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Journal of the Optical Society of America B

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

Sheng-Chang Li, Li-Chen Zhao

Published Feb 26, 2014• 5 citations
Publisher

Abstract

We investigate the properties of phase transitions in a weakly coupled ultracold atom-molecule boson system based on the phase space analysis approach. We identify the pure molecular and mixed atom-molecule phases of the system by different values of the time average of molecular population. When applying a periodic modulation on the energy detuning, we find that the atom-molecule mixing dynamics can be well controlled. For both high- and low-frequency modulations, it is shown that the transition points can be shifted effectively by choosing parameters of the periodic modulation appropriately. The analytical expressions for the dependence of the transition parameters on the modulation parameters are also obtained for the two cases. In particular, when the modulation with a frequency near the atom-molecule transition frequency is applied, the resonance between the periodic modulation and atom-molecule Rabi oscillation will emerge, which can affect the atom-molecule mixing dynamics dramatically and lead to the complex chaos phenomenon.

DOI
10.1364/josab.31.000642

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We investigate the properties of phase transitions in a weakly coupled ultracold atom-molecule boson system based on the phase space analysis approach. We identify the pure molecular and mixed atom-molecule phases of the system by different values of the time average of molecular population. When applying a periodic modulation on the energy detuning, we find that the atom-molecule mixing dynamics can be well controlled. For both high- and low-frequency modulations, it is shown that the transition points can be shifted effectively by choosing parameters of the periodic modulation appropriately. The analytical expressions for the dependence of the transition parameters on the modulation parameters are also obtained for the two cases. In particular, when the modulation with a frequency near the atom-molecule transition frequency is applied, the resonance between the periodic modulation and atom-molecule Rabi oscillation will emerge, which can affect the atom-molecule mixing dynamics dramatically and lead to the complex chaos phenomenon.
With phase space analysis approach, we investigate the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BECs) in a symmetric double well potential. We identify two kinds of self-trapping by their different relative phase behavior. By applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, in other words, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high- and low-frequency modulations. For an intermediate-frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affect the tunneling dynamics and demonstrate many phenomena. Finally, we study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.
We numerically demonstrate the dynamic stabilization of a strongly interacting many-body bosonic system which can be realized by coupled ultracold atom-molecule gases. The system is initialized to an unstable equilibrium state corresponding to a saddle point in the classical phase space, where subsequent free evolution gives rise to atom-molecule conversion. To control and stabilize the system, periodic modulation is applied that suddenly shifts the relative phase between the atomic and the molecular modes and limits their further interconversion. The stability diagram for the range of modulation amplitudes and periods that stabilize the dynamics is given. The validity of the phase diagram obtained from the time-average calculation is discussed by using the orbit tracking method, and the difference in contrast with the maximum absolute deviation analysis is shown as well. A brief quantum analysis shows that quantum fluctuations can put serious limitations on the applicability of the mean-field 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.
Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly coupled atom-cavity system with atomic center-of-mass motion included is modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigenfrequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of extremal sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low-frequency translational motion is modulated by the high-frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultracold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, which is the effect of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is 1∕21∕21∕2 (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.