Dark resonances for ground-state transfer of molecular quantum gases

One possible way to produce ultra-cold, high-phase-space-density quantum gases of molecules in the rovibronic ground state is given by molecule association from quantum-degenerate atomic gases on a Feshbach resonance and subsequent coherent optical multi-photon transfer into the rovibronic ground state. In ultra-cold samples of Cs₂ molecules, we observe two-photon dark resonances that connect the intermediate rovibrational level |v=73,J=2〉 with the rovibrational ground state |v=0,J=0〉 of the singlet X ¹ Σ _g ⁺ ground-state potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level |v=73,J=2〉 by two-photon transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the two-photon resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state |v=0,J=0〉.     

Calculation of the quenching rate constants for electronically excited singlet molecular nitrogen

The quenching rate constants for the singlet states (a′)⁽¹⁾Σ _u ⁻ (v = 1−17), a ⁽¹⁾Π _g (v = 0−14), and w ⁽¹⁾Δ _u (v = 0−13) of molecular nitrogen colliding with an N₂ molecule are calculated using quantum-chemical approximations. It is shown for the first time that both the intramolecular and intermolecular processes of electronic excitation transfer are significant for these states. Calculated rate constants are in satisfactory agreement with experimental data.     

Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

Motivated by the study of multivortices in the Electroweak Theory of Glashow–Salam–Weinberg [33], we obtain a concentration-compactness principle for the following class of mean field equations: on M, where (M,g) is a compact 2-manifold without boundary, 0 < a≤K(x)≤b, x∈M and λ > 0. We take with α _i > 0, δ _{p i} the Dirac measure with pole at point p _i ∈M, i= 1,…,m and ψ∈L ^∞(M) satisfying the necessary integrability condition for the solvability of (1)_λ. We provide an accurate analysis for solution sequences of (1)_λ, which admit a “blow up” point at a pole p _i of the Dirac measure, in the same spirit of the work of Brezis–Merle [11] and Li–Shafrir [35]. As a consequence, we are able to extend the work of Struwe–Tarantello [49] and Ding–Jost–Li–Wang [21] and derive necessary and sufficient conditions for the existence of periodic N-vortices in the Electroweak Theory. Our result is sharp for N= 1, 2, 3, 4 and was motivated by the work of Spruck–Yang [46], who established an analogous sharp result for N= 1, 2. Received: 24 September 2001 / Accepted: 7 December 2001     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Weak exchange interactions in the heteronuclear crystal CuPr2(CCl3COO)8·6H2O

The new heteronuclear crystal CuPr₂(CCl₃COO)₈·6H₂O, constructed of chains containing copper and praseodymium atoms, has been synthesized and investigated by EPR at 9.3 GHz at temperatures ranging from room temperature down to 10 K. At temperatures T∼300–130 K, EPR spectra are observed which are characteristic of isolated polyhedra of copper ions with g _z=2.330±0.005, g _x,y =2.053±0.005, A _z=139×10⁻⁴ cm⁻¹, and A _x,y <26×10⁻⁴ cm⁻¹. At temperatures T<130 K a complex spectrum is observed, associated with the appearance of weak exchange interactions between the copper ions in the chain (J _Cu-CuΣS _i·S _i+1), comparable in magnitude with the hyperfine interactions J _Cu-Cu=0.015 cm⁻¹ at T=10 K. The magnitude of the exchange interaction decreases smoothly as the temperature is raised. It is conjectured that orbitals of the praseodymium ions participate in the process of indirect exchange between the copper ions. Fiz. Tverd. Tela (St. Petersburg) 41, 2154–2157 (December 1999)     

Method of Quantum Characters in Equivariant Quantization

 Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 _h (M) is a 𝕌 _h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 _h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 _h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌^* _h (g) and quotients of 𝔸 _h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 _h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ ⁿ ), and 𝔸 _h (M) the so-called reflection equation algebra associated with the representation of 𝕌 _h (g) on ℂ ⁿ . For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits. Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003 RID="*" ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01. Communicated by L. Takhtajan     

High-spin states of<Superscript>125</Superscript>Sb: Particle-core excitation coupling

Excited states of¹²⁵Sb have been studied using in-beam γ spectroscopy techniques via the¹²⁴Sn(⁷Li, α2n) reaction at a beam energy of 32 MeV. A high-spin level scheme including 21 new γ-transitions and 14 new excited states have been established. Three isomers have been identified at 1970, 2110 and 2471 keV and the ranges of their half-lives have been estimated from the delayed coincidence data. The level structure of¹²⁵Sb is discussed in terms of particle-core excitation coupling. With the help of empirical shell model calculations the three isomers are proposed to have three-quasiparticle πg_7/2⊗v(h _11/2 s _1/2)₅₋, πg_7/2⊗v(h _11/2 d _3/2)₇₋ and πg_7/2⊗v(h ₁₁^2/2)₁₀ ⁺ configurations, respectively.     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

Overlapping B3Π0u ← X1Σ g/+ and 1Π1u ← X1Σ g/+ non-radiative characteristic of Br2 vapour in the wavelength region 505–541 nm

The vibronic vapour phase photoacoustic spectrum of Br₂ in the wavelength region 505–541 nm (19796–18480 cm⁻¹) has been recorded using microphone as well as pump-probe method. Discrete vibronic bands superimposed on a monotonically increasing continuum background towards the dissociation limit results from the overlapping B ³Π _0u ^/+ ← X ¹Σ _g ^/+ and ¹Π_1u ← X ¹Σ _g ^/+ electronic transitions. Vibronic bands originating from υ″=0 have been used to estimate the relative rate of non-radiative relaxation as a function of the excited state B ³Π_0u vibrational quantum number υ′. A comparison with the optical absorption spectroscopy of Br₂ leads to the identification of three broad spectral regions between 505 and 541 nm (19796 and 18480 cm⁻¹) on the basis of different non-radiative relaxation processes.     

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function F₂^gp(x,Q²)F_{2}^{\gamma p}(x,Q^{2}). We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/s ^β for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power v ^β−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10⁻⁶ obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q ²=5 GeV² down to the lower virtuality Q ²=1.69 GeV². For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.     

Generalized holographic and Ricci dark energy models

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ρ _R =3c ² M _pl² Rf(H ²/R) and ρ _h =3c ² M _pl² H ² g(R/H ²), respectively; here f(x), g(y) are positive defined functions of the dimensionless variables H ²/R or R/H ². It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function f(x)=g(y)≡1 or f(x)=Id and g(y)=Id are taken, respectively (for example f(x),g(x)=1−ε(1−x), ε=0or1, respectively). Also, when f(x)≡xg(1/x) is taken, the Ricci and holographic dark energy models are equivalent to a generalized one. When the simple forms f(x)=1−ε(1−x) and g(y)=1−η(1−y) are taken as examples, by using current cosmic observational data, generalized dark energy models are considered. As expected, in these cases, the results show that they are equivalent (ε=1−η=1.312), and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And the suggested combination of holographic and Ricci dark energy components would be 1.312R−0.312H ², which is 2.312H²+1.312[(H)\dot]2.312H^{2}+1.312\dot{H} in terms of H ² and [(H)\dot]\dot{H} .     

Paramagnetische Resonanz an Einkristallen einiger Selten-Erd-Oxide

The paramagnetic resonance of Nd³⁺ in Y₂O₃ has been measured at 4.2°K and 9.25 kMe/s. The values of theg-tensors are: ions onC _3i -sites:g _∥=2.434±0.007;g _⊥=0.702±0.005; ions onC ₂-sites:g _x =4.395±0.012;g _y =0.433±0.009;g _z =1.648±0.006. Further measurements have been performed on La₂O₃ crystals doped with Ce³⁺, Dy³⁺, and Er³⁺; the results are (C _3v -sites only): .      

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Spin-orbit coupling of the NaK 3Π and 3Π states: Determination of the coupling constant and observation of quantum interference effects

We have studied the mutually perturbing 3³Π_Ω=0(v = 32, J = 19) ∼ 3¹Π_Ω=1(v = 6, J = 19) levels of NaK that are coupled together by the spin-orbit interaction. We note that this coupling is nominally forbidden by the ΔΩ = 0 selection rule for spin-orbit perturbations. However 3³Π levels labeled by different values of Ω are mixed by rotational coupling; i.e. the 3³Π_Ω levels are best described by a coupling scheme intermediate between Hund’s cases (a) and (b). Thus the 3¹Π_Ω=1 level couples to the 3³Π_Ω=0 level via the small admixture of 3³Π_Ω=1 character in the latter. The 3³Π_Ω=0(v = 32, J = 19) ∼ 3¹Π_Ω=1(v = 6, J = 19) f symmetry pair is of particular interest since it appears to be very close to a 50-50 mixture of triplet and singlet character, and the splitting between these levels provides a direct measure of the 3³Π ∼ 3¹Π spin-orbit coupling constant. On the other hand, excitation spectra of the 3³Π_Ω=0(v = 32, J = 19) ∼ 3¹Π_Ω=1(v = 6, J = 19) e symmetry pair through the mixed “window” levels 1(b)³Π_Ω=0(v = 17, J = 18, 20) ∼ 2(A)¹Σ⁺(v = 18, J = 18, 20) display dramatic quantum interference effects associated with “singlet” and “triplet” excitation channels. Almost complete cancellation for populating one or the other of the two upper states is observed for excitation from the predominantly triplet members of the window level pairs.     

Determination of the helium-4 mass in a Penning trap

The determination of the rotational quadrupole alignment of diatomic molecules via REMPI detection is investigated. In this process a high focal intensity usually increases the detection probability. At high intensities the AC Stark effect may cause a splitting of the normally degenerate m_J sublevels of a rotational state J beyond the spectral width of the exciting radiation. This leads to a selective detection of only certain m_J states with the consequence that deduced alignment factors can be misleading. From the theoretical considerations line profiles are explicitly calculated for dynamic polarizabilities which represent the B ¹Σ⁺ _u←X ¹Σ⁺ _g transition of H₂, in order to fit an experimental (3+1) REMPI spectrum and to predict (1+1') line shapes as a function of laser intensity. It is further shown that the deduced quadrupole alignment factor A ₀ ⁽²⁾ is significantly changed by the second order AC Stark effect when the intensities are chosen high enough to observe asymmetric broadened line profiles. Different combinations of relative linear polarizations of the exciting and ionizing laser beams are discussed. Received 1st August 2000 and Received in final form 2 May 2001     

Anomalous light-induced drift of linear molecules

The sudden approximation in energy is used to derive analytic formulas that describe the anomalous light-induced drift (LID) of linear molecules absorbing radiation in the rovibrational transition nJ _i −mJ _f (n and m are the ground and excited vibrational states, and J _α is the rotational quantum number in the vibrational state α=m, n). It is shown that for all linear molecules with moderate values B≲1 cm⁻¹ of the rotational constant, anomalous LID can always by observed under the proper experimental conditions; temperature T, rotational quantum number J _i , and type of transition (P or R). The parameter γ=B[J _i (J _i +1)−J _f (J _f +1)] ν _n /2k _BT (ν _m −ν _n ) is used to derive a condition for observing anomalous LID: γ∼1 (k _B is the Boltzmann constant and ν _α is the transport rate of collisions of molecules in the vibrational state α and buffer particles at moderate molecular velocities , where is the most probable velocity of the buffer particles). For ν _m >ν _n anomalous LID can be observed only in P-transitions, while for ν _m <ν _n it can be observed only in R-transitions. It is shown that anomalous LID is possible for all ratios β=M _b /M of the masses of the buffer particles (M _b ) and of the resonant particles (M) and any absorption-line broadening (Doppler or homogeneous). The optimum conditions for observing anomalous LID are realized when the absorption line is Doppler-broadened in an atmosphere of medium-weight (β∼1) and heavy (β≫1) buffer particles. In this case, anomalous LID can be observed in the same transition within a broad temperature interval ΔT∼T. If the buffer particles are light (β≪1) or if the broadening of the absorption line is homogeneous, anomalous LID in the same transition can be observed only within a narrow temperature range ΔT≪T. Zh. éksp. Teor. Fiz. 115, 1664–1679 (May 1999)     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.     

Magnetic moments for lithium quartet S states

The fully correlated calculations of the Zeeman g_J factors for the first three quartet S states of lithium are presented, including relativistic and radiative corrections of orders α², α² m/M, and α³. The isotope shifts in g_J are predicted precisely for various isotopes of lithium. Received 4 December 2000 and Received in final form 26 September 2001