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manyChirality is ubiquitous in nature and fundamental in science, from particle physics to metamaterials. The most established technique of chiral discrimination -photoabsorption circular dichroism -relies on the magnetic properties of a chiral medium and yields an extremely weak chiral response. We propose and demonstrate a new, orders of magnitude more sensitive type of circular dichroism in neutral molecules: photoexitation circular dichroism. It does not rely on weak magnetic effects, but takes advantage of the coherent helical motion of bound electrons excited by ultrashort circularly polarized light. It results in an ultrafast chiral response and the efficient excitation of a macroscopic chiral density in an initially isotropic ensemble of randomly oriented chiral molecules. We probe this excitation without 1 arXiv:1612.08764v1 [physics.atm-clus] 27 Dec 2016 Here d 01 , d 02 and d 12 are the dipole transition vectors connecting the ground |0 and the two excited states |1 , |2 (Fig. 1b), ∆E 21 is the energy spacing between the excited states. For more than two states, Eq.(1) will contain the sum over all pairs of excited states n, m, leading to oscillations at all relevant frequencies ∆E nm . As a function of time the induced dipole vector maps out a helix (Fig. 3 1b) and the z-component of the helical current is j P XCD z ∝ σ[ d 01 × d 02 ] d 12 ∆E 21 cos(∆E 21 t). (2) Both d P XCD z and j P XCD z are quintessential chiral observables (see e.g. 19, 20 ). Indeed, both are proportional to the light helicity σ = ±1 and to the triple product of three vectors [ d 01 × d 02 ] d 12 . This product presents a fundamental measure of chirality: it changes sign upon reflection and thus has an opposite sign for left and right enantiomers. For randomly oriented non-chiral molecules d P XCD z = j P XCD z = 0. Eqs.(1,2) lead to the following conclusions. First, the coherent excitation of electronic states leads to a charge displacement in the light propagation direction. Hence, a macroscopic dipole d P XCD z and the corresponding chiral density are created in the excited states, with a chiral current oscillating out of phase for the two enantiomers. Second, PXCD requires no magnetic or quadrupole effects. Hence, it is orders of magnitude stronger than standard photoabsorption CD. While photoabsorption CD exploits the helical pitch of the laser field in space, PXCD takes advantage of the sub-cycle rotation of the light field in time and is inherently ultrafast. Indeed, PXCD arises only if the excitation dipoles d 01 , d 02 are non-collinear: for the angle φ between the two transition dipoles, the PXCD (Eqs. (1,2)) is proportional to σ sin(φ). Since σ = ±1, σ sin(φ) = sin(σφ) = sin(σωτ ), where ω is light frequency and τ = φ/ω is the required time for the light field to rotate by the angle φ. PXCD vanishes if the coherence between excited states |1 and |2 is lost and reflects dynamical symmetry breaking in an isotropic medium.The oscillations of the PXCD signal Eqs.(1,2) appear to suggest that probing it requires the

We present a unified description of several methods of chiral discrimination based exclusively on electric-dipole interactions. It includes photoelectron circular dichroism (PECD), enantio-sensitive microwave spectroscopy (EMWS), photoexcitation circular dichroism (PXCD) and photoelectron-photoexcitation circular dichroism (PXECD). We show that, in spite of the fact that the physics underlying the appearance of a chiral response is very different in all these methods, the enantio-sensitive and dichroic observable in all cases has a unique form. It is a polar vector given by the product of (i) a molecular pseudoscalar and (ii) a field pseudovector specified by the configuration of the electric fields interacting with the isotropic ensemble of chiral molecules. The molecular pseudoscalar is a rotationally invariant property, which is composed from different molecule-specific vectors and in the simplest case is a triple product of such vectors. The key property that enables the chiral response is the non-coplanarity of the vectors forming such triple product. The key property that enables chiral detection without relying on the chirality of the electromagnetic fields is the vectorial nature of the enantio-sensitive observable. Our compact and general expression for this observable shows what ultimately determines the efficiency of the chiral signal and if, or when, it can reach 100%. We also discuss the differences between the two phenomena, which rely on the bound states, PXCD and EMWS, and the two phenomena using the continuum states, PECD and PXECD. Finally, we extend these methods to arbitrary polarizations of the electric fields used to induce and probe the chiral response.

Photoelectron circular dichroism results from one-photon ionization of chiral molecules by circularly polarized light and manifests itself in forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane. To expose the physical mechanism responsible for asymmetric electron ejection, we first establish a rigorous relation between the responses of unaligned and partially or perfectly aligned molecules. Next, we identify a propensity field, which is responsible for the chiral response in the electric-dipole approximation, i.e. a chiral response without magnetic interactions. We find that this propensity field, up to notations, is equivalent to the Berry curvature in a two-band solid.The propensity field directly encodes optical propensity rules, extending our conclusions regarding the role of propensity rules in defining the sign of forward-backward asymmetry from the specific case of chiral hydrogen [1] to generic chiral systems. Optical propensity rules underlie the chiral response in photoelectron circular dichroism. The enantiosensitive flux of the propensity field through the sphere in momentum space determines the forwardbackward asymmetry in unaligned molecules and suggests a geometrical origin of the chiral response. This flux has opposite sign for opposite enantiomers and vanishes for achiral molecules.