This isn't possible with the WP_Query API:
Note: The queries above return posts for a specific date period in history, i.e. "Posts from X year, X month, X day". They are unable to fetch posts from a timespan relative to the present, so queries like "Posts from the last 30 days" or "Posts from the last year" are not possible with a basic query, and require use of the posts_where filter to be completed. The examples below use the posts_where filter, and should be modifyable for most time-relative queries.
So you will need to add a custom filter before your query, perform the query and then remove the query again (so it doesn't effect other queries).
// Create a new filtering function that will add our where clause to the query
function my_restrict_to_years( $where = '' ) {
// posts in years 2008-2010
$where .= " AND post_date >= '2008-01-01' AND post_date <= '2010-12-31'";
return $where;
}
add_filter( 'posts_where', 'my_restrict_to_years' );
$args=array(
'cat' => '11', //Category I'm targeting
);
$my_query = new WP_Query($args);
remove_filter( 'posts_where', 'my_restrict_to_years' );
Not tested