Two strong nonlinearity regimes in cold molecule formation

Two distinct strongly non-linear scenarios of molecule formation in an atomic Bose-Einstein condensate (either by photoassociation or Feshbach resonance) corresponding to large and small field detuning are revealed. By examining arbitrary external field configurations, we show that the association process in the first case is almost non-oscillatory in time while in the second case the evolution of the system displays strongly pronounced Rabi-type oscillations. We construct highly accurate approximate solutions for both limit cases. We show that at strong coupling limit the non-crossing models are able to provide conversion of no more than one third of the initial atomic population. Finally, we show that for constant-amplitude models involving a finite final detuning the strong interaction limit is not optimal for molecule formation.     

Time evolution of atomic inversion in a standing wave light field

The interaction between an atomic beam of two-level atoms and a standing wave light field has been studied by the exact solution of a time-dependent quantum system developed recently. When the initial atomic state is choosen to be ground, we find that with the limit of zero detuning the atoms will oscillate between the upper and the lower levels with a decaying amplitude. The most interesting result obtained in this paper is when the initial atomic state is a particular superposition of the two levels, now the system does not oscillate at any time.     

Photon emission from a two-level atom moving in a cavity

The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.     

Thermal Entanglement Between a Jaynes-Cummings Atom and an Isolated Atom

We studied the entanglement of a quantum system consisting of a Jaynes-Cummings atom, thermal lossless cavity and an isolated atom. The analytical expressions of the atom-atom negativity for separable and entangled initial atomic states were obtained. The influence of a detuning between the atomic transition frequency and the field frequency and direct dipole-dipole interaction on an atom-atom entanglement is examined. We showed that for a separable initial atomic states a detuning might cause high atom-atom entanglement in the presence of the dipole-dipole interaction. We also obtained that for an entangled initial atomic state a detuning causes a stabilization of an entanglement oscillations both for model with dipole-dipole interaction and model without such interaction.     

Quantum phase properties of the field in a two-photon micromaser

In this paper, we study the quantum phase properties of the field in a two-photon micromaser, including the effects of the finite detuning of the intermediate level. For initial coherent state of the cavity field and atoms initially in their excited state multipeak phase structure appears which eventually leads to the randomization of the cavity field phase. However, the approach towards the randomization depends upon the detuning. If the atoms are injected in a coherent superposition of their upper and lower atomic states then the phase distribution evolves into two-peak structure. For initial thermal state and atoms in polarized state, cavity field acquires some phase. We also consider the effect of finite Q of the cavity, random injection of the atoms and fluctuations in the interaction time.     

An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3 × 10^?6 for the final transition probability while at certain time points it might increase up to 10^?3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.     

Ionization of atoms in strong low-frequency electromagnetic field

The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.     

Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included

We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over.     

反Tavis-Cummings模型中纠缠原子布居的时间演化

利用反Tavis-Cummings模型研究了初始处于纠缠态的两个全同二能级原子与单模二项式光场的相互作用.在强经典驱动和大失谐的情况下,原子与光场的相互作用可以转化为有效的Tavis-Cummings模型和反Tavis-Cummings模型.主要是研究了反Tavis-Cummings模型下纠缠原子布居的时间演化.结果表明,纠缠原子布居的时间演化和光场的强度以及光场的初始状态有关.     

Effect of Cavity Decay on Entanglement of Ladder-Type Three-Level Atoms and a Two-Mode Cavity Field

Considering the adiabatical approximation and the large detuning condition, we give the effective Hamiltonian of a ladder-type three levels atom interacting with a bimodal cavity field. If two identical three-level atoms are sent through the cavity one by one, a two-atom entangled state can be generated. With the choice of the appropriate interaction time, a maximally entangled state of two atoms can be obtained if decoherence effect is ignored. Moreover, we discuss the effect of cavity decay on four physical quantities including atomic population probability, residual entanglement of the first atom and the cavity field, concurrence between the two atoms, and fidelity for generating atomic EPR state, all of which decrease with the increase of cavity decay when the other parameters are fixed.     

Kerr介质中耦合V型三能级原子与相干态光场作用场的量子性质

研究了Kerr介质中相干态光场与耦合V型三能级原子相互作用过程中场的量子性质.利用量子光学中光场与原子相互作用的耦合Tavis-Cummings模型,对系统的动力学过程进行了求解.讨论了系统初始状态、失谐量、原子间偶极相互作用强度及Kerr系数对光场量子性质随时间演化的影响.数值计算结果表明:初态中场的平均光子数比较小时,光场能够展现出明显的量子效应|初始时刻原子激发态概率幅从小变大时,光场的反聚束效应变得越明显,而光场的压缩深度会先增大后减小|失谐量的变化对场的量子性质的影响不大,只是改变光场二阶相关函数和压缩参量振荡的周期|原子间耦合强度的增大使光场的反聚束效应减弱和光场的压缩深度变浅|Kerr系数的增大会增强光场的反聚束效应,而使光场的压缩深度变浅.     

Adiabatic cavity QED with pairs of atoms

We study the dynamics of a pair of atoms, resonantly interacting with a single mode cavity, in the situation where the atoms enter the cavity with a time delay between them. Using time dependent coupling functions to represent the spatial profile of the mode, we considered the adiabatic limit of the system. Although the time evolution is mostly adiabatic, energy crossings play an important role in the system dynamics. Following from this, entanglement, and a procedure for cavity state teleportation are considered. We examine the behaviour of the system when we introduce decoherence, a finite detuning, and potential asymmetries in the coupling profiles of the atoms.     

Magnetic-field control of subradiance states of a system of two atoms

A method is proposed for the creation of an entangled metastable (subradiance) excited state in a system of two closely spaced identical atoms. The system of unexcited atoms is first placed in a magnetic field that is directed at a magic angle of \({\alpha _0} = {\text{arccos}}\left( {1/\sqrt 3 } \right) \approx 54.7^\circ \) to the line connecting the atoms and has a transverse gradient. The gradient of the field results in the detuning of frequencies of an optical transition of the atoms. Then, the resonant laser excitation of an atom with a higher transition frequency is performed with the subsequent adiabatic switching-off of the gradient of the magnetic field. It is shown that the excited atomic system in this case transits with overwhelming probability to an entangled subradiance state. Requirements on the spectroscopic parameters of the transitions and on the rate of varying the gradient of the magnetic field necessary for the implementation of this effect are analyzed.     

非线性Rosen-Zener跃迁

研究了非线性两模系统的Rosen-Zener跃迁.在绝热近似下，对基态能相同的两个模态，非线性相互作用使原子表现出强烈的集体行为，它们总是趋向于聚集到同一个模态上.因此外场的绝热调制能够把原子从一种模式彻底转移到另一种模式上.在经典相空间中，可以成功地解释该现象.提议利用现有的玻色爱因斯坦凝聚实验观测这一效应. 关键词： Bose-Einstein凝聚 Rosen-Zener跃迁 Rabi振荡 受激Raman绝热暗通道     

Entanglement between two qubits interacting with a slightly detuned thermal field

In this paper, we investigate entanglement between two two-level atoms when they simultaneously interact with a single-mode thermal field in the strong-coupling regime. We show that a slight detuning between the atomic transition frequency and the field frequency might cause high entanglement between the atoms. More interestingly, if we choose the detuning appropriately, both atoms would somehow get entangled even when both atoms are initially in the excited state.     

存在相位退相干时原子与光场相互作用的纠缠演化和保持

应用全量子理论研究了存在相位退相干时单模相干光场与一个二能级原子相互作用系统纠缠的时间演化规律;分别讨论了原子—光场耦合常数、光场的平均光子数以及失谐量的大小对场与原子纠缠的影响.结果表明:随着原子—光场耦合常数的增大和光场平均光子数的增加,系统纠缠的振荡频率都会明显增大.不存在相位退相干时,纠缠的时间演化明显受到失谐量的影响,若选取适当的失谐量,系统的纠缠可长时间保持在最大纠缠态.若考虑相位退相干的影响,则在共振情况下系统纠缠的时间演化是一个逐渐衰减的过程,且最终衰减到零;但若存在适当的失谐量,则在初始一段时间内系统的纠缠也是一个波动幅度逐渐衰减的过程,但随着时间的演化,失谐量抵消了相位退相干的影响,使系统的纠缠不再衰减到零.如果增大失谐量,纠缠在初始一段时间内波动的幅度会相应的减小,并且纠缠趋于稳定的时间也随着失谐量的增大而缩短;当失谐量适当时,系统可保持在纠缠相对较大的状态而无消纠缠态.     

Cooperative transient for atoms driven by a weak coherent field

We present a simple quantum-mechanical treatment of the cooperative interaction between an ensemble of two-level atoms initially in their ground state and the electromagnetic field inside a Fabry-Perot cavity, in the weak field limit. In this limit the atoms have to be considered as being collectively dressed by the field and important cooperative effects are expected in the transient regime. It is shown that, in a first approximation, the evolution of the atom-field system in the general case can be deduced from the very simple “one-excitation” problem. A Rabi nutation at a frequency which depends essentially on the number of atoms is predicted. At resonance, these oscillations are closely related to superradiance “ringing” oscillations and have been observed very recently.     

Damping of Bloch oscillations in the Hubbard model

Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an ac-type response with Bloch oscillations. The transition from ac to dc response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.     

Vacuum Rabi Oscillation of an Atom without Rotating-Wave Approximation

We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes-Cummings （J-C） model. The results show that for resonant ease, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.