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Bulletin of the American Physical Society

Static Gross-Pitaevskii equations for the molecular achiral-chiral transitions

Chong Ye, Quansheng Zhang, Yong Li

Published Jul 25, 2018• 0 citations
OpenAlex

Abstract

In the mean-field theory, the stabilization of chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states due to the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give static Gross-Pitaevskii equations without free parameters in the vibrational dimension to explore the achiral-chiral transitions of chiral molecules. We find that the achiral-chiral transitions can be classified into two categories: in one category the mean-field ground state changes continuously with the increase of the intermolecular interaction, in the other category the mean-filed ground state changes discontinuously. In order to summarize our results, we give the mean-field phase diagram of the achiral-chiral transitions.

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In the mean-field theory, the stabilization of chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states due to the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give static Gross-Pitaevskii equations without free parameters in the vibrational dimension to explore the achiral-chiral transitions of chiral molecules. We find that the achiral-chiral transitions can be classified into two categories: in one category the mean-field ground state changes continuously with the increase of the intermolecular interaction, in the other category the mean-filed ground state changes discontinuously. In order to summarize our results, we give the mean-field phase diagram of the achiral-chiral transitions.
In the mean-field theory, the stabilization of polar chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states as the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give the static nonlinear Schr\"odinger equations without free parameters to explore the achiral-chiral transitions of polar chiral molecules. We find that the polar chiral molecules of different species can be classified into two categories: At the critical point for the achiral-chiral transition, the mean-field ground state changes continuously in one category and changes discontinuously in the other category. We further give the mean-field phase diagram of the achiral-chiral transitions for both two categories.
We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energy and the decoherence. We focus on factors affecting the distinguishability as measured by population difference between the initially pure and mixed states and on the chiral stability as measured by the purity decay.
We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energies, and the decoherence in determining: the distinguishability as measured by a population difference between the initially pure and mixed states, and the decoherence process; the chiral stability as measured by the purity decay; and the stationary state of the system at times long relative to the time scales of the system dynamics and of the environmental effects.
We investigate the ground state and low-lying excitations of a Bose-Einstein condensate (BEC) of dipolar molecules interacting via short-range contact and long-range dipole­ dipole interactions (ddi). We find the mean field ground state via the variational principle using a separable bosonic wave function as the variational state. This state can be refined to include small excitations in the form of plane waves, and the results of the variational calculation are a set of dispersion relations for the low-lying excitations. We analyze the polarization and stability of the ground state as a function of the strength of the external polarizing electric field, the strength of the ddi, and the strength of the contact interactions. In a certain parameter regime of strong contact interactions that oppose the dipole -dipole interactions, we identify a possible signature of a first -order phase transition: the polarization of the gas discontinuously flips as the electric field is continuously ramped through zero field. By examining the dispersion relations, we find that the ground state in this parameter regime is unstable.
The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.
We consider a homogeneous two-dimensional Bose gas with repulsive dipole-dipole interactions. The ground-state equation of state, calculated using the diffusion Monte Carlo method, shows quantitative differences from the predictions of the commonly used Gross-Pitaevskii mean-field theory. The static structure factor, pair distribution function, and condensate fraction are calculated in a wide range of the gas parameter. Differences from mean-field theory are reflected in the frequency of the lowest ``breathing'' mode for harmonically trapped systems.