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arXiv:1212.4933 · Physical Review A

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

Sheng-Chang Li, Libin Fu, Fuli Li

Published Jul 1, 2013• 7 citations
arXivHTMLPDF

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 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.

DOI
10.1103/physreva.88.013602

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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 \ensuremathπ/3\ensuremath{\pi}/3\ensuremathπ/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.
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.
Abstract We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete Z 2 symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous U (1) symmetry. For a large enough but finite η , the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.
Quantum phase transition is a fundamental physical phenomenon in a quantum many-body system. This work aims to explore the quantum phase transition in an atom–molecule conversion system through quantum information tools. We show that the ground state of the system undergoes significant changes in the quantum critical region, with both atomic number fluctuation and the quantum information embedded in the ground state exhibiting drastic alterations. As the rescaled phase transition parameter increases, the atomic state sharply transits into the molecular state in the critical region. Even for finite total number, the phase transition point can be accurately predicted through finite-size scaling laws. Our study confirms that the finite-size scaling analysis based on quantum coherence and quantum Fisher information is a reliable method for studying critical phenomena in the atom–molecule system from a quantum information perspective.
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.