foreign-born infant son with the US consulate in Toronto in 1994) that physical presence in the US for at least one year (even if it was as an infant) is considered sufficient to establish that a parent had a "residence" in the US for purposes of transmitting citizenship.
If one parent is a US citizen, and the other is not, and the parents are married, then the current law says the child is a US citizen if the American parent was physically present in the US for one or more periods of time totalling at least five years, at some time or times in his or her life prior to (but not necessarily immediately prior to) the child's birth. Additionally, at least two years out the required five years of physical presence must have taken place after the parent's 14th birthday; thus, for example, a parent who was born and grew up in the US, but who left before reaching age 16 and never returned, doesn't meet the requirement.
Prior to 14 November 1986, the physical presence requirement in this case was ten years (instead of five) -- including five years (instead of two) spent after the parent's 14th birthday. The requirement was reduced in 1986, but the change did not retroactively make US citizenship available to people born previously who did not meet the old requirement. (Congress's intent not to make this change retroactive was affirmed in 1988 with the passage of Public Law 100-525, § 8(d), 102 Stat. 2619).
Note that physical presence does not require residence in the US. Time spent on vacation in the US may be counted toward the five-year total. Indeed, Americans living abroad with foreign-born children would be well advised to keep track of the exact dates of each trip the children make to the US, in case the question of a grandchild's US citizenship should arise sometime in the future. After we moved back to the US from Canada, I wrote up an affidavit detailing all the times each of my two children had been in the US; I signed it under oath before a notary, sealed it in an envelope, and have filed it with our important documents for possible future use.
If a non-US-born child's parents are not married, the child's claim to US citizenship depends on whether the American parent is the mother or the father. Section 309 of the INA [8 USC § 1409] grants US citizenship at birth to an "illegitimate" child if his/her American mother had previously spent at least one continuous full year in the US. If the child's American parent is his/her father, however, the child has US citizenship at birth only if the father's paternity is formally established and the father agrees in writing to support the child financially. This sex-based disparity was upheld by the Supreme Court in 2001 (Nguyen v. INS).
It is important to note that a foreign-born child whose parents have fulfilled the residency or physical presence requirements is a US citizen by birth. This citizenship is automatic; it is not dependent on the parents' registering the child with a US consulate (though such registration is strongly encouraged) or getting the child a US passport.
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