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arXiv:2603.14874

Quantum simulation of the Haldane phase using open shell molecules

Suman Aich, Ceren B. Dag, H. A. Fertig, Debayan Mitra, Babak Seradjeh

cond-mat.quant-gascond-mat.str-elphysics.atom-phquant-phSubmitted Mar 16, 2026• Announced Mar 17, 2026• 1 citation
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Abstract

Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the $^2Σ$ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for $^2Σ$ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.

Comments
12 pages, 9 figures

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Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the N=0,J=1/2,F=1N=0,J=1/2,F=1N=0,J=1/2,F=1 state is coupled to the N=1,J=3/2,F=2N=1,J=3/2,F=2N=1,J=3/2,F=2 manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the 2Σ^2Σ2Σ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for 2Σ^2Σ2Σ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.
Strongly interacting ultracold dipolar molecules are a rich platform for quantum information and quantum simulation of phenomena relevant to condensed matter systems. This dissertation presents novel theoretical and computational studies of ultracold dipolar molecules relevant to these areas in three broad categories.First, the path integral ground state quantum Monte Carlo method is extended to simulations with both translational and rotational degrees of freedom, including the development of a novel estimator of the elementary excitation energies of a system with these degrees of freedom based on the well known Feynman-Bijl approximation. This is then used to study dipolar molecular ensembles confined to one-dimensional optical lattices. The ground state phase diagram is characterized with both a mean-field method and the aforementioned quantum Monte Carlo method. A quantum phase transition is found for very short optical lattice spacings or very large dipole moments. The prospects for experimentally realizing a system which exhibits this phase transition are discussed.Second, the path integral ground state quantum Monte Carlo method is utilized to study the ground state of dipole molecules confined to two-dimensional optical lattices. On square lattices a crossover from a weakly interacting disordered phase to a strongly interacting striped phase is found for short lattice spacings or large dipole moments. On triangular lattices a crossover between a disordered phase and a completely polarized phase is found, also for short lattice spacings or large dipole moments. The relevance of such simulations to self-assembled dipolar crystals in two dimensions is discussed and simulation results of these systems are presented. Simulations of polarized and harmonically confined molecular systems in two dimensions with translations and rotations are also presented and a realistic interaction potential using highly accurate ab initio quantum chemistry techniques is calculated for LiH--LiH interactions as a preliminary step toward developing a high quality trial wave function for the simulation of systems possessing both translational and rotational degrees of freedom.Finally, several novel applications for dipolar molecules confined to optical lattices are proposed. An experimental realization of a topological phase using 2Sigma^2\\Sigma2Sigma ground state molecules with applied near resonant microwave fields and transverse magnetic fields is proposed. A method to create an array of dipole-coupled two-level molecules exhibiting superradiance and possessing novel spectroscopic properties using 1Sigma^1\\Sigma1Sigma ground state molecules in the combination of a far off-resonant laser field and a moderate magnetic field is proposed. Additionally, a method to create entangled pairs of molecules using closed-shell dipolar molecules immersed in an intense far off-resonant laser field is reviewed and an extension in which parallel optical lattices are merged and molecules are allowed to collide in the presence of a far off-resonant laser field is proposed. Simulation results are presented indicating that a significant amount of entanglement may be generated in such a way in realistic molecular systems.
We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin $S\ensuremath{\ge}1/2$ and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases---previously studied only in the nearest-neighbor case---survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed.
Abstract. We describe how to design a large class of always on spin−1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipoledipole coupled excited states. Using multiple fields anistropic models in one, two, or three dimensions, can be built with tunable spatial range. An illustrative example in one dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases. PACS numbers: 75.10.Jm, 74.20.Mn, 34.20GjDesigning spin−1 lattice models using polar molecules 2 1.
We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipole–dipole coupled excited states. Using multiple fields, anistropic models in one, two, or three dimensions can be built with tunable spatial range. An illustrative example in one-dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases.
Dysprosium atoms have proven to be a promising platform for quantum simulation due to their strong magnetic moment and high tunability of interactions. In this work, we propose dysprosium atoms for simulating the one-dimensional spin-1 XXZ Heisenberg model, which is known to have a rich phase diagram including the famous Haldane phase. To realize the model, we make use of the strong dipolar exchange interactions that naturally occur in the ground state of dysprosium due to its large electron angular momentum of JJJ = 8. To implement spin-1 particles, we encode the spin degree of freedom into three Zeeman sublevels, which are energetically isolated by applying a magnetic field. Using the density-matrix renormalization group, we analyze the ground-state properties of the resulting effective model. We find that a chain of fermionic dysprosium atoms in a suitable magnetic field can form a Haldane state with the characteristic spin-1/2 edge modes. Furthermore, we discuss the use of AC Stark shifts and Raman-type schemes for bosonic dysprosium to isolate effective spin-1 systems and to increase the tunability of model parameters.
Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87 Rb 133 Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.