The electric quadrupole moment and the magnetic moment of the 11 Li halo nucleus have been measured with more than an order of magnitude higher precision than before, |Q| = 33.3(5) mb and µ = 3.6712(3) µN , revealing a 8.8(1.5)% increase of the quadrupole moment relative to that of 9 Li. This result is compared to various models that aim at describing the halo properties. In the shell model an increased quadrupole moment points to a significant occupation of the 1d orbits, whereas in a simple halo picture this can be explained by relating the quadrupole moments of the proton distribution to the charge radii. Advanced models so far fail to reproduce simultaneously the trends observed in the radii and quadrupole moments of the lithium isotopes.PACS numbers: 21.10. Ky, 27.30.+t, 21.60.Cs Since nuclear physicists could produce and investigate bound systems of nucleons in many possible combinations, a wealth of isotopes with unexpected properties have been discovered. For example, some neutron-rich isotopes of light elements, such as 11 Li, were found to have exceptionally large radii [1]. Upon discovery in 1985, this phenomenon was attributed to either large deformation or to a long tail in the matter distribution [2]. Deformation was soon excluded by the spin and magnetic moment of 11 Li belonging to a spherical πp 3/2 state [3]. Considering the weak binding of the last two neutrons [4], one could conclude that such a nuclear system consists of a core with two loosely bound neutrons around it [5]. This is the concept of 'halo' nuclei which has been related to similar phenomena in atomic and molecular physics [6], showing the universality of the concept. To fully unravel the mechanisms leading to the existence of halo nuclei, many types of experiments have been devoted to the investigation of their properties. An observable that gives information on the nuclear charge deformation is the spectroscopic quadrupole moment. By comparing the quadrupole moment of 11 Li to that of 9 Li, one can investigate how the two halo neutrons modify the deformation of the core which contains the three protons. Already fifteen years ago, a first attempt to do so giving Q( 11 Li)/Q( 9 Li) = 1.14(16), suggested just a slight increase in agreement with the halo concept [7]. Unbiasedly, for a nucleus with a neutron magic number of N = 8 one would expect a minimum value of the quadrupole such as for 13 B [8]. If 11 Li has a larger quadrupole moment than 9 Li, it can not be considered as semi-magic, and the two halo neutrons have to be responsible for an expansion or polarization of the proton distribution in the core. The latter, in terms of the shell model, must be understood by an excitation of halo neutrons to the 1d orbits, and a precise value of the 11 Li quadrupole moment may provide evidence for this. The effect of a more extended charge distribution can be estimated on the basis of a recent laser spectroscopy measurement of the charge radius [9]. The increase of the charge radius for 11 Li, as well as other properties of Li isoto...