  Time delays of electrons emitted from an isotropic initial state and leaving
behind an isotropic ion are assumed to be angle-independent. Using an
interferometric method involving XUV attosecond pulse trains and an IR probe
field in combination with a detection scheme, which allows for full 3D momentum
resolution, we show that measured time delays between electrons liberated from
the $1s^2$ spherically symmetric ground state of helium depend on the emission
direction of the electrons relative to the linear polarization axis of the
ionizing XUV light. Such time-delay anisotropy, for which we measure values as
large as 60 attoseconds, is caused by the interplay between final quantum
states with different symmetry and arises naturally whenever the
photoionization process involves the exchange of more than one photon in the
field of the parent-ion. With the support of accurate theoretical models, the
angular dependence of the time delay is attributed to small phase differences
that are induced in the laser-driven continuum transitions to the final states.
Since most measurement techniques tracing attosecond electron dynamics involve
the exchange of at least two photons, this is a general, significant, and
initially unexpected effect that must be taken into account in all such
photoionization measurements.
