Correlations of polarizations and entangled states in the two-photon system

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π⁰ → 2γ, η → 2γ, K _L ⁰ → 2γ, K _S ⁰ → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.     

Magnetically trapped atoms for compact atomic clocks

We investigate the hyperfine transition of magnetically trapped non-condensed atoms. The two principal frequency shifts, the second order Zeeman effect and the mean field interaction are considered. Analytic models of the mean frequency and its trap induced spread are developed. Comparisons with existing experiments evaluate the role of the atoms’ oscillatory motion. The analytic model proves to be equivalent to existing Monte Carlo simulations. The formulae provide a simple tool for optimising the design of a new experiment. Applied to the two-photon transition |F=1,m _F =−1〉→|F=2,m _F =1〉 in ⁸⁷Rb and the conditions of a typical atom chip experiment, a line spread as small as 11 mHz is predicted giving a quality factor of 10¹². The system is promising for application in precision instruments such as compact atomic clocks.     

The v10=1 Level of Propyne, H3CCCH, and Its Interactions with v9=1 and v10=2

Almost 300 new rotational transitions within the fundamental vibrational level v₁₀=1 of propyne have been measured in selected regions between 495 and 925 GHz spanning the quantum numbers 28≤J≤54 and 0≤K≤16. The accuracies are mostly between 10 and 20 kHz. In addition, the J″=4 and 5 transitions near 85 and 103 GHz have been remeasured. Simultaneous analyses with refined rovibrational data have been performed, showing that even this lowest and seemingly isolated vibrational level needs a global treatment when high K transitions are involved. The global model with the v₁₀=1 level coupled to the next higher cluster of levels, v₁₀=2/v₉=1, by Fermi and Coriolis resonances is necessary for a quantitative reproduction of both the rovibrational and rotational data within their experimental uncertainties. Included are also improved ground state spectroscopic parameters from a fit of previous pure rotational data and Δk=3 ground state combination loops as well as additional data obtained in course of the present study.     

Coherent population trapping involving Rydberg states in xenon probed by ionization suppression

We report the observation of pronounced coherent population trapping and dark resonances in Rydberg states of xenon. A weak two-photon coupling with radiation of = 250 nm is induced between the 5p^{6 1} S ₀ ground state of xenon and state 5p ⁵6p[1/2]₀, leading to (2+1) resonantly enhanced three-photon ionization. The state 5p ⁵6p[1/2]₀ is strongly coupled by radiation with ≃ 600 nm to 5p ⁵ ns[J _C]₁ or 5p ⁵ nd[J _C]₁ Rydberg states with principal quantum numbers n in the range 18 ?n? 23 and with the rotational quantum number of the ionic core J _C = 1/2 or J _C = 3/2. The ionization is monitored through observation of the photoelectrons with an energy resolution ΔE = 150 meV which is sufficient to distinguish the ionization processes into the two ionization continua. Pronounced and robust dark resonances are observed in the ionization rate whenever is tuned to resonance with one of the ns- or nd-Rydberg states. The dark resonances are due to efficient population trapping in the atomic ground state 5p^{6 1} S ₀ through the suppression of excitation of the intermediate state 5p ⁵6p[1/2]₀. The resolution is sufficient to resolve the hyperfine structure of the ns-Rydberg levels for odd xenon isotopes. The hyperfine splitting does not vary significantly with n in the given range. Results from model calculations taking the natural isotope abundance into account are in good agreement with the observed spectral structures. Pronounced dark resonances are also observed when the dressing radiation field with is generated from a laser with poor coherence properties. The maximum reduction of the ionization signal clearly exceeds 50%, a value which is expected to be the maximum, when the dip is caused by saturation of the transition rate between the intermediate and the Rydberg state due to incoherent radiation. This work demonstrates the potential of dark resonance spectroscopy of high lying electronic states of rare gas atoms. Received 7 May 2000 and Received in final form 25 June 2001     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Phase control in a coherent superposition of degenerate quantum states through frequency control

We demonstrate a controlled phase change of π in a degenerate superposition by altering a laser frequency by only 10 MHz. The method relies on the preparation of an adiabatic state involving the M = ±2 and M = 0 states of the ³P₂ (J = 2) level of metastable neon. Dependent on the frequency, the preparation proceeds either by stimulated Raman adiabatic passage (STIRAP) or by coherent population trapping (CPT). In the former case the superposition is prepared by adiabatic transfer induced in an extended tripod linkage scheme. In the latter case population is optically pumped into the Zeeman manifold of the level ³P₂. The population which does not reach a dark state decays to the ground state of neon. The amplitudes and relative phases of the dark states differ for the two cases. The phase change is monitored using the method of phase-to-population mapping.     

Effect of magnetic field on the sound velocity of a dilute Kramers-ion glass at low temperature

Recent results on the effect of magnetic field on the sound velocity V in aluminosilicate glasses doped with dysprosium are analyzed on the basis of a minimal model for the ground state of Dy³⁺ (Kramers ion with J=15/2) described by a wave function ϕ _± = ϕ _± J _m + ηϕ _{± 1/2}. The first term represents a state with a large J projection on the local crystal field axis and the random parameter η(〈η〉=0, 〈η ²〉≪1) introduces a small admixture of the state ϕ _±1/2 into the ground state. The relative variation of V due to the resonance interaction of sound waves with this state split by H is determined as a function of H and T. It possesses a universal asymptotic behavior. Our results are in reasonable agreement with the experiment. A possible structure of the crystal fields that can induce this state is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 341–346 (25 February 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The ν1 and ν3 stretching fundamental bands of PD3

The infrared (IR) spectrum of PD₃ has been recorded in the 1580–1800 cm⁻¹ range at a resolution of 0.0027 cm⁻¹. About 2400 rovibrational transitions with J^′=K^′22 have been measured and assigned to the ν₁ (A₁) and ν₃ (E) stretching fundamentals. These include 506 “perturbation-allowed” transitions with selection rules Δ(k−l)=±3. Splittings of the K^′′=3 lines have been observed. Effects of strong perturbations are evident in the spectrum. Therefore the rovibrational Hamiltonian adopted for the analysis explicitly takes into account the Coriolis and k-type interactions between the v₁=1 and v₃=1 states, and includes also several essential resonances within these states. The rotational structure in the v₁=1 and v₃=1 vibrational states up to J^′=K^′=18 was reproduced by fitting simultaneously all experimental data. Thirty-four parameters reproduced 1950 transitions retained in the final cycle with a standard deviation of the fit equal to 4.9 × 10⁻⁴ cm⁻¹ (about the precision of the experimental measurements).     

Spectroscopic constants of the ground and lower vibrational states of CH2BrF: A combined high resolution infrared and microwave study

The enriched ⁸¹Br isotopic species of bromofluoromethane has been investigated in the infrared and microwave regions. The rovibrational spectrum of the ν₅ fundamental has been studied by high resolution FTIR spectroscopy, while the rotational spectra of the ground and v₆ = 1 states have been observed by means of microwave spectroscopy. More than 2700 transitions have been assigned in the ν₅ band and the analysis of the rovibrational structure reveals a first-order c-type Coriolis resonance with the v₆ = 2 state. The present study improves the ground state constants available in the literature and enables the determination of further centrifugal distortion parameters together with the full bromine quadrupole coupling tensor. A set of spectroscopic parameters up to the sextic distortion terms for the vibrational excited states has been accurately evaluated for the first time.     

Effect of polarization on population transfer in H2 by stimulated Raman transition with partially overlapping laser pulses

Polarization effects on population transfer by stimulated Raman transition using overlapping time dependent pump and Stokes laser pulses from the ground X ¹Σ _g ^/+ (v _g=0, J _g=1) level of H₂ to the final X ¹Σ _g ^/+ (v _f=1, J _f=1) level via the intermediate B ¹Σ _u ^/+ (v _i=14, J _i=0,2), C ¹Π _u ^/+ (v _i=3, J _i=2) and C ¹Π _u ^/− (v _i=3, J _i=1) levels have been theoretically investigated by applying the density matrix formalism. We have studied in detail the dependence of the population transfer on time delay between two pulses for the cases of on-resonance excitations considering linear parallel and same-sense circular polarizations of the fields. The pump and Stokes fields are taken as having Gaussian pulse shapes with peak intensities I _P ^/0 (I _S ^/0 )=2 × 10⁶ and 1 × 10⁷ W/cm². Density matrix equations have been solved for each value of the magnetic quantum number M _g(0, ±1) of the initial ground level taking into account the M _g dependence of the Rabi frequencies. M _g — averaged population transfer to the final level has also been calculated. For resonance excitations to the B(14, 0) or C(3, 1) levels, appreciable population transfer is achieved for intuitive pulse order for some particular values of M _g and M _i (magnetic quantum number of the resonant intermediate level) depending on the nature of polarizations. The calculated values of M _g — averaged population transfer for the two cases of polarizations show that for on-resonance excitation to the B(14, 0) or the C(3, 1) level, linear parallel polarization of the laser fields yield more transfer efficiency whereas for resonance excitation to the B(14, 2) level, larger population transfer results from the same-sense circular polarizations. For resonance excitation to the C(3, 2) level, M _g — averaged population is found to be almost polarization independent. The calculations for the six-level H₂ system reveal some interesting features of polarization effects on the population transfer efficiency.     

The total yields of K *(892)+, Σ+(1385), and Σ0 in neutrino-induced reactions at ? E v? ≈ 10 GeV

Using the data obtained with the SKAT bubble chamber, the total yields of K*(892)⁺, Σ⁺(1385), and Σ⁰ are estimated for the first time in neutrino-induced reactions at moderate energy 〈E _v〉 = 10.4 GeV. It is shown that the recently observed enhancement of the K ⁰ and Λ yields in vA interactions as compared to vN interactions is contributed only slightly by the K*(892)⁺ and Σ⁺(1385) production. The contribution of resonances to the K ⁰ and Λ yields is found to be in qualitative agreement with higher energy (〈E _v〉 ≳ 40 GeV) data. It is shown that the energy dependence of the K*(892)⁺ mean multiplicity in vN interactions is approximately linear in the range of 〈E _v〉 ≈ 10−60 GeV, while that for Σ⁰ in vA interactions (A = 20−21) is approximately logarithmic in the range of 〈E _v〉 ≈ = 10−150 GeV. The text was submitted by the authors in English.     

Entanglement and Mixedness of Locally Cloned Non-Maximal W-State

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W-state or W-type state |X〉=α|001〉₁₂₃+β|010〉₁₂₃+γ|100〉₁₂₃,α ²+β ²+γ ²=1 shared by three distant partners. Also we have considered the case β=γ, to obtain a range for α ², for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixedness of inseparable states with their amount of inseparability, for that range of α ².     

The ν12 band of C2D4

The Fourier transform infrared (FTIR) absorption spectrum of the ν₁₂ fundamental band of ethylene-d₄ (C₂D₄) was recorded in the 1017-1137 cm⁻¹ region with an unapodized resolution of 0.0063 cm⁻¹. Upper state (v₁₂ = 1) rovibrational constants consisting of three rotational and five quartic constants were improved by assigning and fitting 2103 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The band centre of the A-type ν₁₂ band is found to be 1076.98480 ± 0.00002 cm⁻¹. The present analysis covering a wider wavenumber range and higher J and K_c values yielded upper state constants including the band centre which are more accurate than previously reported. The rms deviation of the upper state fit is 0.00045 cm⁻¹. Improved ground state rovibrational constants were also determined from the fit of 1247 ground state combination differences (GSCD) from the presently-assigned infrared transitions of the ν₁₂ band of C₂D₄. The rms deviation of the GSCD fit is 0.00049 cm⁻¹. In the rovibrational analysis, local frequency perturbations were not detected even at high J and K_a values. The calculated inertial defect Δ₁₂ is 0.32551 ± 0.00001 μŲ. The line intensities of the individual transitions in the ν₁₂ band were measured and the band strength of 39.8 ± 2.0 cm⁻² atm⁻¹ was derived for the ν₁₂ band of C₂D₄.     

Electron spin resonance studies of Cu2+ doped in cadmium maleate dihydrate single crystals

Electron spin resonance studies have been carried out on Cu²⁺ ion doped in single crystals of cadmium maleate dihydrate at 303 and 77K. It has been found that Cu²⁺ enters this lattice interstitially. The spin Hamiltonian parameters have been evaluated and the ground state wave function is found to be predominantly |X ² −Y ²〉 with a slight admixture of |3Z ² −r ²〉.     

Observation of rotational energy transfer in iodine by two-photon time delayed spectroscopy

The temporal evolution for individual rovibrational levels of the B state of the iodine molecule is observed by two-photon delayed spectroscopy. In particular the rotational energy transfer (RET) process due to collisions of the molecules in the B state with molecules in the ground state is studied. Thermal averaged rate constants for pairs of rotational levels of the v=27 vibrational state are measured. The results are discussed in terms of the dynamics of the collision process and numerical fits to the most important parametric fitting laws for RET are presented.     

Quantum states transfer between coupled fields

We study the exchange of states in coupled fields along their time evolution. The coupling is described by a quadratic form in terms of annihilation and creation operator in the field Hamiltonian. An analytical approach is employed to describe the time evolution of the field state in Fock's space and the conditions for an arbitrary initial states to be transferred with 100% fidelity is determined. We show that only for initial states C₀|0>+C_N|N>, this situation can occurs. The important |1〉↔|0〉 qubits transfer is a particular case of this transference of number state. The relation between the coupling constant and characteristic field frequencies for complete state transference is also determined.     

Echo spectroscopy of atomic dynamics in a Gaussian trap via phase imprints

We present a simultaneous analysis of the X¹ Σ ⁺ and the a³ Σ ⁺ electronic ground states of the NaK molecule. Excitation of the [B ¹ Π, c³ Σ ⁺]-system made it possible to record fluorescence to rovibrational levels of both ground states simultaneously with a Fourier-transform spectrometer. For the first time high lying levels in the triplet state with v = 17 and v = 18 were seen, the highest possible v = 19 for ²³Na-³⁹K was not observed. The joint evaluation of the retrieved data leads to accurate potential energy curves, that describe the experimental data within their experimental uncertainty of 0.005 cm⁻¹. Cold collision properties like scattering length and Feshbach resonance positions are calculated with these potentials and compared to other predictions.     

Generalized Two-Mode Squeezed States and Some Nonclassical Characteristics

A class of generalized two-mode squeezed states |φ〉 is presented, which are generated from the generalized two-mode squeezing operator U(γ,λ) acting on the two-mode coherent state |α ₁,α ₂〉. We first investigate some mathematical properties of U(γ,λ) including the squeezing transformation under U(γ,λ), ket-bra integral form in the coordinate representation, normally ordered form. Then we evaluate some nonclassical characteristics of the state |φ〉 such as higher-order squeezing behavior, entanglement analysis and analytical expression of the Wigner function.     

Time-resolved Stark effect in rapidly varying fields

The cycle-averaged ac Stark effect associated with the ^[ A _]2Σ⁺v^′=2?^[ X _]2Π1/2v^′=0 two-photon absorption of NO at intensities between 7.7 and 15.2 TW cm^-2 has been characterized in real time through a synergic combination of bichromatic laser experiments and quantum-dynamics calculations. Measurements of the fluorescence emitted by the Rydberg ^[ A _]2Σ⁺v^′=2 level as a function of time between Stark and probe components of a bichromatic field exhibit a characteristic evolution in temporal peak structure with Stark-field intensity, which is interpreted in terms of a time-dependent Floquet analysis of the laser–matter interaction. The experimental observations are consistent with a dynamic Stark shift of Δε_s(ω₁,ω₂)≤0.23 eV of the optical transition at these intensities. Received: 18 January 2002 / Revised version: 6 March 2002 / Published online: 24 April 2002