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Physical Review A

Virtual monopoles in a bosonic atom–diatomic-molecule system

Sheng-Chang Li, Libin Fu, Jie Liu

Published Feb 21, 2014• 4 citations
Publisher

Abstract

We investigate the virtual monopoles in an ultracold bosonic atom--diatomic-molecule system with a three-level second-quantized model. In the quantum theory, we show that the monopole field of the ground state does not have a spherical symmetry. We calculate the monopole charge and find that it is an integer multiple of the elementary charge ${g}_{0}=\frac{1}{2}$. This multiple exactly reflects the degeneracy properties of the ground state and strongly depends on the total particle number and the atom-number imbalance between two atomic species. In the mean-field limit, we illustrate that the system can create continuous monopole charges in the case of heteronuclear molecules. The underlying mechanism associated with the degeneracy properties and the application related to the quantum phase transition of the monopoles are briefly discussed as well.

DOI
10.1103/physreva.89.023628

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We investigate the virtual monopoles in an ultracold bosonic atom--diatomic-molecule system with a three-level second-quantized model. In the quantum theory, we show that the monopole field of the ground state does not have a spherical symmetry. We calculate the monopole charge and find that it is an integer multiple of the elementary charge g0=12{g}_{0}=\frac{1}{2}g0​=21​. This multiple exactly reflects the degeneracy properties of the ground state and strongly depends on the total particle number and the atom-number imbalance between two atomic species. In the mean-field limit, we illustrate that the system can create continuous monopole charges in the case of heteronuclear molecules. The underlying mechanism associated with the degeneracy properties and the application related to the quantum phase transition of the monopoles are briefly discussed as well.
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\n\nWe investigate the role of asymmetry in the geometric phase of an ultracold bosonic atom-heteronuclear molecule system where the asymmetry denotes the particle-number imbalance between two atomic species. Based on the mean-field approach, we derive the analytical expression of the geometric phase and confirm it by our numerical simulations. It is found that the geometric phase strongly depends both on the atom-number imbalance and the nonlinear particle interaction. We show that the geometric phase can be dramatically enhanced by increasing the imbalance or the repulsive interaction strength. For the symmetric case, a discontinuous behavior for the first-order derivative of the ground-state geometric phase at a critical point is seen which gives a distinct signal of a phase transition from mixed atom-molecule phase to pure molecule phase. The virtual magnetic field interpretation for the geometric phase is also given.\n
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy-level structure, fidelity, and adiabatic geometric phase, we confirm that the system exhibits a second-order phase transition from an atom-molecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular, we find that both the critical exponents and the behavior of the ground-state geometric phase have obviously changed in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to $\ensuremath{\pi}/3$ at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.
Abstract We adopt a modified spin-boson model to investigate the quantum phase transition in an ultracold atom-molecule conversion system involving molecule–molecule interaction. We explore the properties of ground state, entanglement entropy, and many-body dynamics, which confirm that the system exhibits a second-order phase transition from a pure atom phase to a mixed atom-molecule phase when the energy detuning is below a critical value. We obtain three scaling laws and the corresponding two critical exponents to characterize the phase transition. In particular, we discuss the effects of both the speed of ground-state dynamical evolution and the strength of molecular interaction on the phase transition. The adiabatic evolution condition is obtained as well. Our results show that the molecular interaction can greatly reduce the upper bound of the adiabatic condition, which provides a theoretical basis for easier observation of the phase transition in experiments.
Excited-state quantum phase transitions (ESQPTs) strongly influence the spectral properties of collective many-body quantum systems, changing degeneracy patterns in different quantum phases. Level degeneracies in turn affect the system's dynamics. We analyze the degeneracy dependence on the size of two-level boson models with a u(n+1)u(n+1)u(n+1) dynamical algebra, where nnn is the number of collective degrees of freedom. Below the ESQPT critical energy of these models, the energy gap between neighboring levels that belong to different symmetry sectors gets close to zero as the system size increases. We report and explain why this gap goes to zero exponentially for systems with one collective degree of freedom but algebraically in models with more than one degree of freedom. As a consequence, we show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with n=1n=1n=1, but in systems with n>1n>1n>1, this average only works as an order parameter in the mean-field limit.
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a ``continuous supersolid,'' which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.