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Simulating quantum magnets with symmetric top molecules

Michael L. Wall, Kenji Maeda, Lincoln D. Carr

Published Aug 14, 2016• 40 citations
OpenAlex

Abstract

We establish a correspondence between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole matrix elements of a magnetic dipole associated with an elemental spin $F$. It is shown that this correspondence makes it possible to perform quantum simulation of the single-particle spectrum and the dipole-dipole interactions of magnetic dipoles in a static external magnetic field $\bf{B}$ with symmetric top molecules subject to a static external electric field $\bf{E}_{\mathrm{DC}}$. We further show that no such correspondence exists for $^1\Sigma$ molecules in static fields, such as the alkali metal dimers. The effective spin angular momentum of the simulated magnetic dipole corresponds to the rotational angular momentum of the symmetric top molecule, and so quantum simulation of arbitrarily large integer spins is possible. Further, taking the molecule CH$_3$F as an example, we show that the characteristic dipole-dipole interaction energies of the simulated magnetic dipole are a factor of 620, 600, and 310 larger than for the highly magnetic atoms Chromium, Erbium, and Dysprosium, respectively. We present several applications of our correspondence for many-body physics, including long-range and anisotropic spin models with arbitrary integer spin $S$ using symmetric top molecules in optical lattices, quantum simulation of molecular magnets, and spontaneous demagnetization of Bose-Einstein condensates due to dipole-dipole interactions. Our results are expected to be relevant as cold symmetric top molecules reach quantum degeneracy through Stark deceleration and opto-electrical cooling.

Related papers

Simulating quantum magnets with symmetric top molecules

Michael L. Wall, Kenji Maeda, Lincoln D. Carr

A correspondence is established between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole matrix elements of a magnetic dipole associated with an elemental spin F. It is shown that this correspondence makes it possible to perform quantum simulation of the single‐particle spectrum and the dipole‐dipole interactions of magnetic dipoles in a static external magnetic field with symmetric top molecules subject to a static external electric field . It is further shown that no such correspondence exists for 1Σ molecules in static fields, such as the alkali metal dimers. The effective spin angular momentum of the simulated magnetic dipole corresponds to the rotational angular momentum of the symmetric top molecule, and so quantum simulation of arbitrarily large integer spins is possible. Further, taking the molecule CH3F as an example, it is shown that the characteristic dipole‐dipole interaction energies of the simulated magnetic dipole are a factor of 620, 600, and 310 larger than for the highly magnetic atoms Chromium, Erbium, and Dysprosium, respectively. Several applications of the correspondence for many‐body physics are presented, including long‐range and anisotropic spin models with arbitrary integer spin S using symmetric top molecules in optical lattices, quantum simulation of molecular magnets, and spontaneous demagnetization of Bose‐Einstein condensates due to dipole‐dipole interactions. These results are expected to be relevant as cold symmetric top molecules reach quantum degeneracy through Stark deceleration and opto‐electrical cooling.

arXiv:1305.1236•Annalen der Physik•Sep 23, 2013•50 citations

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Rotational properties of two interacting cold polar molecules: Linear, symmetric, and asymmetric tops

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We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024

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Entanglement of polar symmetric top molecules as candidate qubits

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Proposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is second-order, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a first-order Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.

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Yi Li, Congjun Wu

Recently, cold atomic Fermi gases with the large magnetic dipolar interaction have been laser cooled down to quantum degeneracy. Different from electric-dipoles which are classic vectors, atomic magnetic dipoles are quantum-mechanical matrix operators proportional to the hyperfine-spin of atoms, thus provide rich opportunities to investigate exotic many-body physics. Furthermore, unlike anisotropic electric dipolar gases, unpolarized magnetic dipolar systems are isotropic under simultaneous spin-orbit rotation. These features give rise to a robust mechanism for a novel pairing symmetry: orbital p-wave (L = 1) spin triplet (S = 1) pairing with total angular momentum of the Cooper pair J = 1. This pairing is markedly different from both the (3)He-B phase in which J = 0 and the (3)He-A phase in which J is not conserved. It is also different from the p-wave pairing in the single-component electric dipolar systems in which the spin degree of freedom is frozen.

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Zero field splittings in paramagnetic dysprosium dimers

Hui Li, Eite Tiesinga, Ming Li +2 more

Zero field splittings in molecules originate from the intrinsic spin and orbital angular momentum of unpaired electrons. Here, we close a knowledge gap on a diatomic molecule built from spin-8 ground-state dysprosium atoms, where zero-field splittings correspond to the energies of states with different alignments of the two spins. We predict a paramagnetic molecular ground state with parallel Dy spins aligned along the internuclear axis. A diamagnetic state with anti-parallel spins is the first excited state with a small energy cost of hc × 2 cm−1 predominantly due to the magnetic dipole-dipole interaction. We also determine the rotations and vibrations of the diatom and show that centrifugal forces double the splittings between these para- and dia-magnetic states. The vibrational spacings and zero-field splittings have similar magnitude. Finally, the Dy2 ground state has a magnetic moment that is twice that of the atom and, thus, arrays of ultracold Dy2 can be used to simulate strongly interacting magnets. Zero-field splittings in molecules arise from the spin and orbital angular momentum of unpaired electrons, yet their behaviour in diatomic molecules with spin-8 dysprosium atoms remains underexplored. Here, the authors predict a paramagnetic ground state with parallel Dy spins and reveal implications for simulating strongly interacting magnets using ultracold Dy2 arrays.

Communications Physics•May 28, 2026•1 citation
We establish a correspondence between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole matrix elements of a magnetic dipole associated with an elemental spin FFF. It is shown that this correspondence makes it possible to perform quantum simulation of the single-particle spectrum and the dipole-dipole interactions of magnetic dipoles in a static external magnetic field B\bf{B}B with symmetric top molecules subject to a static external electric field EDC\bf{E}_{\mathrm{DC}}EDC​. We further show that no such correspondence exists for 1Σ^1\Sigma1Σ molecules in static fields, such as the alkali metal dimers. The effective spin angular momentum of the simulated magnetic dipole corresponds to the rotational angular momentum of the symmetric top molecule, and so quantum simulation of arbitrarily large integer spins is possible. Further, taking the molecule CH3_33​F as an example, we show that the characteristic dipole-dipole interaction energies of the simulated magnetic dipole are a factor of 620, 600, and 310 larger than for the highly magnetic atoms Chromium, Erbium, and Dysprosium, respectively. We present several applications of our correspondence for many-body physics, including long-range and anisotropic spin models with arbitrary integer spin SSS using symmetric top molecules in optical lattices, quantum simulation of molecular magnets, and spontaneous demagnetization of Bose-Einstein condensates due to dipole-dipole interactions. Our results are expected to be relevant as cold symmetric top molecules reach quantum degeneracy through Stark deceleration and opto-electrical cooling.
A correspondence is established between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole matrix elements of a magnetic dipole associated with an elemental spin F. It is shown that this correspondence makes it possible to perform quantum simulation of the single‐particle spectrum and the dipole‐dipole interactions of magnetic dipoles in a static external magnetic field with symmetric top molecules subject to a static external electric field . It is further shown that no such correspondence exists for 1Σ molecules in static fields, such as the alkali metal dimers. The effective spin angular momentum of the simulated magnetic dipole corresponds to the rotational angular momentum of the symmetric top molecule, and so quantum simulation of arbitrarily large integer spins is possible. Further, taking the molecule CH3F as an example, it is shown that the characteristic dipole‐dipole interaction energies of the simulated magnetic dipole are a factor of 620, 600, and 310 larger than for the highly magnetic atoms Chromium, Erbium, and Dysprosium, respectively. Several applications of the correspondence for many‐body physics are presented, including long‐range and anisotropic spin models with arbitrary integer spin S using symmetric top molecules in optical lattices, quantum simulation of molecular magnets, and spontaneous demagnetization of Bose‐Einstein condensates due to dipole‐dipole interactions. These results are expected to be relevant as cold symmetric top molecules reach quantum degeneracy through Stark deceleration and opto‐electrical cooling.
We demonstrate that ultracold symmetric top molecules loaded into an optical lattice can realize highly tunable and unconventional models of quantum magnetism, such as an XYZ Heisenberg spin model. We show that anisotropic dipole–dipole interactions between molecules can lead to effective spin–spin interactions which exchange spin and orbital angular momentum. This exchange produces effective spin models which do not conserve magnetization and feature tunable degrees of spatial and spin–coupling anisotropy. In addition to deriving pure spin models when molecules are pinned in a deep optical lattice, we show that models of itinerant magnetism are possible when molecules can tunnel through the lattice. Additionally, we demonstrate rich tunability of effective model parameters using only a single microwave frequency, in contrast to proposals with diatomic molecules, which often require many microwave frequencies. Our results are germane not only for experiments with polyatomic symmetric top molecules, such as methyl fluoride (CH 3 F), but also diatomic molecules with an effective symmetric top structure, such as the hydroxyl radical OH.
We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024
Proposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is second-order, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a first-order Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.
Recently, cold atomic Fermi gases with the large magnetic dipolar interaction have been laser cooled down to quantum degeneracy. Different from electric-dipoles which are classic vectors, atomic magnetic dipoles are quantum-mechanical matrix operators proportional to the hyperfine-spin of atoms, thus provide rich opportunities to investigate exotic many-body physics. Furthermore, unlike anisotropic electric dipolar gases, unpolarized magnetic dipolar systems are isotropic under simultaneous spin-orbit rotation. These features give rise to a robust mechanism for a novel pairing symmetry: orbital p-wave (L = 1) spin triplet (S = 1) pairing with total angular momentum of the Cooper pair J = 1. This pairing is markedly different from both the (3)He-B phase in which J = 0 and the (3)He-A phase in which J is not conserved. It is also different from the p-wave pairing in the single-component electric dipolar systems in which the spin degree of freedom is frozen.
Zero field splittings in molecules originate from the intrinsic spin and orbital angular momentum of unpaired electrons. Here, we close a knowledge gap on a diatomic molecule built from spin-8 ground-state dysprosium atoms, where zero-field splittings correspond to the energies of states with different alignments of the two spins. We predict a paramagnetic molecular ground state with parallel Dy spins aligned along the internuclear axis. A diamagnetic state with anti-parallel spins is the first excited state with a small energy cost of hc × 2 cm−1 predominantly due to the magnetic dipole-dipole interaction. We also determine the rotations and vibrations of the diatom and show that centrifugal forces double the splittings between these para- and dia-magnetic states. The vibrational spacings and zero-field splittings have similar magnitude. Finally, the Dy2 ground state has a magnetic moment that is twice that of the atom and, thus, arrays of ultracold Dy2 can be used to simulate strongly interacting magnets. Zero-field splittings in molecules arise from the spin and orbital angular momentum of unpaired electrons, yet their behaviour in diatomic molecules with spin-8 dysprosium atoms remains underexplored. Here, the authors predict a paramagnetic ground state with parallel Dy spins and reveal implications for simulating strongly interacting magnets using ultracold Dy2 arrays.