Atom-molecule Conversion Research Articles

Dynamical quantum phase transitions in an atom-molecule system

We conduct an investigation on the dynamical quantum phase transition within an atom-molecule Bose–Einstein condensate. We explore the dynamics of atom-molecule conversion and utilize the fraction population of the atom as an order parameter for probing dynamical quantum phase transitions. It is shown that the quench dynamics of the atom presents a non-analytical change regarding the atom binding energy, and it is demonstrated that this dynamics can detect both the quantum phase transition at the ground state and at the highest energy level. Furthermore, we analyze the dynamics of the Loschmidt echo and present its connection with the dynamical quantum phase transitions.

Pairing Superfluid–Insulator Transition Induced by Atom–Molecule Conversion in Bosonic Mixtures in Optical Lattice

Motivated by the recent experiment on bosonic mixtures of atoms and molecules, we investigate pairing superfluid–insulator (SI) transition for bosonic mixtures of atoms and molecules in a one-dimensional optical lattice, which is described by an extended Bose–Hubbard model with atom–molecule conservation (AMC). It is found that AMC can induce an extra pair–superfluid phase though the system does not demonstrate pair-hopping. In particular, the system may undergo several pairing SI or insulator–superfluid transitions as the detuning from the Feshbach resonance is varied from negative to positive, and the larger positive detuning can bifurcate the pair–superfluid phases into mixed superfluid phases consisting of single-atomic and pair-atomic superfluid. The calculation of the second-order Rényi entropy reveals that the discontinuity in its first-order derivative corresponds to the phase boundary of the pairing SI transition. This means that the residual entanglement in our mean-field treatment can be used to efficiently capture the signature of the pairing SI transition induced by AMC.

Efficient atom-molecule conversion in Bose–Einstein condensates based on nonlinear dressed-state scheme

We investigate the dynamics of atomic and molecular Bose–Einstein condensates via nonlinearly dressed states. Under the resonance-locking condition, we add a correction for an initial Hamiltonian to construct the dressed states with only second-order nonlinearity. Compared to the nonlinear stimulated Raman adiabatic passage, atomic-molecular conversion in our protocol is realized by following the dressed states instead of the dark state, thus it can produce a fast conversion passage. Furthermore, we introduce a control parameter to reduce the occupancy of the excited molecule state, and the conversion efficiency can be improved significantly by increasing the value of this parameter.

Quantum phase transition of a modified spin-boson model

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.

Ultracold atom-molecule conversion dynamics in a closed-loop three-level system

The production of ultracold molecules is one of the most exciting topics in the field of ultracold physics, which has important theoretical values and broad application prospects. We propose an ultracold atom-molecule conversion model in a closed-loop three-level system based on three available transitions, in which the population dynamics depends on three coupling fields and global phase. We investigate the atom-molecule conversion dynamics in the closed-loop three-level system. We show the distribution of population on excited molecular state and ground molecular state with arbitrary proportion can be achieved by adjusting pulse amplitudes of the external fields properly. We also explore the effects of time delay, pulse width and global phase on the conversion process. The results show that, by tuning these parameters, the stable atom-molecule conversion with arbitrary proportion can be realized.

Fast-forward scaling of atom-molecule conversion in Bose-Einstein condensates

Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with the wide applications ranging from ultracold molecules, non-linear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with the nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by fast-forward driving field. Finally, our results are extended to the fractional stimulated Raman adiabatic processes for the coherent superposition of atomic and molecular states.

Atom-molecule conversion with quantum manipulations

In this paper, we investigate quantum manipulations in an open atom-molecule conversion system. Through the transformation for the basis of the system, a set of time-dependent equations are derived under mean field approximation. We find that transitions between different dynamic areas of the system can be realized through manipulating an external rotating magnetic field, which corresponds to the tunneling rate in the equation. Through investigating the phase space of the system, we design an efficient method to combine pure cold molecule and pure molecular state so that it can be reached with much shorter time. Furthermore, manipulation of laser signal modulation, external diving and the distance-selective diffusion are also discussed in this paper.

Ultracold bosonic atom–molecule conversion dynamics with a linearly chirped Gaussian pulse

We investigate the conversion dynamics of ultracold bosonic atoms to molecules in an external field with a Gaussian temporal shape and a linear frequency sweep. Under the mean-field theory, we study the atom–molecule conversion efficiency and the dynamics in the conversion process. By using the Fock-state basis, we further research the quantum many-body dynamics, wherein the many-body effect on the conversion is discussed. We find that the atom–molecule conversion dynamics depend on the particle interaction, peak coupled strength, sweep rate, and total particle number. Notably, some analytical results are derived in the regime without particle interactions and in the sudden limit, respectively. Our theory indicates that the ultracold atom–molecule conversion can be achieved stably and efficiently in the Gaussian external field model.

Adiabatic conversion of ultracold atoms into molecules via square-shaped pulse field

On the basis of the stimulated Raman adiabatic passage technology, we study the conversion of ultracold atoms into diatomic molecules by using a square-shaped pulse field. By the method of adiabatic fidelity, we analyze the dynamical evolution process of the coherent population trapping state for the atom-molecule conversion system. We introduce two adiabatic fidelities to describe the efficiency of ultracold atom-molecule conversion, i.e.:1) the final adiabatic fidelity, which gives the value of the adiabatic fidelity at the end of the evolution:the closer to 1 it is, the higher the conversion efficiency is; 2) the final maximum adiabatic fidelity, which denotes the maximum value that can be achieved at the end of evolution, indicating the highest conversion efficiency. With these two quantities, we discuss how to achieve higher adiabatic fidelity for the coherent population trapping state through optimizing the pulse-delay time and the pulse-laser intensity of the stimulated Raman adiabatic passage. In addition, we also discuss the effects of the width of pulses on the ultracold atom-molecule conversion efficiency and the feasibility of continuous light. It is shown that the final adiabatic fidelity of the coherent population trapping state demonstrates a large periodic oscillation with the pulse-laser intensity. By calculating and analyzing the final adiabatic fidelity and the final maximum adiabatic fidelity, we obtain the conditions for higher efficiency conversion, which gives the best choice of the pulse-laser intensity, the pulse-delay time, and the width of pulses. The results show that the scheme of square-shaped pulses we discussed has obvious advantages compared with that of Gaussian-shaped pulses, which can achieve high adiabatic fidelity and realize higher ultracold atom-molecule conversion efficiency via employing the pulse-laser field with low intensity. Further detailed comparison between the square-shaped pulses and the Gaussian-shaped pulses is also given. Particularly, we find that the final adiabatic fidelity shows a periodic oscillation with the pulse width, which means that the high efficiency atom-molecule conversion can be achieved by using a pulse field with small width. Moreover, we find that the high efficiency conversion can also be achieved by using special continuous light under certain conditions.

Effective Atom-Molecule Conversions Using Radio Frequency Fields.

The present study is inspired by the Wieman group experiment [Phys. Rev. Lett. 2005, 95, 190404], in which they use a slow modulated magnetic field to effectively transfer rubidium atoms into cold molecules near a Feshbach resonance. We develop a time-dependent collision theory based on two channel model potentials to study the atom-molecule population transfer induced by a single-color radio frequency field in an ultracold 87 Rb gas. Wave-packet dynamical simulations allow an investigation of both bound-bound transitions and free-bound transitions. The effects of temperature, detuning and the RF amplitude on the population transfer are discussed in detail. Some of our simulations suggest that oscillatory atom-molecule conversion could originate from the long coherence time of the wave packet. This coherence time is unusually long in ultracold gases because the collision energy is typically quite well-defined.

Atom-molecule conversion in a periodically driven spin-boson model

We have investigated the dynamics of atom-molecule conversion using a periodically driven spin-boson model both quantum mechanically and semiclassically. The semiclassical dynamics is fully chaotic for small driving frequencies, so that the regular atom-molecule conversion gradually vanishes. In quantum mechanics, however, the periodic conversion takes place at small frequencies since the quantum adiabatic condition is fulfilled. Moreover, it survives for rather larger frequencies that breaks the adiabatic condition, which is understood by considering the so-called dynamical localization. It implies that the periodic atom-molecule conversion is more robust than we expect from the semiclassical approximation. We also show that for much larger frequencies delocalization takes place so that the dynamics becomes diffusive.

Dynamic stabilization of a coupled ultracold atom-molecule system.

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.

Semiclassical quantization for a bosonic atom-molecule conversion system

We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field dynamics takes place on a deformed version of the Bloch sphere, a teardrop shaped surface with a cusp singularity. We analyse the mean-field and many-particle correspondence, which shows typical features of quantum-classical correspondence. We demonstrate that semiclassical methods can be employed to recover full many-particle features from the mean-field description in cold atom systems with atom-molecule conversion, and derive an analytic expression for the many-particle density of states in the limit of large particle numbers.

Feshbach molecule formation through an oscillating magnetic field: subharmonic resonances

The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom–molecule conversion process.

Quantum phase transition in an atom–molecule conversion system with atomic transition

The quantum phase transition in an atom–molecule conversion system with atomic transition between two hyperfine states is studied. In the mean-field approximation, we give the phase diagram in which the phase boundary only depends on the atomic transition strength and the atom–molecule energy detuning, but not on the atomic interactions. Such a phase boundary is further confirmed by calculating the fidelity of the ground state and the energy gap between the first excited state and the ground state. As a comparison to the mean-field results, we also study the quantum phase transition with the full quantum method where the phase boundary depends on the particle number. Analysing the finite-size scaling behaviours of the energy gap, the fidelity susceptibility and the first-order derivative of entanglement entropy with respect to the atomic transition strength, we obtain their critical exponents by numerical calculation and show that in the thermodynamic limit, one can obtain the same phase boundary as in the mean-field approximation. Our results show a new way to manipulate the quantum phase transition by regulating the atomic transition strength with the intensity of the laser.

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

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.

Atom-molecule-conversion system subject to phase noises

The dynamics of atom-molecule conversion system subject to dephasing noises is studied in this paper. With the dephasing master equation and the mean-field theory, we drive a Bloch equation for the system, this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equations and the master equation, comparison between these two calculations suggests that while in a short time the mean-field theory is a good approximation for the atom-molecule conversion system, a high order hierarchy truncation approach is necessary for the system in a long time scale. Although the MFT can not predict correctly the fixed points, its prediction on the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters.

Atom-molecule conversion in the self-trapping regime

The dynamics of atom-molecule conversion in the Bose-Einstein condensate state, with the formation of a homonuclear molecule in the self-trapping mode, has been studied. The conditions and bifurcation values at which self-trapping occurs in this system are found.

Linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules

In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40K and 6Li atom—molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.

Atom-molecule conversion with particle losses

Based on the mean-field approximation and the phase space analysis, we study the dynamics of an atom-molecule conversion system subject to particle loss. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schr\"odinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundary, which separate different dynamical regimes have been calculated and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored.