Precise control over rotational angular momentum is at the heart of recent advances in quantum chemistry, quantum simulation, and quantum computation with ultracold bialkali molecules. Each rotational state comprises a rich manifold of hyperfine states arising from combinations of rotation and nuclear spins; this often yields hundreds of transitions available between a given pair of rotational states, and the efficient navigation of this complex space is a current challenge for experiments. Here, we describe a general approach based on a simple heuristic and graph theory to quickly identify optimal sets of states in ultracold bialkali molecules. We explain how to find pathways through the many available transitions to prepare the molecule in a specific state with maximum speed for any desired fidelity. We then examine networks of states where multiple couplings are present at the same time. As example applications, we first identify a closed loop of four states in the RbCs molecule where there is minimal population leakage out of the loop during simultaneous microwave coupling; we then extend the optimisation procedure to account for decoherence induced by magnetic-field noise and obtain an optimal set of 3 states for quantum computation applications.
Precise control over rotational angular momentum is at the heart of recent advances in quantum chemistry, quantum simulation, and quantum computation with ultracold bialkali molecules. Each rotational state comprises a rich manifold of hyperfine states arising from combinations of rotation and nuclear spins; this often yields hundreds of transitions available between a given pair of rotational states, and the efficient navigation of this complex space is a current challenge for experiments. Here, we describe a general approach based on a simple heuristic and graph theory to quickly identify optimal sets of states in ultracold bialkali molecules. We explain how to find pathways through the many available transitions to prepare the molecule in a specific state with maximum speed for any desired fidelity. We then examine networks of states where multiple couplings are present at the same time. As example applications, we first identify a closed loop of four states in the RbCs molecule where there is minimal population leakage out of the loop during simultaneous microwave coupling; we then extend the optimisation procedure to account for decoherence induced by magnetic-field noise and obtain an optimal set of 3 states for quantum computation applications.
This thesis presents the development of a toolbox for the coherent control of ultracold polar molecules. Such systems of molecules promise the creation of long-lived, highly dipolar quantum gases with applications spanning the fields of quantum state controlled chemistry, quantum information, quantum simulation, and precision measurement. However, the addition of vibrational and rotational degrees of freedom leads to molecular systems being significantly more complex than their widely used atomic counterparts. In this work we demonstrate full control of the quantum state down to the hyperfine level of an optically trapped sample of ultracold bosonic 87Rb133 Cs molecules, and exploit that control to begin an investigation into the collision processes which take place in an ultracold molecular gas. We create a sample of up to ∼ 4000 optically trapped molecules in their rovibronic and hyperfine ground state. We characterise the molecules by measuring their temperature, binding energy, and molecule-frame electric dipole moment. We perform spectroscopy of the first rotationally excited state with hyperfine state resolution using microwaves to determine accurate values of rotational and hyperfine coupling constants. We use coherent π pulses to perform complete transfer population between selected hyperfine levels of the ground, first-excited, and second-excited rotational states. We investigate the effect of the off-resonant light of our optical dipole trap on the rotational and hyperfine structure of the molecules. Through a combination of high-resolution microwave spectroscopy and parametric heating measurements, we characterise the polarisability of the 87Rb133Cs molecule. We demonstrate that coupling between neighbouring hyperfine states manifests in rich structure with many avoided crossings in any rotational state other than the ground state. This coupling may be tuned by rotating the polarisation of the linearly polarised trapping light. Finally, we study the lifetime of polar bosonic 87Rb133Cs molecules in our 3D optical dipole trap. We examine the lifetime of the molecules as a function of dipole trap intensity, magnetic field, and hyperfine and rotational state. Despite the chemical stability of the 87Rb133 Cs molecule, we observe lifetimes of ∼1 s corresponding to 2-body decay rates close to the universal limit.
Abstract Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of arccos(1/√3)≈55°. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation.
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable ^{23}Na^{40}K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, J=1, we observe lifetimes of more than 3 s, comparable to those in the rovibrational ground state, J=0. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements, and quantum information processing.
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.
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable 23 Na 40 K molecules.Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure.Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, J ¼ 1, we observe lifetimes of more than 3 s, comparable to those in the rovibrational ground state, J ¼ 0. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements, and quantum information processing.
We present a theoretical framework for universal single-qutrit control in asymmetric-top molecules, advancing molecular quantum information processing. In this approach, the qutrit is encoded in three rotational eigenstates, with an auxiliary state providing independent phase control within the computational manifold. We explore an analytic protocol for arbitrary single-qutrit gates, combining directly addressable SU(2) rotations with auxiliary-state-mediated phase operations. To support this, we derive a multilevel pulse-area theorem that provides an explicit analytic mapping between gate parameters and control fields, enabling systematic design of high-fidelity microwave pulse sequences. Numerical simulations with 1,2-propanediol confirm the robustness of our approach, achieving Walsh-Hadamard gates with minimal leakage from the computational subspace. We further examine four SU(2) decomposition strategies and find that phase-error sensitivity depends on the decomposition sequence, while amplitude errors propagate along specific coherence pathways. Our results establish asymmetric-top molecules as a viable platform for qutrit-based quantum operations and offer an analytical method for precise quantum control of complex multilevel systems.