The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two-, and many-body scenarios, thereby allowing one to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed-matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control—from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting.

Quantum control of molecular rotation

Light is one of the most powerful and precise tools allowing us to control, shape and create new phases of matter. In this task, the magnetic component of a light wave has so far played a unique role in defining the wave's helicity, but its influence on the optical response of matter is weak. Chiral molecules offer a typical example where the weakness of magnetic interactions hampers our ability to control the strength of their chiral optical response. It is limited several orders of magnitude below the full potential. Here we introduce freely propagating locally and globally chiral electric fields, which interact with chiral quantum systems extremely efficiently. To demonstrate the degree of control enabled by such fields, we focus on the nonlinear optical response of randomly oriented chiral molecules. We show full control over intensity, polarization and propagation direction of the chiral optical response, enabling its background-free detection. This response can be fully suppressed or enhanced at will depending on the molecular handedness, achieving the ultimate limit in chiral discrimination. Our findings open a way to extremely efficient control of chiral matter and to ultrafast imaging of chiral structure and dynamics in gases, liquids and solids.

Locally and globally chiral fields for ultimate control of chiral light matter interaction

Three-wave mixing spectroscopy of chiral molecules, which exist in left-handed and right-handed conformations, allows for enantioselective population transfer despite random orientation of the molecules. This is based on constructive interference of the three-photon pathways for one enantiomer and the destructive one for the other. We prove here that three mutually orthogonal polarization directions are required to this end. Two different dynamical regimes exist to realize enantioselective population transfer, and we show that they correspond to different phase conditions in the three-wave mixing. We find the excitation scheme used in current rotational three-wave mixing experiments of chiral molecules with C1 symmetry to be close to optimal and discuss the prospects for rovibrational three-wave mixing experiments of axially chiral molecules. Our comprehensive study allows us to clarify earlier misconceptions in the literature.

Principles of enantio-selective excitation in three-wave mixing spectroscopy of chiral molecules.

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation, and purification of chiral mixtures.

Controlled Enantioselective Orientation of Chiral Molecules with an Optical Centrifuge.

Light is a very powerful and precise tool, allowing us to control1, shape2,3 and create new phases4 of matter. In such tasks, the magnetic component of a light wave is essential in defining the wave’s helicity, but it influences the optical response of matter only weakly. Chiral molecules offer a typical example, in which the weakness of magnetic interactions hampers our ability to control the strength of their chiro-optical response5, limiting it at several orders of magnitude below the full potential. Here, we introduce and theoretically analyse a new type of chiral light: freely propagating, locally and globally chiral electric fields, which interact with chiral matter extremely efficiently. We show that this synthetic chiral light enables full control over the intensity, polarization and propagation direction of the nonlinear enantio-sensitive optical response of randomly oriented chiral molecules. This response can be quenched or enhanced at will in a desired enantiomer, opening up efficient ways to control chiral matter and for ultrafast imaging of chiral dynamics in gases, liquids and solids. Freely propagating, locally and globally chiral electric fields are introduced, enabling full control over intensity, polarization and propagation direction of the nonlinear enantio-sensitive optical response of randomly oriented chiral molecules.

Synthetic chiral light for efficient control of chiral light-matter interaction

We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH3CHCH2O), and ethyl oxirane (CH3CH2CHCH2O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

Shachar Gold

Papers

Selective Orientation of Chiral Molecules by Laser Fields with Twisted Polarization.