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Europhysics Letters (EPL)

Role of asymmetry in the geometric phase of a coupled atom-heteronuclear molecule system

Sheng-Chang Li, Li-Chen Zhao

Published Dec 1, 2013• 1 citation
Publisher

Abstract

\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

DOI
10.1209/0295-5075/104/66002

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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.
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.
Recently, the finite-number effect of initial atoms in coherent atom-molecule conversion was investigated by Zhao et al. [Phys. Rev. Lett. 101, 010401 (2008)]. Here, by extending to the atom-heteronuclear molecule dark state, we find that the initial populations imbalance of the atoms plays a significant role in quantum conversion rate and adiabatic fidelity. In particular, even for the finite total number of imbalanced two-species atoms, the mean-field conversion rate, contrary to the general belief, still can be remarkably close to the exact quantum results.
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.
We investigate the quantum phase transition in an ultracold atom-molecule conversion system. It is found that the system undergoes a phase transition from a mixed atom-molecule phase to a pure molecule phase when the energy bias exceeds a critical value. By constructing a coherent state as variational state, we get a good approximation of the quantum ground state of the system. Using this variational state, we deduce the critical point analytically. We then discuss the scaling laws characterizing the transition and obtain the corresponding critical exponents. Furthermore, the Berry curvature signature of the transition is studied. In particular, we find that the derivatives of the Berry curvature with respect to total particle number intersect at the critical point. The underlying mechanism of this finding is discussed as well.
The quantum phase transition in an atom-molecule conversion system with atomic hopping between different hyperfine states is studied. In mean field approximation, we give the phase diagram whose phase boundary only depends on the atomic hopping strength and the atom-molecule energy detuning but not on the atomic interaction. Such a phase boundary is further confirmed by the fidelity of the ground state and the energy gap between the first-excited state and the ground one. In comparison to mean field approximation, we also study the quantum phase transition in full quantum method, where the phase boundary can be affected by the particle number of the system. Whereas, with the help of finite-size scaling behaviors of energy gap, fidelity susceptibility and the first-order derivative of entanglement entropy, we show that one can obtain the same phase boundary by the MFA and full quantum methods in the limit of N→∞N\rightarrow \inftyN→∞. Additionally, our results show that the quantum phase transition can happens at the critical value of the atomic hopping strength even if the atom-molecule energy detuning is fixed on a certain value, which provides one a new way to control the quantum phase transition.