We investigate quantum control of isotope-selective molecular orientation using optimal control theory. The target in this study is to inversely orient two isotopologues, 7Li37Cl and 7Li35Cl, along the field polarization vector. The Hamiltonian includes dipole and polarization interactions and we prepare two laser sources, one of which is responsible for resonant transitions through the dipole interaction and the other is stronger and responsible for nonresonant transitions through the polarization interaction. Total time of the control pulse is set to twice the rotational period that is defined as the inverse of the J = 1 ← 0 transition frequency (J: the rotational quantum number). As a result of the calculation at 0 K, an optimal field leads to the expectation values of cosθ (θ: the angle between the field polarization vector and the molecular axis) for the two isotopologues, 0.76 and -0.78, indicating that the control is successful. It is found that in the optimal field the resonant and nonresonant pulses cooperatively interact with the molecules to enhance the control efficiency.
We investigate quantum control of isotope-selective molecular orientation using optimal control theory. The target in this study is to inversely orient two isotopologues, 7Li37Cl and 7Li35Cl, along the field polarization vector. The Hamiltonian includes dipole and polarization interactions and we prepare two laser sources, one of which is responsible for resonant transitions through the dipole interaction and the other is stronger and responsible for nonresonant transitions through the polarization interaction. Total time of the control pulse is set to twice the rotational period that is defined as the inverse of the J = 1 ← 0 transition frequency (J: the rotational quantum number). As a result of the calculation at 0 K, an optimal field leads to the expectation values of cosθ (θ: the angle between the field polarization vector and the molecular axis) for the two isotopologues, 0.76 and -0.78, indicating that the control is successful. It is found that in the optimal field the resonant and nonresonant pulses cooperatively interact with the molecules to enhance the control efficiency.
The design of shaping pulse fields for controlling molecular orientation is of great importance in fields of stereochemical reactions, strong-field ionization, and quantum information processing. Traditional quantum optimal control algorithms typically solve the problem of molecular orientation in an infinite-dimensional rotational space, but they often overlook the constraints imposed by experimental limitations. In this work, a multi-objective and multi-constraint quantum optimal control algorithm is proposed to design a pulse field that conforms to the constraints of pulse area and energy. Specifically, the algorithm enforces a zero pulse area condition to eliminate the static field components and maintains constant pulse energy, ensuring compatibility with realistic experimental setups. Under these constraints, the algorithm optimizes the population and phase distribution of a selected number of low-lying rotational states in ultracold molecules to achieve maximum molecular orientation. The effectiveness of the proposed algorithm is demonstrated through numerical studies involving two- and three-state target subspaces, where the creation of a coherent superposition state with optimized population and phase distribution leads to the desired molecular orientation. Furthermore, its scalability is validated by applying it to a more complex 17-state subspace, where a maximum orientation value of 0.99055 is obtained, approaching the global optimal value of 1. Our findings demonstrate that by effectively managing these constraints, the influence of rotational states in the non-target state subspace can be substantially suppressed. The time-frequency analysis of the optimized pulses, combined with the Fourier transform spectrum of the time-dependent degree of orientation, indicates that the maximum molecular orientation is mainly achieved through ladder-climbing excitation of multi-color pulse fields, with the contributions from highly excited states being minimal. This work provides a valuable reference for designing experimentally feasible pulse fields using multi-constraint optimization algorithms, which helps to precisely control a limited number of rotational states to achieve maximum molecular orientation.
The lack of a direct map between control fields and desired control objectives poses a significant challenge in applying quantum control theory to quantum technologies. Here, we propose an analytical framework to precisely control a limited set of quantum states and construct desired coherent superpositions using a well-designed laser pulse sequence with optimal amplitudes, phases, and delays. This theoretical framework that corresponds to a multilevel pulse-area theorem establishes a straightforward mapping between the control parameters of the pulse sequence and the amplitudes and phases of rotational states within a specific subspace. As an example, we utilize this approach to generate 15 distinct and desired rotational superpositions of ultracold polar molecules, leading to 15 desired field-free molecular orientations. By optimizing the superposition of the lowest 16 rotational states, we demonstrate that this approach can achieve a maximum orientation value of | 〈 cos θ 〉 | max above 0.99, which is very close to the global optimal value of 1 that could be achieved in an infinite-dimensional state space. This work marks a significant advancement in achieving precise control over multilevel subsystems within molecules. It holds potential applications in molecular alignment and orientation, as well as in various interdisciplinary fields related to the precise quantum control of ultracold polar molecules, opening up considerable opportunities in molecular-based quantum techniques.
Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.
We demonstrate selective control over rotational motion of small, linear molecules. By means of sequential excitation of the rotational motion by ultrashort pulses, we first prepare transiently aligned molecules with periodically revived angular distribution. Upon further, properly timed excitation, the rotational energy can be increased or decreased, depending on the exact timing of the second pulse. We show how this approach can be applied for selective rotational control of a single component in a molecular mixture. We discuss this selectivity in the context of molecular isotopes ( 14 N 2 , 15 N 2 ), where the difference in isotopic mass gives rise to different rotational revival times. We further apply the method to the selective addressing of molecular spin isomers (para, ortho 15 N 2 ) in a mixture, where wavefunction symmetry differences replace the mass differences as the origin of the selectivity. In both cases the method is demonstrated experimentally and the results are analysed theoretically.
The capability to control molecular rotation for field-free orientation, which arranges molecules in specific spatial directions without external fields, is crucial in physics, chemistry, and quantum information science. However, conventional methods typically lead to transient orientations characterized by periodic directional reversals and necessitate the generation of coherent superpositions across a broad spectrum of rotational states of ultracold molecules. In this work, we develop a theoretical framework for achieving unidirectional field-free orientation by selectively manipulating two specific rotational states of symmetric top molecules. By leveraging the interplay between coherent superpositions and the precise selection of initial states, we demonstrate that both the maximum achievable orientation and its direction can be effectively controlled. To attain the desired two-state orientation, we present a quantum control strategy that utilizes a single control pulse, significantly simplifying the complexities of conventional multistate or multipulse schemes. Numerical simulations validate the effectiveness and feasibility of this approach for methyl iodide (CH3I) molecules, even when accounting for molecular centrifugal distortion.The results highlight the critical roles of initial-state selection and quantum coherence in achieving long-lasting, high unidirectional molecular orientation, opening new directions in stereochemistry, precision spectroscopy, and quantum computing.
We discuss an approach to quantum control based on initial adiabatic tuning of the field-free Hamiltonian by a strong laser field to optimize the system for the desired transitions induced by the control laser pulse. As an illustration, we describe single-qubit, two-qubit, and some qudit logical gates within rotational and vibrational states of a diatomic molecule. Gate operations use resonant Raman transitions, and the prior adjustment of the Hamiltonian is done by a strong nonresonant aligning field.