Influence of the hyperfine structure of the atomic states on the collective effects in the Rb<Subscript>2</Subscript> quasi-molecule

A consistent quantum approach is used to study the influence of intraatomic spin–orbit and hyperfine interactions on the character of a resonance dipole–dipole interatomic interaction and, hence, collective effects. For this purpose, the collective spontaneous decay of excited states and the spectral dependence of the total scattering cross section of a monochromatic light wave are analyzed in the system consisting of two rubidium-87 atoms. The modification of the radiation properties and the interaction of the atoms with external radiation are studied as functions of the interatomic distance. The presence of a complex structure of the sublevels of both the ground and excited states is shown to modify the collective effects substantially as compared to the case when this structure is absent.     

Superradiant cascade emissions in an atomic ensemble via four-wave mixing

We investigate superradiant cascade emissions from an atomic ensemble driven by two-color classical fields. The correlated pair of photons (signal and idler) is generated by adiabatically driving the system with large-detuned light fields via four-wave mixing. The signal photon from the upper transition of the diamond-type atomic levels is followed by the idler one which can be superradiant due to light-induced dipole–dipole interactions. We then calculate the cooperative Lamb shift (CLS) of the idler photon, which is a cumulative effect of interaction energy. We study its dependence on a cylindrical geometry, a conventional setup in cold atom experiments, and estimate the maximum CLS which can be significant and observable. Manipulating the CLS of cascade emissions enables frequency qubits that provide alternative robust elements in quantum network.     

Ferromagnetic to antiferromagnetic transition of one-dimensional spinor Bose gases with spin-orbit coupling

The effect of the interatomic dipole-dipole interaction on the single-photon transmission spectrum is investigated theoretically in the single-mode optical waveguide containing a pair of dipole interaction two-level atoms and the incident photon, respectively. The results show that the interatomic dipole-dipole interaction can induce a remarkable change in the photon-atom on-resonance frequency in the single-photon transmission spectrum compared with the nonexistence of the interatomic dipole-dipole interaction. As a consequence, the original zero transmission probability at the original photon-atom resonant frequency increases to one directly thanks to the appropriately-chosen dipole-dipole interaction strength. Consequently, this characteristic reveals that the interatomic dipole-dipole interaction treated as an important internal physical mechanism can perform as a functional quantum switching to manipulate the photon’s transmission in the optical waveguide. The corresponding interpretations responsible for this phenomenon are presented.     

Near-field effect in two-atom system

The self-consistent problem is solved for the interaction of two dipole atoms situated at arbitrary distance from one another with the field of quasiresonant light wave. Atoms are considered to be linear Lorenz oscillators. Polarizing fields inside the system include both Coulomb and retarding parts. The solutions obtained are investigated for the case when atoms have the same polarizabilities and interatomic distance is much less than external light wavelength. Formulas for electric fields inside and outside of small object are obtained. It is shown that longitudinal and transverse optical oscillations are possible to exist inside small two-atom object. Dispersion laws of these oscillations depend upon interatomic distance and upon angle between axis of the system and the direction of propagation of external wave. The field outside the small object in wave zone is linearly polarized with the choice of linear polarization of external field. However, the directions of polarization of these waves are different and depend essentially upon frequency. The amplitude of field outside small object in wave zone is shown to depend essentially on the frequency of external field and interatomic distance. The results obtained are treated as near-field effect in the optics of small objects making it possible to investigate the structure of small objects with optical radiation. Received 26 October 1998 and Received in final form 26 January 2000     

Nonlinear resonances in the near-field interaction between atoms

It has been shown that nonlinear near-field optical resonances occur in diatomic nanostructures consisting of identical or different two-level atoms in the presence of a radiation field when the dipole-dipole interaction is taken into account. The frequencies of these resonances depend strongly on the intensity of the external optical radiation, on the initial conditions, on the polarization of the external field with respect to the axis of the nanostructure, and on the interatomic distance. The interatomic interaction is taken into account beyond perturbation theory. For this reason, the effective polarizabilities of the atoms of the nanostructure are expressed in terms of the polynomials of both the interatomic distance and the electric field strength of the external optical wave. A “falling tower” effect that is caused by the nonlinear behavior of the local dipole moments of atoms in the nanostructure is predicted.     

Experimental demonstration of switching entangled photons based on the Rydberg blockade effect

The long-range interaction between Rydberg-excited atoms endows a medium with large optical nonlinearity. Here, we demonstrate an optical switch to operate on a single photon from an entangled photon pair under a Rydberg electromagnetically induced transparency configuration. With the presence of the Rydberg blockade effect, we switch on a gate field to make the atomic medium nontransparent thereby absorbing the single photon emitted from another atomic ensemble via the spontaneous fourwave mixing process. In contrast to the case without a gate field, more than 50% of the photons sent to the switch are blocked,and finally achieve an effective single-photon switch. There are on average 1-2 gate photons per effective blockade sphere in one gate pulse. This switching effect on a single entangled photon depends on the principal quantum number and the photon number of the gate field. Our experimental progress is significant in the quantum information process especially in controlling the interaction between Rydberg atoms and entangled photon pairs.     

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.     

Specific Features of Interatomic Dipole–Dipole Interaction near a Perfectly Conducting Charged Surface

Specific features of dipole–dipole interaction between two motionless point atoms located near a perfectly conducting charged plate are investigated theoretically within a consistent quantum microscopic approach. These features are analyzed on the basis of the dynamics of cooperative spontaneous decay of excited states of a diatomic quasimolecule. The decay rate is investigated as a function of the interatomic distance, the orientation angle of the quasimolecule with respect to the plane of the plate, and the distance between the quasimolecule and the plate. It is shown that the conducting plate significantly modifies the character of dipole–dipole interaction even when the plate is not charged. When the plate is charged, the Stark splitting of atomic levels leads to an additional modification of the interatomic interaction. The features observed are explained on the basis of the analysis of the spectrum of collective states of diatomic molecules.     

The problem of two electrons in an external field and the method of integral equations in optics

This paper solves the problem of the interaction, via the field of virtual photon field with the emission or absorption of a real photon, of two atomic electrons located at arbitrary distances from one another. The interaction is interpreted as a third-order QED effect in the coordinate representation. The role of intermediate states with positive and negative frequencies is studied. A general expression is derived for the matrix elements of the operator of the effective electron-electron interaction energy for different types of quantum transitions. The expression makes it possible to calculate the probabilities of the corresponding transitions and to examine various patterns of induction of polarizing fields by one atom at the point occupied by the other atom. The exchange of virtual photons between the atoms located at arbitrary distances from one another is shown to lead to additional terms in the operators of spin-orbit and spin-spin coupling of the atomic electrons, over and above those in the corresponding Breit operators. It is shown that there is an important difference between the induction of polarizing fields and the transfer of optical photons. In particular, it is found that when polarizing fields are induced, a situation may arise in which the disappearance (production) of a photon takes place at the point occupied by one atom, while absorption (emission) of the same photon occurs at the place occupied by the other atom. A block diagram of an experimental device that could be used to study this property of polarizing fields is presented. Finally, a method of deriving integral field equations is proposed. The method is based on allowing for polarizing fields, and its effectiveness is demonstrated by the example of electric dipole and spin transitions in the spectrum of interacting atomic electrons. Zh. éksp. Teor. Fiz. 114, 1555–1577 (November 1998)     

基于Tavis-Cummings模型实现非定域三原子系统量子特性的远程控制

运用全量子理论并结合数值计算方法,研究了三个二能级原子系统的量子特性。初始三原子处于W纠缠态,让其中的两原子A、B与相干态光腔场发生共振作用,经腔QED演化以后,对原子进行Bell基测量,通过调节相干态光场的强度和原子间的偶极相互作用,来控制腔外原子C的布居差演化;对相干态光场进行光子探测,通过改变探测到的光子数、相干光场参量和原子间偶极相互作用,来控制腔外原子C的偶极压缩,最终实现了远程操纵腔外原子非经典特性的目的。     

Near-field effect in optics of small objects composed of dipole atoms

A self-consistent problem of interaction of two dipole atoms separated by an unrestricted distance with the field of a quasi-resonance light wave was solved on the assumption that the investigated atoms are Lorentz linear oscillators and the polarizing fields inside the system consist of the Coulomb and the retarded parts. The solution obtained was investigated for the case where the atoms have the same polarizability and the distance between them is much smaller than the length of the external light wave. Formulas for the electric fields inside a small object and outside it have been obtained. It is shown that inside a small two-atom object there can take place longitudinal and transverse optical vibrations accompanied by corresponding dispersion effects depending on the interatomic distance and the angle between the axis of the system and the direction of propagation of the external light wave. The field outside the small object in the wave zone is linearly polarized when the external wave has linear polarization. However, the direction of polarization of the corresponding waves is largely determined by their frequency. It is also shown that the amplitude of the field outside the small object in the wave zone depends greatly on the frequency of the external field and the interatomic distance. The effects observed are considered as a near-field effect in optics of small objects. This phenomena makes it possible to investigate the structure of small objects with the use of optical radiation. Ul'yanovsk Branch of the Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 48 Goncharov Str., Ul'yanovsk, 432700, Russia; e-mail: gadomsky@quant.univ.simbirsk.su. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 765–770, November–December, 1999.     

Effect of magnetic field on the character of fluorescence of dense and cold atomic ensembles excited by pulsed radiation

Specific features of fluorescence of dense and cold nondegenerate atomic ensembles in an external constant magnetic field are analyzed theoretically. The angular distribution, polarization properties, as well as the spectral composition of fluorescence radiation are calculated. The time variation of these characteristics after the end of the excitation pulse is analyzed. The dependence of the properties of secondary radiation on the duration and carrier frequency of the pulse is investigated. It is shown that, for dense clouds in which the free path length of quasiresonance photons is commensurate with the interatomic distance, the magnetic field significantly modifies all the observable properties of the radiation. Under these conditions, the trapping time may increase by tens of times. Magnetic field enhances the effect of quantum beats observed on time scales commensurate with the lifetime of the excited states of atoms. For individual polarization channels, this field also intensifies the phenomenon of coherent backscattering (CBS). The phenomena found are explained by the effect of magnetic field on the character of resonance dipole–dipole interaction and, as a result, on the specific features of collective phenomena in dense atomic ensembles.     

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bonded interaction of three S-state atoms it appears that representing the non-additive energy by the non-additive coulomb energy is not reliable until the interatomic separations are somewhat larger than R*, the interatomic distance associated with the van der Waals minimum in the corresponding non-bonded dimer interaction. Further, the use of the triple-dipole interaction energy, with or without charge overlap corrections, to represent the non-additive coulomb energy is of doubtful validity until the interatomic separations are considerably greater than R*.     

非简谐性离子晶格在光场中的能谱动态斯塔克效应

以文献（５）在偶极近似与旋转波近似下导出的哈密顿算符（Ｈａｍｉｌｔｏｎｉｎａｎ）为基础,并以单模光频支声子与单模光场的共振耦合系统为简化模型,取得该耦合系统相互作用能谱的比较严格的解析解,同时还发现一种起源于声子－声子耦合的真空（能级）平移效应,可以预期,本文所研究的能谱将是有关晶体物质结构的又一种信息源。     

Resonant inelastic contact scattering of X-ray photons on atoms and ions

The existence of an extended resonance structure outside the X-ray emission regions is theoretically predicted in the total double differential cross section for the scattering of linearly polarized photons on free atoms (ions). This structure is almost entirely determined by inelastic photon scattering of the contact type. The amplitude of the inelastic contact scattering probability is described using an analytical expression for a non-relativistic transition operator, which was previously obtained by the author outside the dipole and momentum approximations. The resonant inelastic contact scattering of X-ray photons on a neon atom and neonlike ions of argon, titanium, and iron has been studied. Calculations were performed in a nonrelativistic approximation for the wave functions of the scattering states, with allowance for many-body effects of the radial relaxation of one-electron orbitals in the Hartree-Fock field of a deep 1s vacancy and (for neon atom) the double excitation/ionization of the ground atomic state.     

An atom and a photon

The coherent control of single-photon emitters as, e.g., single ions or atoms, is a crucial element for mapping quantum information between light and matter. The possibility of generating entanglement between a photon and the emitter system provides an interface between matter-based quantum memories and photonic quantum communication channels, which is the essential resource for quantum repeaters and other future quantum information applications. To generate entangled atom-photon states, in our experiment, we store a single ⁸⁷Rb atom in an optical dipole trap. The single-atom/single-photon character is confirmed by the observation of photon antibunching in the detected fluorescence light. The spectral properties of single photons emitted by the atom allowed us to determine the mean kinetic energy of the atom corresponding to 105 μK. We describe a single-atom state analysis method which allowed us to characterize the entanglement between the atom and a single photon emitted in the spontaneous decay. We obtain an entanglement fidelity of 89% that clearly shows the high degree of entanglement in our system and potential for further applications in quantum communication.     

Atom-photon cluster as an elementary emitter

The interaction of an atomic ensemble localized in a microcavity with external electromagnetic fields under Raman resonance conditions with an optically forbidden atomic transition involving photons of the microcavity mode has been described in terms of third-order polynomial algebra. It has been shown that atoms and photons localized in the microcavity under these conditions form a united object, an atom-photon cluster, on the states of which the irreducible representations of polynomial algebra are implemented. Classical coherent and quantum broadband electromagnetic fields are considered as external fields. The effective Hamiltonian, effective dipole moment operator, and relaxation operator of the atom-photon cluster are expressed in terms of the generators of polynomial algebra, which is the algebra of the dynamical symmetry of the problem. The developed mathematical technique has been applied to describe the main radiative processes—spontaneous emission and nutation effect—on atom-photon clusters. All of these effects are peculiar and differ from similar phenomena on two-level atoms, but only simple cases of the mentioned radiative processes have been considered.     

Superfluid state of coherent light in nonlinear waveguides

We establish the photonic superfluid theory in waveguides made of self-defocussing polar crystals. In quantum theory it is shown that photons can sense an attractive effective interaction by exchange of virtual optical phonons. Such an interaction leads to the photonic superfluid state, in which a propagating photon pair consists of a combination of two photons with opposite transverse wave vector and spins. The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations. The traveling-wave superfluid state has the squeezing property and the soliton effect.     

Polarization fields in the positronium atom undergoing emission or absorption of optical photons

This paper solves the problem of the interaction of an electron and positron via the field of soft and hard photons with emission or absorption of a real photon. The interaction is interpreted as a third-order QED effect in the coordinate representation. The role of intermediate states with positive and negative frequencies is studied. A general expression is derived for the matrix elements of the operator of the effective electron-positron interaction energy for different types of quantum transitions. The expression makes it possible to calculate the probabilities of the corresponding transitions in the nonrelativistic approximation. Electric dipole transitions in the positronium atom accompanied by emission (absorption) of an optical photon are investigated. Two-particle wave functions of the positronium atom are used to introduce the concept of polarization fields inside the positronium atom. It is found that the polarization fields depend on the coordinates and time and on the choice of the pair of states between which a quantum transition with emission or absorption of a photon takes place. Zh. éksp. Teor. Fiz. 113, 471–488 (February 1998)