Quantum phase transition in a three-level atom-molecule system

Abstract

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 adiabatical geometric phase, we confirm that the system exists a second-order phase transition from an atommolecule 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 behaviors of ground-state geometric phase change obviously in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to ?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.Comment: 8 pages,8 figure

Quantum phase transition of a modified spin-boson model

“…zν = 1 2 is the critical exponent, which is usually universal due to its independence of most of microscopic details of the Hamiltonian Ĥ (q). Relation ( 6) is verified by the results illustrated in figure 4(c) for different c. We emphasize that the above characteristic scaling laws and corresponding critical exponents for the QPT are quite different from those obtained for both two-and three-level bosonic atom-bosonic molecule conversion systems in previous works [23,42]. This implies that our QPT for the modified spinboson model and the QPTs for previous two-or three-level bosonic model belong to different universality classes.…”

“…Before concluding, by comparing the bosonic atom-molecule conversion model [23,41,42] with our modified spin-boson model, we have three remarks. First, it is found that the critical point for the QPT in the former system depends on the molecular interaction while that in the latter system does not.…”

“…Currently, researchers have conducted a series of research in view of the dynamical QPTs [36][37][38][39]. There are many methods about how to identify and characterise QPTs, including symmetry breaking [39,40], von Neumann entanglement entropy and fidelity [41], critical behaviors and scaling laws [42], Berry curvature [23], dynamical evolution [43], and Monte Carlo method versus variational approach à la Feynman [44].…”

Periodic modulation effects on phase transitions in an ultracold atom-molecule system

“…In experiments, the atom-molecule oscillations using either identical bosons in a BEC [8,14] or confined pairs in a deep optical lattice potential [12] can be well described by a twolevel model. This two-level boson system can be a paradigm model used to demonstrate quantum dynamics [15] and quantum phase transition (QPT) [16][17][18]. Recently, the process of production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic-field modulation [19] has been discussed, and this method has been successfully applied to produce molecules with high efficiency [11].…”