Nonlinear theory of resonant beam-plasma interaction: Nonrelativistic case

Analytic and numerical methods are used to study the nonlinear dynamics of the resonant interaction between a dense nonrelativistic electron beam and a plasma in a spatially bounded system. Regimes such as collective (Raman) and single-particle (Thomson) Cherenkov effects are considered. It is shown that in the first case, the motion of both the beam and plasma electrons exhibits significant nonlinearities. However, because of the weak coupling between the beam and the plasma, the nonlinear dynamics of the instability can be studied analytically and it can be strictly shown that saturation of instability is caused by a nonlinear shift of the radiation frequency and loss of resonance. In the second case, the nonlinear instability dynamics can only be studied numerically. In this regime, at low beam densities significant nonlinearity is only observed in the motion of the beam electrons while the plasma remains linear and saturation of the instability is caused by trapping of beam electrons in the field of the beam-excited plasma wave.     

Controlled entanglement of two atoms in photonic crystals

The exact entanglement dynamics of two dipole-dipole interacting two-level atoms coupled to a common photonic band-gap (PBG) environment has been investigated. We show that the detuning conditions and the dipole-dipole interaction (DDI) are two essential ingredients and their interplay plays a crucial role in controlling the entanglement of the two-qubit system. For the negative detuning, corresponding to the case where the atomic transition frequency is inside the band gap, the entanglement of the two-qubit system can survive in the long-time limit. For the positive detuning, although the fast disentanglement presents, the DDI effects can be used to fight against the deterioration of the entanglement. The theoretical results could be applied to the implementation of quantum information processing in nanostructured materials.     

A modified Jaynes-Cummings model for an atom interacting with a classical multifrequency field

An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ in the dynamics of the populations of the quasienergy states, can be realized. Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997)     

Superradiance by a system of highly polarized exchange-coupled nonequivalent spins

We propose a model of radiofrequency (rf) superradiance by a system of interacting nonequivalent spins in a point specimen. In contrast to the rf superradiance observed and described earlier, here spin-spin coupling acts as the interaction with the cavity. To be definite, we examine the spins of two isotopes of a metal that are coupled by the Ruderman-Kittel interaction. The analysis of such a system when the magnetization of one spin species is inverted shows that the system can have one resonance frequency and two different decay times, instead of two resonance frequencies and one decay time in the usual situation. When such “repulsion” of decay times occurs and the absolute values of the spin polarizations are large, transverse magnetization increases and exhibits features characteristic of superradiance. Finally, we calculate the parameters of this superradiance: the voltage across the terminals of an rf pickup coil, the pulse length, the delay time, and the superradiant intensity. Zh. éksp. Teor. Fiz. 112, 551–563 (August 1997)     

Quantum chaos of an ion trapped in a linear ion trap

We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model and the initial conditions are close to the real physical situation which can be realized in the system of cold trapped ion perturbed by two lasers fields with close frequencies. (c) 2000 American Institute of Physics.     

Cooperative population dynamics of an ensemble of Λ atoms in a bichromatic field

Equations are derived which describe the dynamics of three-level atoms with a Λ level scheme, interacting with two coherent resonance fields under conditions such that cooperative relaxation predominates over incoherent spontaneous emission. A numerical calculation of the temporal dynamics of the values of the atomic populations is performed. It is shown that coherent population trapping in the presence of cooperative decay is possible. The quantities characterizing this phenomenon are calculated—the width of the black line and the transition time to coherent trapping in this scheme. Zh. Tekh. Fiz. 68, 19–24 (June 1998)     

The Effect of Electromagnetically Induced Transparency in Classical Systems

We develop a classical model of the recently popular parametric effect of electromagnetically induced transparency (EIT), i.e., the formation of a “transparency window” inside a resonance absorption line of a three-level quantum system, which is accompanied by a record strong slowing of the probe wave. Based on this model, we consider the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma. The parametric (three-wave) interaction of two electromagnetic modes (the frequency of one of these modes is equal to the electron gyrofrequency) with the electrostatic mode is considered. It is shown that the resonance growth in the electron oscillations at the gyrofrequency can be damped due to the parametric coupling with the collective electrostatic oscillations. Similar to analogous quantum systems, the group slowing of the probe electron-cyclotron wave in the transparency window takes place in the case considered.     

Dipolar drag in bilayer harmonically trapped gases

We consider two separated pancake-shaped trapped gases interacting with a dipolar (either magnetic or electric) force. We study how the center of mass motion propagates from one cloud to the other as a consequence of the long-range nature of the interaction. The corresponding dynamics is fixed by the frequency difference between the in-phase and the out-of-phase center of mass modes of the two clouds, whose dependence on the dipolar interaction strength and the cloud separation is explicitly investigated. We discuss Fermi gases in the degenerate as well as in the classical limit and comment on the case of Bose-Einstein condensed gases.     

The entanglement dynamics of interacting qubits embedded in a spin environment with Dzyaloshinsky-Moriya term

We investigate the entanglement dynamics of two interacting qubits in a spin environment, which is described by an XY model with Dzyaloshinsky-Moriya (DM) interaction. The competing effects of environmental noise and interqubit coupling on entanglement generation for various system parameters are studied. We find that the entanglement generation is suppressed remarkably in weak-coupling region at quantum critical point (QCP). However, the suppression of the entanglement generation at QCP can be compensated both by increasing the DM interaction and by decreasing the anisotropy of the spin chain. Beyond the weak-coupling region, there exist resonance peaks of concurrence when the system-bath coupling equals to external magnetic field. We attribute the presence of resonance peaks to the flat band of the self-Hamiltonian. These peaks are highly sensitive to anisotropy parameter and DM interaction.     

Quantum control of two interacting electrons in a coupled quantum dot

Quantum-state engineering, i.e. active manipulation over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. Here we discuss the dynamics of two interacting electrons in a coupled quantum dot driven by an external electric field. The results show that the two quantum dots can be used to prepare a maximally entangled Bell state by changing the strength and duration of an oscillatory electric field. Different from the suggestion made by Loss \textit et al (1998 Phys. Rev. A 57 120, the present entanglement involves the spatial degree of freedom for the two electrons. We also find that the coherent tunnelling suppression discussed by Grossmann \textit et al (1991 Phys. Rev. Lett. 67 516 persists in the two-particle case: i.e. two electrons initially localized in one dot can remain dynamically localized, although the strong Coulomb repulsion prevents them from behaving so. Surprisingly, the interaction enhances the degree of localization to a large extent compared with that in the non-interacting case. This phenomenon is referred to as the Coulomb-enhanced dynamical localization.     

Chaotic dynamics of coupled two-level atoms in the optical cavity

Spin systems are one of the most promising candidates for quantum computation. At the same time, control of a system's quantum state during time evolution is one of the main problems. It is usually considered that in magnetic resonance the so-called resonance condition is sufficient to control the spin system. However, because of the nonlinearity of the system, obstructions to the control of the system's quantum state may emerge. In particular, the quantum dynamics of coupled two-level atoms in the optical cavity are studied in this work. The problem under consideration is a generalization of the paradigmatic model for Cavity Quantum Electrodynamics of the Jaynes-Cummings model in the case of interacting spins. In this work, it is shown that the dynamics are chaotic when taking into account the center-of-mass motion of the system and the recoil effect. Furthermore, even in the case of zero detuning, chaotic dynamics emerge in the system. It is also shown in this work that, because of the chaotic dynamics the system executes an irreversible transition from a pure quantum-mechanical state to a mixed one. Irreversibility, in turn, is an obstacle for controlling the state of the quantum-mechanical system.     

Polarization response of interacting atomic systems in an intense resonance laser field

The dynamics and quantum correlations are studied in a system of two interacting atoms in a resonance femtosecond laser field. The polarization response of a medium consisting of such pairs of interacting atoms is analyzed. Regimes are found in which the polarization response of the medium under study contains the intense component at a tunable low frequency. It is shown that the dipole response of the medium can be suppressed using the entanglement effect and symmetry properties of collective atomic states.     

Master equations for time correlation functions of a quantum system interacting with stochastic perturbations and applications to emission and absorption line shapes

The stochastic and quantum dynamics of open quantum systems interacting with stochastic perturbations in considered. The master equations for one time and multi-time correlation functions of such a system are derived to all orders in the interaction with the stochastic perturbations. The importance of the non-markovian character of such equations in the study of various problems in optical resonance is discussed. The simplified form of the non-markovian master equations in Born approximation is also given. It is shown that such non-markovian master equations in Born approximation are exact if there is only one random perturbation, of the telegraphic signal type, acting on the system. The master equations for the linear response functions of an open system interacting with stochastic perturbations are also derived. The non-markovian master equations for multitime correlations are used to study the behaviour of two level atoms interacting with fluctuating laser fields. Both amplitude and phase fluctuations are taken into account. Explicit results are presented for the spectrum of resonance fluorescence, absorption spectrum, photon antibunching effects etc. The calculations are done for arbitrary values of the relaxation parameters and intial conditions. In general the fluorescence spectrum is found to be asymmetric for off resonant fields.     

两二能级原子在共同环境下的量子关联动力学

通过精确求解带有偶极-偶极相互作用的两个二能级原子与一个共同热库相互作用模型, 得到了两原子间量子纠缠和量子失谐(quantum discord)的解析表达式. 综合考虑了环境的非马尔可夫效应、原子间的偶极-偶极相互作用以及原子的本征频率同腔模中心频率之间的失谐量对两原子间量子纠缠和quantum discord的影响. 研究显示: 在非马尔可夫机制下, 且原子的本征频率与腔模中心频率是共振时, 当两原子初态处于纠缠态时, 原子间偶极-偶极相互作用可以显著抑制包括量子纠缠和quantum discord等量子关联的衰减, 更特别的是, 如果原子的本征频率同腔模中心频率有一定的失谐时, 利用原子间偶极-偶极相互作用可大大地延长两原子退纠缠的时间; 当两原子初态处于可分离态时, 从短时间来看, 原子间偶极-偶极相互作用可以提高量子纠缠和quantum discord振荡的振幅,而在长时间极限下, 原子间偶极-偶极相互作用不会改变量子纠缠和quantum discord达到的稳定值. 最后, 讨论了原子间偶极-偶极相互作用对量子纠缠和quantum discord动力学不同的影响. 关键词： 量子纠缠 量子失谐 共同环境 偶极-偶极相互作用     

The role of primary and secondary delays in the effective resonance frequency of acoustically interacting microbubbles

Acoustically excited microbubbles (MBs) are known to be nonlinear oscillators with complex dynamics. This has enabled their use in a wide range of applications from medicine to industry and underwater acoustics. To better utilize their potential in applications and possibly invent new ones a comprehensive understanding of their dynamics is required. In this work, we explore the effect of bubble-bubble interactions on the resonance frequency of MB suspensions. MBs oscillate in response to an external acoustic wave and since bubbles in a cluster are at different locations compared to the excitation source, they are excited at different times. In this work we refer to these delays as primary delays. Interactions between the scattered pressure fields from adjacent bubbles have also been shown to alter the dynamics of MBs that exist within clusters. These secondary waves generated by MBs reach MBs in their proximity at different times that depend on their spatial location in the cluster. Here we refer to these delays as secondary delays. Inclusion of the secondary delays modifies the class of the differential equations governing the oscillations of interacting MBs in a cluster from ordinary differential equations to neutral delay differential equations. Previous work has not considered the all the delays associated with the bubble distances when modeling the interactions between bubbles. In this work we investigate the effect of both the primary and secondary delays on the effective resonance frequency of MB clusters. It is shown that primary delays cause spreading the resonance frequency of identical MBs within a range where the closest MB to the acoustic source exhibits the lowest resonance frequency and the furthest MB resonates at the highest frequency. This range has been shown to be up to 0.12 MHz for the examples investigated in this work. The effect of secondary delays is shown to be very significant. In the absence of secondary delays, the ordinary differential equation model predicts a decrease of up to 26% in the resonance frequency of 4 identical interacting MBs as the inter-bubble distances are decreased. However, we show that inclusion of the secondary delays result in the increase of the resonance frequency of MBs if they are situated close to each other. This increase is shown to be significant and for the case of 4 identical interacting MBs we show an increase of 58% in the resonance frequency.     

Interaction of Three Electromagnetic Fields with a Resonance Medium in EPR. The Case of a Small Local Field in Comparison with the Saturating One

A system of Bloch equations modified with allowance for the presence of a dipole–dipole reservoir for the case where the local magnetic field is small in comparison with the saturating one is suggested. The system is used for solving the problem of interaction of three electromagnetic fields: a saturating field, a probe one, and the third - a combination field resulting from the interaction of the first two in a resonance medium. The imaginary and real parts of the system susceptibility at the probe-field frequency have been investigated in detail at both different frequencies of interacting waves and coinciding ones (degenerate case). For the degenerate case, the dependence of the coefficient of the parametric connection of waves on the frequency is considered. The results of the present work are compared with those obtained by us earlier for the case where the local magnetic field is much in excess of the saturating one (Provotorov's case). It is shown that in the problem considered the amplification of weak waves when they pass through the layer of an absorbing resonance medium is inaccessible.     

Enhancement of stationary state quantum discord in Tavis-Cummings model by nonlinear Kerr-like medium

We investigate the influence of nonlinear Kerr-like medium and dipole-dipole interaction on the dynamics of quantum discord in Tavis-Cummings model with phase decoherence. We show that in the resonance case (i) atom-field quantum discord rapidly decays with phase decoherence and doesn't exist the stationary state quantum discord, but the stationary state quantum discord appears if we choose the suitable values of Kerr coefficient χ and dipole-dipole interaction Ω, (ii) the quantum discord of two atoms survives in the stationary state and the amount of stationary state quantum discord could be improved by adjusting the values of χ and Ω. In the non-resonance case, the arbitrary bipartite quantum discord of the system could not be completely destroyed by the phase decoherence and can be improved by applying nonlinear Kerr-like medium and dipole-dipole interaction.     

Dimensional resonances and second-harmonic generation in a semibounded nonlinear layered periodic medium

A theory for the nonlinear interaction of electromagnetic waves in a semibounded periodic dielectric structure is developed using the example of second-harmonic generation. One of the layers forming a period is assumed to have nonlinear polarization. The theory is an improved perturbation theory based on the Green theorem. The phase-matching conditions for interacting waves are shown to correspond to dimensional resonances for individual layers or for the structure period. The interaction efficiency is maximum at passband edges for the case of resonance for the entire period. For this resonance, the phase-matching conditions are met for a frequency spectrum rather than for a single frequency. This feature makes it possible to convert spectra from one frequency range to another.     

Frequency‐sensitive switching control effect induced by two‐photon resonance in an EIT‐based layered medium

The optical response of an atomic vapor can be coherently manipulated by tunable quantum interference occurring in atomic transition processes. A periodic layered medium whose unit cells consist of a dielectric and an EIT (electromagnetically induced transparency) atomic vapor is designed for light propagation manipulation. Such an EIT‐based periodic layered medium exhibits a flexible frequency‐sensitive optical response, where a very small change in probe frequency can lead to a drastic variation of reflectance and transmittance. As the destructive quantum interference relevant to two‐photon resonance arises in EIT atoms interacting with both control and probe fields, the controllable optical processes that depend sensitively on the external control field will take place in this EIT‐based periodic layered medium. Such a frequency‐sensitive and field‐controlled optical behavior of reflection and transmission in the EIT photonic crystal can be applicable to designs of new devices such as photonic switches, photonic logic gates and photonic transistors, where one laser field can be controlled by the other one, and would have potential applications in the areas of integrated optical circuits and other related techniques (e.g., all‐optical instrumentations).