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arXiv:2409.13322 · Physical Review Research

Coherent dynamics of a nuclear-spin-isomer superposition

Tamar Levin, Ziv Meir

Published Mar 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Preserving quantum coherence with the increase of a system's size and complexity is a major challenge. Molecules, with their diverse sizes and complexities and many degrees of freedom, are an excellent platform for studying the transition from quantum to classical behavior. While most quantum-control studies of molecules focus on vibrations and rotations, we focus here on creating a quantum superposition between two nuclear-spin isomers of the same molecule. We present a scheme that exploits an avoided crossing in the spectrum to create strong coupling between two uncoupled nuclear-spin-isomer states, hence creating an isomeric qubit. We model our scheme using a four-level Hamiltonian and explore the coherent dynamics in the different regimes and parameters of our system. Our four-level model and approach can be applied to other systems with a similar energy-level structure.

DOI
10.1103/physrevresearch.7.013274

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Preserving quantum coherence with the increase of a system's size and complexity is a major challenge. Molecules, with their diverse sizes and complexities and many degrees of freedom, are an excellent platform for studying the transition from quantum to classical behavior. While most quantum-control studies of molecules focus on vibrations and rotations, we focus here on creating a quantum superposition between two nuclear-spin isomers of the same molecule. We present a scheme that exploits an avoided crossing in the spectrum to create strong coupling between two uncoupled nuclear-spin-isomer states, hence creating an isomeric qubit. We model our scheme using a four-level Hamiltonian and explore the coherent dynamics in the different regimes and parameters of our system. Our four-level model and approach can be applied to other systems with a similar energy-level structure.
A theoretical model of nuclear spin conversion in molecules controlled by an external electromagnetic radiation resonant to a rotational transition is developed. It is shown that one can produce an enrichment of spin isomers and influence their conversion rates in two ways, through coherences and through level population changes induced by radiation. The effect on conversion ranges from significant speed-up to almost complete inhibition of the process by proper choice of frequency and intensity of the external field.
Coherent superpositions and entanglement are hallmarks of quantum mechanics, but they are fragile and can easily be perturbed by their environment. Selected isolated physical systems can maintain coherence and generate entanglement using well-controlled interactions. Chemical reactions, where bonds break and form, are highly dynamic quantum processes. A fundamental question is whether coherence can be preserved in chemical reactions and then harnessed to generate entangled products. Here we investigate this question by studying the 2KRb →\rightarrow→ K2_22​ + Rb2_22​ reaction at 500 nK, focusing on the the nuclear spin degrees of freedom. We prepare the initial nuclear spins in KRb in an entangled state and characterize the preserved coherence in nuclear spin wavefunction after the reaction. The data are consistent with full coherence at the end of the reaction. This suggests that entanglement can be prepared within the reactants, followed by a chemical reaction that produces separate, entangled molecules. We additionally demonstrate control of the reaction product state distribution by deliberately decohering the reactants.
This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
We formulate a quantum phase space for rotational and nuclear-spin states of rigid molecules. For each nuclear spin isomer, we re-derive the isomer's admissible angular momentum states from molecular geometry and nuclear-spin data, introduce its angular position states using quantization theory, and develop a generalized Fourier transform converting between the two. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We discuss two general features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, we quantify when and how an isomer's state space is completely rotation-spin entangled, meaning that it does not admit any separable states. Second, we identify isomers whose position states house an internal pseudo-spin or "fiber" degree of freedom, and the fiber's Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline how the fiber can be used as a quantum error-correcting code and discuss scenarios where these features can be experimentally probed
Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically active electron, nuclear spins can be rapidly polarized, controlled, and read via lasers and radio-frequency (rf) fields. Possessing typical coherence times of several milliseconds at room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond are thus intriguing systems to observe how classical physical rotation at quantum timescales affects a quantum system. In this work, we demonstrate optical nuclear-spin polarization and rapid quantum control of nuclear spins in a diamond physically rotating at 1kHz1\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}1kHz, faster than the nuclear-spin coherence time. Free from the need to maintain strict field alignment, we are able to measure and control nuclear spins in the presence of a large, time-varying magnetic field that makes an angle of more than ${100}^{\ensuremath{\circ}}$ to the nitrogen-lattice vacancy axis. The field induces spin mixing between the electron and nuclear states of the qubits, decoupling them from oscillating rf fields. We are able to demonstrate that coherent spin state control is possible at any point of the rotation. We combine continuous dynamical decoupling with feed-forward control to eliminate decoherence induced by imperfect mechanical rotation. Our work liberates a previously inaccessible degree of freedom of the NV nuclear spin, unlocking new approaches to quantum control and rotation sensing.
Molecules, with their rich spectrum of internal states as well as strong and tunable dipolar interactions, are promising candidates for a broad range of experiments including quantum information, quantum chemistry, precision measurement and probing physics beyond the Standard Model, and quantum simulation of interacting many-body systems. At the same time, the complexity that made them attractive also poses a significant challenge to achieve a high level of quantum control that is required in many of their potential applications. Multiple approaches are being pursued for full quantum control of molecules including association of atomic gases and direct cooling of molecules, yet it remains challenging to control molecules at single particle level due to the difficulty in tuning the atom-atom interaction and laser cooling of molecules. In this thesis, we achieved full control on a single weakly bound ground state molecule created by coherent optical association from single atoms. We first discuss the trapping and imaging of the atoms in the optical tweezer and the cooling into a single quantum state in order to achieve the quantum control of atoms. Combining this control with the resolution and flexibility of tweezers. we developed a versatile platform to study interactions between single atoms and properties of single molecules, using precise optical spectroscopy on pairs of atoms in the tweezer. Based on these studies, we proposed a promising pathway for coherent all-optical creation of molecules and experimentally demonstrated full control on the molecule including all degrees of freedom.