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arXiv:0905.1052 · Physical Review Letters

Conical Intersections in Laboratory Coordinates with Ultracold Molecules

Alisdair O. G. Wallis, S. A. Gardiner, Jeremy M. Hutson

Published Aug 17, 2009• 22 citations
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Abstract

For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.

DOI
10.1103/physrevlett.103.083201

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Nature Communications•Jul 30, 2015•95 citations
For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.
There is great interest within the physics and chemistry communities in the properties of ultracold molecules. Electromagnetic fields can be used to create, trap, and modify the collisional dynamics of ultracold molecules, and thus the properties of ultracold molecules in electromagnetic fields is of growing importance. This thesis examines some of the effects of externally applied electromagnetic fields on ultracold molecules. Initially, magnetic Feshbach resonances in combined electric and magnetic fields are examined in the collisions of He(1S^1S1S)+SO(3Σ−^3\Sigma^-3Σ−). Through detailed quantum scattering calculations, it is then shown that the sympathetic cooling of NH(3Σ−^3\Sigma^-3Σ−) molecules with Mg atoms has a good prospect of success, a first for a neutral molecular system. Detailed quantum scattering calculations are performed for a wide range of collision energies and magnetic field strengths and it is found that the ratio of elastic to inelastic collisions is large for temperatures below 10 mK, and increases as the collision energy and magnetic field strength decrease. The near threshold collision properties of Mg+NH have been examined using a multichannel quantum defect theory approach. A new type of conical intersection, that is a function of applied electromagnetic fields only, is also demonstrated. For states of opposite parity, brought into degeneracy with a magnetic field, the degeneracy can be resolved by the addition of an electric field, forming a conical intersection. A suitable arrangement of fields could thus be used to create a conical intersection in laboratory coordinates within an ultracold trapped gas. For a Bose-Einstein condensate, in the mean-field approximation, the resultant geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.
We show that conical intersections can be created in laboratory coordinates by dressing a parabolic trap for ultracold atoms or molecules with a combination of optical and static magnetic fields. The resulting ring trap can support single-particle states with half-integer rotational quantization and many-particle states with persistent flow. Two well-separated atomic or molecular states are brought into near resonance by an optical field and tuned across each other with an inhomogeneous magnetic field. Conical intersections occur at the nodes in the optical field.
There is great interest within the physics and chemistry communities in the properties of ultracold molecules. Electromagnetic fields can be used to create, trap, and modify the collisional dynamics of ultracold molecules, and thus the properties of ultracold molecules in electromagnetic fields is of growing importance. This thesis examines some of the effects of externally applied electromagnetic fields on ultracold molecules. Initially, magnetic Feshbach resonances in combined electric and magnetic fields are examined in the collisions of He(1S )+SO(3Σ−). Through detailed quantum scattering calculations, it is then shown that the sympathetic cooling of NH(3Σ−) molecules with Mg atoms has a good prospect of success, a first for a neutral molecular system. Detailed quantum scattering calculations are performed for a wide range of collision energies and magnetic field strengths and it is found that the ratio of elastic to inelastic collisions is large for temperatures below 10 mK, and increases as the collision energy and magnetic field strength decrease. The near threshold collision properties of Mg+NH have been examined using a multichannel quantum defect theory approach. A new type of conical intersection, that is a function of applied electromagnetic fields only, is also demonstrated. For states of opposite parity, brought into degeneracy with a magnetic field, the degeneracy can be resolved by the addition of an electric field, forming a conical intersection. A suitable arrangement of fields could thus be used to create a conical intersection in laboratory coordinates within an ultracold trapped gas. For a BoseEinstein condensate, in the mean-field approximation, the resultant geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.
It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off".
The topology of the electronic structure for an avoided crossing and a conical intersection (CI) is different and is characterized by the presence of the geometric phase in the electronic wavefunction in the latter. Using the linear Jahn-Teller model, we show that an avoided crossing can be created from the conical intersection while preserving the nontrivial topology of the latter by adding a Pauli σyσ_yσy​ term to the Hamiltonian. Analogously to solid state systems, we derive a half-integer topological invariant as the integral of the Berry curvature over the CI nuclear branching space. We investigate the influence of electronic topology on chemical dynamics by conducting fewest-switches surface hopping simulations and find distinct hopping rates on identical eigensurfaces but with different topologies. Our work extends the influence of topology on molecular excited state dynamics beyond the Berry phase that can be practically realized through electron-nuclear and spin-orbit coupling.
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.