Periodic Reporting for period 1 - NeqMolRot (Non-Equilibrium Field Theory of Molecular Rotations)
Reporting period: 2023-02-01 to 2025-01-31
In the last century, Quantum Mechanics has been a story of unabashed success, reshaping our understanding of physical reality not only at the smallest length scales of elementary particles, but providing us with an exquisite control over many phenomena which are crucial for the technology development of our species. Examples span from transistor and light-emitting diodes, through lasers and superconductors, up to the disruptive potential of quantum information science. Many concepts once thought to be definitely settled have been uprooted over the decades, and rotations are no exceptions.
Now, interest in rotational dynamics dates back to ancient astronomy and its mathematical description proved highly non-trivial even in the classical world of our macroscopic experience, whether we look at kids’ tops or at gyroscopes and other engine components. Quantum mechanically, it was clear that a certain divide emerged over the last decades. On one hand, the mathematical formulation of quantized angular momentum (i.e. the “propensity” of a body to rotate) was quite quickly implemented in the Fifties by towering figures like E. Wigner and G. Racah; they clearly had in mind how, for instance, reactivity of molecules depends on their relative orientation, a crucial issue for chemistry. However, coupling different angular momenta can quickly escalate to an intractable problem, hindering our understanding about quantum rotations happening in quantum liquids (Helium, cold atoms, even light in properly engineered cavities).
Here, we aim exactly to untangle this dynamics, by making use of a versatile set of theoretical tools, easily expendable in different context, such as molecules in liquid Helium or ultracold atomic vapours, nanoparticles trapped by electromagnetic radiation or electronic devices whose conduction properties are modified by the presence of molecular potential. The perspective is often the one of “impurity problem”, originally employed for electrons moving in positively charged ionic crystals (the so-called “polaron problem”). If there is no internal structure, and the impurity is point-like, the particle experiences friction, i.e. a linear slowing-down force. On the other hand, we show how objects able to perform rotations in real space can exchange angular momentum with their environment; the features of this exchange dynamics can help us parse different behaviour, depending on how the system is prepared initially, or on how strongly it is coupled with its environment. In parallel, it is crucial to keep in mind the rotational dynamics being affected by the surrounding environment is only half of the story, and the medium can itself be modified by the presence of the impurity. A clear example is provided by chiral molecules (i.e. structures not superimposable with their mirror image, like our hands or DNA helices).
Now, interest in rotational dynamics dates back to ancient astronomy and its mathematical description proved highly non-trivial even in the classical world of our macroscopic experience, whether we look at kids’ tops or at gyroscopes and other engine components. Quantum mechanically, it was clear that a certain divide emerged over the last decades. On one hand, the mathematical formulation of quantized angular momentum (i.e. the “propensity” of a body to rotate) was quite quickly implemented in the Fifties by towering figures like E. Wigner and G. Racah; they clearly had in mind how, for instance, reactivity of molecules depends on their relative orientation, a crucial issue for chemistry. However, coupling different angular momenta can quickly escalate to an intractable problem, hindering our understanding about quantum rotations happening in quantum liquids (Helium, cold atoms, even light in properly engineered cavities).
Here, we aim exactly to untangle this dynamics, by making use of a versatile set of theoretical tools, easily expendable in different context, such as molecules in liquid Helium or ultracold atomic vapours, nanoparticles trapped by electromagnetic radiation or electronic devices whose conduction properties are modified by the presence of molecular potential. The perspective is often the one of “impurity problem”, originally employed for electrons moving in positively charged ionic crystals (the so-called “polaron problem”). If there is no internal structure, and the impurity is point-like, the particle experiences friction, i.e. a linear slowing-down force. On the other hand, we show how objects able to perform rotations in real space can exchange angular momentum with their environment; the features of this exchange dynamics can help us parse different behaviour, depending on how the system is prepared initially, or on how strongly it is coupled with its environment. In parallel, it is crucial to keep in mind the rotational dynamics being affected by the surrounding environment is only half of the story, and the medium can itself be modified by the presence of the impurity. A clear example is provided by chiral molecules (i.e. structures not superimposable with their mirror image, like our hands or DNA helices).
Moving from the theoretical toolkit developed for “impurity problems”, we have carefully looked into how the exchange of angular momentum takes place between the impurity and the environment. The theoretical analysis is carried on by modelling the system as a quantum linear rotor, a reliable approximation for diatomic molecules and silicon nanoparticles, coupled to a superfluid environment. Technically speaking, the coupling is established between the impurity and the environment excitations, whose character is encoded in the so-called excitation spectra. For quantum fluids like Helium-4, we are talking about vibration quanta called phonons. By moving to the reference frame of the rotating object, we derive an analytical formula describing the dynamical exchange of angular momentum depending on the initial preparation of the system state. We adopt a variational approach, meaning that we are guessing a reasonable shape for the impurity-environment hybrid state and we optimize the parameters by minimizing the related energy. In doing so, we end up with a set of differential equations that, no matter how involved, are easier to solve than other ab-initio methods employed in the field of quantum chemistry. Their solution helps us identify two different regimes: for slowly-rotating objects (i.e. small values of the initial angular momentum), we see that an exchange channel is open, due to the fact that the impurity rotation is “renormalized” (or “dressed”) by the medium excitations. For fast-rotating objects, the channel closes fast, since medium excitations are not able to follow the impurity motion. Remarkably, small molecules in Helium droplets appear to behave similarly after sufficiently strong laser pulses, breaking free from their solvation shell and rotating as if they were in a gas phase.
A further effort is also ongoing, with the goal of providing an extended and versatile platform to describe rotating objects coupled to quantum environments. The resulting equations can be promisingly tested in different regimes, by looking at the long-time relaxation and angular momentum diffusion in complex environments, up to the so-called optical regime, with potentially novel application for spectroscopic applications.
Now, most of the above mentioned issues rely upon the assumption that the environment is not affected by the impurity presence. This is certainly not the case when we look at how the conduction properties of a magnetized surface are modified by the adsorption of a molecule. Most importantly we focus on chiral molecules, structures where mirror-symmetric partners are not superimposable; mirror-symmetry can be understood in terms of improper rotations, with reflections also included in the set of allowed transformations. Focusing on the role of chirality is strategic, since not only most biologically-relevant molecules fall in this category, but there is a strong interplay between electron spins and the handedness of the medium they move through (a striking example of what is referred to as Chiral-Induced-Spin-Selectivity). In our proposed model, electrons move on a magnetic surface in the presence of potential described in terms of the molecule electric polarizability. Just by means of these two crucial ingredients, we have been able to describe how charge and spin currents are affected by the molecular potentials. Technically speaking, our numerical simulations rely upon the so-called wavefunction scattering approach, where transport coefficients (such as conductances or resistances) are defined in terms of transmission probabilities between two different leads attached to the conducting region.
A further effort is also ongoing, with the goal of providing an extended and versatile platform to describe rotating objects coupled to quantum environments. The resulting equations can be promisingly tested in different regimes, by looking at the long-time relaxation and angular momentum diffusion in complex environments, up to the so-called optical regime, with potentially novel application for spectroscopic applications.
Now, most of the above mentioned issues rely upon the assumption that the environment is not affected by the impurity presence. This is certainly not the case when we look at how the conduction properties of a magnetized surface are modified by the adsorption of a molecule. Most importantly we focus on chiral molecules, structures where mirror-symmetric partners are not superimposable; mirror-symmetry can be understood in terms of improper rotations, with reflections also included in the set of allowed transformations. Focusing on the role of chirality is strategic, since not only most biologically-relevant molecules fall in this category, but there is a strong interplay between electron spins and the handedness of the medium they move through (a striking example of what is referred to as Chiral-Induced-Spin-Selectivity). In our proposed model, electrons move on a magnetic surface in the presence of potential described in terms of the molecule electric polarizability. Just by means of these two crucial ingredients, we have been able to describe how charge and spin currents are affected by the molecular potentials. Technically speaking, our numerical simulations rely upon the so-called wavefunction scattering approach, where transport coefficients (such as conductances or resistances) are defined in terms of transmission probabilities between two different leads attached to the conducting region.
By making use of an impurity-problem formulation, we have shined a light on how angular momentum is exchanged between a rotating impurity and the surrounding environment. Most importantly, this is done by carrying on a fully quantum-mechanical calculation and we do not need to solely rely upon expensive ab-initio methods, such a Quantum MonteCarlo, or density-functional based calculations. While this also means that we cannot always to model fully qualitatively every possible setups involving rotating degrees coupled to an external environment, we can exploit our results from an effective perspective, where ab-initio methods nail down the coupling parameters involved in our theoretical framework. Concerning the issue of transport in electronic systems, our results show the enantiospecific response in charge and spin signals depending on the adsorbed molecule. This minimal framework is certainly relevant for future developments in spintronics and materials design, since they are robust, being activated at room temperatures and they fully rely on feasible experimental setups.
Now, broadly speaking, recent developments in the field of quantum information science and quantum technologies clearly show how the community understands the necessity for a better understanding of quantum rotations in many-body setups, and we provide just a single striking example. Indeed, it has been proposed that qubits can be robustly encoded in the rotational degrees of freedom of a wide range of simple molecules. While the private sector, in its biggest corporate actors, is focused on solid-state setups, it is difficult to overlook how the chemical synthesis of molecular compounds offers unmatched control over nanofabrication processes currently required by Google or IBM architecture. Moreover, strategies for implementing logical operations and quantum error corrections are being developed at this very moment.
Now, broadly speaking, recent developments in the field of quantum information science and quantum technologies clearly show how the community understands the necessity for a better understanding of quantum rotations in many-body setups, and we provide just a single striking example. Indeed, it has been proposed that qubits can be robustly encoded in the rotational degrees of freedom of a wide range of simple molecules. While the private sector, in its biggest corporate actors, is focused on solid-state setups, it is difficult to overlook how the chemical synthesis of molecular compounds offers unmatched control over nanofabrication processes currently required by Google or IBM architecture. Moreover, strategies for implementing logical operations and quantum error corrections are being developed at this very moment.