Generation of superpositions of coherent states on a circle

We propose a simple method to obtain a superposition of coherent states on a circle, including Schr?dinger cat states as a special case, via conditional measurement of the state of three level atoms interacting with a one mode cavity field. In the low amplitude limit, very good approximation of Fock states can also be generated in this way. Received: 8 October 1998 / Accepted: 30 October 1998     

Quantum theory of rotation angles: The problem of angle sum and angle difference

We reconsider the problem of the sum and difference of two angle variables in quantum mechanics. The spectra of the sum and difference operators have widths of , but angles differing by are indistinguishable. This means that the angle sum and difference probability distributions must be cast into a range. We obtain probability distributions for the angle sum and difference and relate this problem to the representation of nonbijective canonical transformations. Received: 6 December 1997 / Revised: 15 April 1998 / Accepted: 7 May 1998     

Squeezed two-mode lasers without and with inversion

On the basis of the nondegenerate quantum-beat laser model, we introduce a coherent field which drives the transition between the upper lasing level and an auxiliary level. We demonstrate that such a four-level system can produce squeezed two-mode laser without and with inversion. When the laser is operated well above threshold, the intensity fluctuation in the average mode is reduced below the shot noise with an optimum Mandel parameter Q=- 1/2. At the same time, the noises in the relative amplitude and the relative phase drop to their vaccum noise levels. Furthermore, regardless of inversion, noninversion, and transition between inversion and noninversion, the optimum Mandel Q parameter of Q=- 1/2 is retained when the system operates well above threshold. A simple physical explanation of the squeezing mechanism for two-mode squeezing is given. Received: 22 December 1997 / Revised: 25 March 1998 / Accepted: 9 September 1998     

Quantum state engineering using conditional measurement on a beam splitter

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed. Received: 17 March 1998 / Revised and Accepted: 8 May 1998     

Phase properties of a Jaynes-Cummings model with Stark shift and Kerr medium

Phase properties of the field interacting with a two-level atom in a lossless cavity Jaynes-Cummings model, taking into account the level shifts produced by Stark effect with an additional Kerr medium for one-mode are studied using the phase formalism of Pegg and Barnett. It is shown in particular that phase properties of the field reflect the collapse and revival phenomena. The results for the time evolution of the phase probability distribution and the phase fluctuations are obtained. The effect of Stark shift on the phase properties in both the absence and presence of a Kerr medium is analyzed. Phase localization is found for certain choice of the parameters. Received: 27 March 1998 / Revised: 8 June 1998 / Accepted: 9 June 1998     

Resonant widths, line intensities and lineshapes for MQDT models with two or more open channels

Approximate analytical formulae describing the energy variation of line intensities, autoionization widths and lineshape asymmetries, are derived for a Phase-Shifted Multichannel Quantum Defect Theory model composed of two closed interacting channels coupled to two effective continua. This is accomplished by putting the two compatibility equation solutions, for the common phase shifts of the two open channels, in such a form so the resonant behavior is attributed to one of them, the other accounting for an energy dependent background. Then, the well-known procedures for the simpler case where only one continuum is considered are applied, using only the resonant solution. The method is quite general and applicable to any MQDT model with two or more open channels. The resulting analytical formulae are tested on experimental spectra of Sr, Ba and Cu and it is shown that they are valid as long as: i) The resonances are non-overlapping, ii) The direct closed channel coupling is much stronger than the indirect one through the continua and (when excitation matrix elements are involved) iii) The open channels excitation strength is smaller or at least comparable to the closed channels one. Received: 26 May 1998 / Accepted: 1st July 1998     

Generation of superpositions of coherent states of the motion of a trapped ion

We propose a method for preparing superpositions of coherent states of the motion of an ion in an anisotropic two-dimensional trap, in which the ion is tightly bound in the y direction. In the scheme the ion is excited by two resonant laser beams with equal amplitude, propagating along the x and y directions, respectively. In the Dicke-Lamb limit, an initial coherent state of the ion motion can be converted into a superposition of several coherent states on a circle through the laser-ion interactions and state-selective measurements on the ion. Received: 30 May 1997 / Revised: 29 July 1997 / Accepted: 22 October 1997     

Spontaneous emission from a three-level atom embedded in an anisotropic photonic crystal

We study the spontaneous emission properties of a V-type three-level atom embedded in a photonic crystal with the anisotropic dispersion relation. We show that the localized field can disappear and the diffusion field can become intense in some regions. This originates from no singularity of the density of states. The quantum interference leads to oscillatory, quasi-oscillatory or complete decay behavior of population. The complete decay can also be realized in certain condition without depending on the initial state. Received 9 April 2000 and Received in final form 1st August 2000     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

Cooling mechanisms in potassium magneto-optical traps

We report on a theoretical and experimental investigation of ³⁹K magneto-optical trapping. The small hyperfine splitting characterizing the upper level of the cooling transition affects the cooling mechanism. In order to model the atom-laser interaction, the whole level structure of the D₂ line has to be taken into account. Two different regimes have been recognized, one optimizing the loading of the trap, the second minimizing the temperature of the atoms. We investigated these two regimes experimentally and found results in agreement with the theoretical predictions. Received: 6 March 1998 / Received in final form: 13 May 1998 / Accepted: 13 May 1998     

Ionization of Rydberg atoms in THz-laser fields at the transition from low to high scaled frequencies

We have studied the ionization of Rydberg-excited xenon atoms in THz-laser fields and by quantum dynamical calculations. The experimental threshold laser field strength for 10% ionization probability follows an n^*-1.68 (1.04 THz) dependence (n^* effective principal quantum number) with additional weak resonance structures and shows that ionization does not occur by a Landau-Zener mechanism. At scaled frequencies of to 5.6 the simulated threshold fields for ionization in oscillatory fields show a dependence on the principal quantum number n of n^-4.1 to n^-1.35. Received: 17 February 1998 / Revised: 20 April 1998 / Accepted: 21 April 1998     

Sisyphus cooling of rubidium atoms on the line: The role of the neighbouring transitions

We study one-dimensional Sisyphus cooling on the transition of ⁸⁷ Rb atoms in the electric field created by two counter-propagating linearly polarized laser beams with an angle of between the polarization directions. The neighbouring F '=0 and F '=2 excited states are found to play an important role in the cooling mechanism, e.g., by inhibiting a significant population of the velocity-selective dark state. Our experimental data, such as temperatures and probe absorption coefficients, agree well with the results of quantum Monte-Carlo wavefunction simulations. Received 26 November 1998 and Received in final form 20 April 1999     

Steady-state populations of a driven three-level atom in a broad-band squeezed vacuum

A theoretical study is made of the steady-state populations of a three-level atom in a ladder configuration, driven by a superposition of a monochromatic laser wave with a broad-band squeezed vacuum. The master equation for the system and the atomic Bloch equations are derived. The steady-state populations are calculated numerically and shown graphically as functions of two-photon detuning for various cases of the squeezed vacuum. It is shown that, the atomic populations depend strongly on the relative phase of the driving field and the squeezed vacuum. When the phase matching condition is fulfilled, there will be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field. Received: 28 May 1997 / Revised and Accepted: 10 December 1997     

Energies and widths of triply excited states of lithiumlike oxygen and neon

Seven low-lying triply exited states of lithium-like oxygen and neon are calculated with the multichannel saddle-point and saddle-point complex-rotation methods. The term energies are given for these excited states, along with level shifts and partial Auger widths from dominant decay channels. The mass polarization effect and relativistic corrections are included. The radiative transition rates are also calculated. These results are compared with other theoretical data in the literature. Received: 25 May 1998 / Revised: 28 July 1998 / Accepted: 25 August 1998     

Statistical properties of the output of linear amplifier with superpositions of squeezed displaced Fock states as an input state

The s-parameterized characteristic function for the output field with the superposition of squeezed displaced Fock states (SDFS's) as input field is given. The s-ordered distribution functions for the output field with superposition of SDFS's as input state are investigated. Various moments are calculated by using the s-ordered characteristic function for that field. The Glauber second-order coherence function is calculated. The quadrature squeezing for the output field are discussed. Some Quasiprobability distribution functions of the output fields are plotted as functions of the interaction time. The quadrature squeezing for the output field are discussed. Received 30 September 1998     

On the continuity in energy of the free-bound one-photon cross-sections

For a charged particle in a central field of force we discuss the continuity in energy of the cross-sections for the related processes of ground state photoeffect and radiative capture. This continuity follows from general arguments, while for a Coulomb potential, where exact analytic expressions are available, the continuity can also be traced explicitly through the calculation. Our analysis allows us to identify an error in papers on radiative muon capture in the ground state which claim the existence of a discontinuity in the cross-section, occurring in hydrogen for muon energies in the neighbourhood of 2.8 keV. As a discontinuity in radiative capture would imply a discontinuity in atomic photoeffect, we note that in the latter case there are extensive experimental results in good qualitative agreement with the usual continuous result (Stobbe formula) for the cross-section. Received: 13 February 1998 / Accepted: 14 May 1998     

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of , whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities. Received: 5 February 1998 / Accepted: 17 April 1998     

Crystallized vortex crystals

Numerical simulations of the equations of motion of 300 charged particles confined to a plane with an additional magnetic field orthogonal to the plane reproduce recently observed self-organization of non-neutral plasmas into a small number of interacting vortices. In the presence of damping we observe crystallized vortices, i.e. vortices with regular internal structure. We also observe crystallized vortex crystals, i.e. geometric patterns of crystallized vortices. Fractal vortex arrangements are investigated and found to be stable. Our results are relevant for quantum dots and artificial atoms. Received: 24 February 1998 / Revised: 4 March 1998 / Accepted: 4 May 1998