When is rotation around double bonds to form cis-trans isomers allowed?
In rhodopsin this normally occurs only after the 11 cis in the chromophore (a retinylidene schiff base) is placed into an electronically excited singlet state after absorbing a visible photon. This excited state has one electron promoted from the HOMO orbital into the LUMO (antibonding) orbital of the conjugated $\pi$ system. Most data has been obtained from the protein bactoeriorhodposin, which acts a  proton pump, as it is easier to use and has a similar chromophore to rhodopsin. 

In the protein the rhodopsin molecule is somewhat strained by adjacent (tryptophan) and other amino acids. The isomerisation takes about 200fs so is extremely fast; among the fastest reaction ever studied. After that there is a series of at least 6 intermediates that slowly returns the trans molecule to the cis form and these thermal reactions take about a second or so. 

The initial reaction is thought to proceed as follows; just after the electronically excited state is formed calculations indicate that the cis bond is rapidly stretched (~20 femtoseconds) and experiments show that a  small barrier exists between the minimum energy of the excited state and the pathway to isomerisation. At or close to this barrier rotation &amp; oscillation of the groups either side of the 'double' bond occur during isomerisation. (Kobayashi et.al Nature, 2001, v414,p531).

Many experiments have ben performed on trans/cis stilbene isomerisation which shows similar behaviour. Trans stilbene is the most stable isomer and can be converted into the cis also by photo excitation. The cis ground state has a relatively low barrier to the trans at room temperature (the opposite is not true) and so reverts to the trans spontaneously. This does not happen in rhodopsin  so the protein has to go through a complex set of reactions.