Single-atom Case Research Articles

Field-dependent atomic relaxation in a squeezed vacuum

The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.

Simultaneous Extension and Enhancement of the HHG Plateau byUsing Combined Lasers Irradiating on a United Two-Atom System

We present the high-order harmonic generation spectrum from aunited two-atom system simultaneously exposed to a fundamentalTi:sapphire and its 33rd harmonic (H33) lasers by numerically solving aone-dimensional time-dependent Schrödinger equation. At a suitableinter-nuclear separation, the harmonic plateau is widened fromIp+3.2Up in the single-atom case up to Ip+5.6Up in theunited-atom case. Furthermore, the plateau is heightened in excess ofsix orders of magnitude by using the combined lasers compared with thecase of the fundamental laser alone. Such a scheme can step by stepaccomplish the following processes: through a single H33 photonresonance transition an appropriate amount of electrons are firstpopulated to an excited state, in which the electrons are easily ionizedand subsequently accelerated by the fundamental laser; then they canrecombine with the neighbouring atom, so that high-efficiency emissionsof the harmonics beyond Ip+3.2Up are successfully realized.

Cluster ion implantation: a molecular dynamics study

The collisions of 5.7 keV silicon atom and clusters with a silicon surface are simulated by molecular dynamics. Using a parameter surveillance system for simultaneous execution of multiple simulations on parallel/distributed computers, we have studied the impact dependence of cluster ions on the surface. The channeling effect of the implanted atoms is inevitable in the single-atom case, but is suppressed by the macroscopic vibrations of the surface in the cluster-ion case.

Photon statistics and the optical Stark effect

We theoretically describe a pump-probe scheme for detecting the optical Stark effect on two-level atoms with a fully quantized pump field. The probe absorption reflects the photon statistics of the pump field for both the single-atom and multiatom case. Nonclassical features, without counterpart in the single-atom case appear in the multiatom absorption and result in strong variations of the absorption amplitude and nonclassical gain or absorption.

Polariton spontaneous emission superradiance and polariton-impurity states in III–V semiconductors

In this paper, we study the polariton energy dispersion of two different types of two-level atoms placed within a III–V semiconductor which has a polariton gap due to photon coupling to optical phonons. We employ the spherical harmonic representation to derive the model Hamiltonian within the framework of the dipole resonance approximation. Two polariton impurity states lying within the polariton gap are found. The spontaneous emission rate of a system with two identical two-level atoms placed within a III–V semiconductor is also studied as a function of interatomic distance when the atomic resonance frequency lies in the polariton continuous spectra. It is found that when the interatomic separation between the atoms is small, the polariton-atom system in the symmetric state can radiate a polariton with a probability that is twice that of the independent or single atom case (i.e. superradiance). On the other hand, when the polariton-atom system in the antisymmetric state, the system is prevented from radiating a polariton (i.e. subradiance). Numerical calculations are performed for polariton-impurity states and polariton spontaneous decay rate of the polariton-atom system for GaAs semiconductor.

Squeezing of light by a collection of atoms

We study squeezing in electromagnetic field quadrature components, produced by a collection of A two-level atoms interacting with a single mode of a strong electromagnetic field. We present analytic results both for short and long interaction times. At short times, squeezing grows with the number of atoms for a given initial number of photons. The maximum squeezing which can be achieved in a strong-field case is 66%. At long interaction times, collective effects increase the quadrature fluctuations, compared to the single-atom case. However, for a given number of atoms A, any initial pure atomic state exhibits squeezing when the mean photon number of the initial coherent field satisfies the condition n-bar>(2A${)}^{4}$ . At times close to the first revival, strong squeezing can be achieved for special initial atomic conditions.

Joint Wigner function for atom - field interactions

We define a joint Wigner function to give a fully phase space description for the interacting system of the quantized electromagnetic field and two-level atoms. We give its equation of motion in the single-atom case using the Jaynes - Cummings model for the interaction.

Collective-resonance fluorescence in an ideal cavity.

We study cooperative properties of the emission spectrum of A two-level atoms interacting with a quantized field in a lossless cavity. We show, in a unified treatment, the system anharmonicity, the fine structure, and size of the spectral bands. Further, we show that for an initially inverted atomic system and a thermal cavity field the atomic cooperativity allows the merging of well-defined sidebands, absent in the single-atom case. Thus the cooperativity reduces the destructive effect of the large dispersion of the blackbody photon distribution. For an increasing number of atoms, the central band is split into a doublet. The dip in the doublet is filled when the cavity field is very strong. Also, the extra sidebands have smaller amplitudes than the time-dependent contributions to the spectrum. \textcopyright{} 1996 The American Physical Society.

Squeezing in the many-atom Jaynes-Cummings model within and without the rotating-wave approximation

The time evolution of the atomic and field squeezing parameters in the many-atom Jaynes-Cummings model is investigated within and without the rotating-wave approximation. Moreover, in the single-atom case the influence of the cavity losses is examined as well.

Amplitude-squared squeezing in collective resonance fluorescence

The amplitude-squared squeezing, defined by Hillery [M. Hillery, Phys. Rev. A 36 (1987) 3796], in collective resonance fluorescence is considered. Contrary to the single-atom case the amplitude-squared squeezing occurs in the mixture of sidebands of the collective fluorescence field. The enhancement of the degree of amplitude-squared squeezing is shown when the number of atoms increases. The influence of the thermal field on the amplitude-squared squeezing is also discussed.

Atoms in fock state fields: I. Exact analytical results

A theoretical analysis of the fundamental problem of two-level atomic systems radiatively decaying and coupled to Fock state radiation fields is presented. First, for a broad-band Fock state field and for a single two-level atom the Einstein radiation rate equation is derived within a scheme of matter-field statistical decorrelation. This holds too for N > 1 “independent” two-level atoms. Second, for a single-mode Fock state field exact analytical solution for the atomic inversion, in the single-atom case, is derived within the rotating wave approximation. For N > 1 cooperative two-level atoms exact results are also derived in the steady state regime. In a thermodynamic limit where N→ ∞, the scaled atomic inversion is expressed as Poisson-Charlier polynomials. Connection with earlier results for coherent and incoherent (chaotic) state fields is made. Of mathematical interest: a formal expression for the cofactor elements in terms of the original elements of a triangular matrix is derived in appendix B.

Two-atom spontaneous emission in a detuned damped cavity

By using a new technique developed recently exact closed equations of motion for expectation values for spontaneous emission from two two-level atoms in a detuned damped cavity are derived. These equations are solved numerically for different values of the cavity damping and detuning. It is pointed out that the spontaneous emission is inhibited if the cavity is detuned. Moreover, by comparing the result of the single-atom case with that of the two-atom case it is shown that the collective effects can be suppressed by changing the cavity damping and detuning.

Interatomic coherence in the redistribution of intense radiation

The authors study cooperative effects on the fluorescence spectrum of several atoms in an intense radiation field. In the secular approximation the spectrum contains three lines, as in the single-atom case. The authors evaluate the strengths of these lines for an arbitrary number of atoms without collisions. In the case of two atoms, collisional interactions with a perturber bath are included. The interatomic coherence in the absence of collisions leads to an enhancement of the line strengths, which is most pronounced for the central Rayleigh line. When collisions are present, the strengths of the two sidebands can actually be diminished by the cooperative effects.

Two-atom resonance fluorescence

Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.

Retardation in the resonant interaction of two identical atoms

The problem considered is that of two identical two-level atoms a fixed distance $r$ apart, one of which is excited at $t=0$. A simple improvement on the usual on-shell approximation (which in the single-atom case is part of the Weisskopf-Wigner approximation) yields new solutions for the various probability amplitudes in the form of infinite series involving all the retardation times $\frac{\mathrm{nr}}{c}$. The truncated solutions involving only the single retardation time $\frac{r}{c}$ are compared with previously published results both when all photon modes are allowed and when only photons propagating along the interatomic axis are allowed. When the retardation times are neglected, the series are summed to give the well-known results of Stephen and others.

The anisotropy of very small cobalt particles

2014 Torque and ferromagnetic resonance measurements on a single crystal of a copper 2014 2 % cobalt alloy have been made at various temperatures to determine the magnetocrystalline anisotropy of small single domain particles of precipitated cobalt. The anisotropy at 4.2 °K is found to be independent of particle radius from 21 A to 77 A, lending support to a crystal field model of the origin of anisotropy. A slight variation of anisotropy with particle size was observed at higher temperatures, and was related to a slight variation in saturation magnetization with particle size at these temperatures. LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 20, FEVRIER-MARS 1959, The magnetocrystalline anisotropy of bulk materials is observed to vary with temperature as a high power of the saturation magnetization the tenth and twentieth power for iron and nickel respectively [1]. Thus the change in anisotropy of small ferromagnetic particles as a function of their size may reflect in a sensitive fashion the change in saturation magnetization with size. Although there has been some disagreement [2], [3], there is no evidence for an abnormal saturation magnetization in particles of iron [4], [5]jor cobalt [6] down to 15 A radius. Naive use of the results on thin films [7], [8] would imply an effect much larger than that observed on small particles. There remains, however, the problem that a transition must exist between atomic paramagnetism and the coupled behavior of a many atom particle. Measurement of the anisotropy of small particles may also yield useful information concerning the origin of anisotropy. There are two basically different approaches to this problem within the framework of a Heitler-London approximation to a solid. The first approach (crystal field) [9], [10], [11] assumes the anisotropy to arise because of the electrostatic environment of a magnetic atom without reference to the magnetism of the adjacent atoms. The second approach (anisotropic exchange) [10], [11], [12] emphasizes the fact that the ordinarily isotropic exchange interaction between magnetic atoms may be modified by the presence of spin-orbit coupling of the initially quenched orbital states to become slightly anisotropic. Consider the anisotropy at absolute zero of one atom of cobalt in an electrostatic environment identical to that of cobalt metal but in which its neighbors are non-magnetic. According to the crystal field picture the anisotropy of this atom is identical to that of the ferromagnetic metal, while in the framework of dominant anisotropic exchange in the ferromagnet, the anisotropy per atom of the single atom case would be much less than in the ferromagnet. We may approach this conceptual experiment by measuring the anisotropy of small particles of cobalt in copper. A spherical particle 20 A in radius will have approximately 25 % of its atoms on the surface. About one-third of the nearest neighbors of each surface atom are non-magnetic atoms of similar electronic structure and lattice spacing. The properties of cobalt-rich single domain particles formed by precipitation in copper have been studied in several laboratories [3], [6], [13], [14], [15]. It has recently been demonstrated that the particles in such alloys are initially equiaxed in shape, fcc in structure and coherent with the lattice of the copper matrix and therefore aligned with each other [13], [16], [17]. When these particles are so small that their direction of magnetization can fluctuate thermally [18] they show a magnetic behavior that has been termed paramagnetique apparente [19] or superparamagnetic [20]. Experimental techniques. A single crystal of 2 % cobalt, balance copper, was grown usingthe Bridgman technique. From this crystal a sample was prepared in the shape of an oblate spheroid with (110) as the major plane. The major axes were 4.3 mm and 1.2 mm. The cobalt was retained in solution by quenching into an ice-water mixture from’ 1 000 °C. Precipitate particles of an average radius of 21 A, 43 A, and 77 A were then produced by aging 15, 150 and Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3029800