Collision-assisted Zeeman cooling of neutral atoms

We propose a new method to cool gaseous samples of neutral atoms. The gas is confined in a non dissipative optical trap in the presence of an homogeneous magnetic field. The method accumulates atoms in the m _F =0 Zeeman sub-level. Cooling occurs via collisions that produce atoms in states. Thanks to the second order Zeeman effect kinetic energy is transformed into internal energy and recycling of atoms is ensured by optical pumping. This method may allow quantum degeneracy to be reached by purely optical means. Received 10 May 2000     

Zero magnetic field splitting and anomalies of intensities in the Zeeman spectra of La(Pr)Cl3-crystals

Optical absorption and Zeeman effect measurements on La(Pr)Cl₃ show a zero magnetic field splitting of the degenerate Pr³⁺ levels and . The site symmetry of the Pr³⁺ ions is lowered fromC _3h toC _s . The resultant splittings of the doublet levels are:I ³ H ₄:2|T _ak |=(0.12±0.05)cm^–1;a ³ P ₁:2|T _al |=(0.10±0.05)cm^–1.The intensities of the optical transitions induced by the deformation decrease with increasing magnetic field. All observations are described by a first order perturbation calculation using a low symmetric part of the crystal field and Zeeman energy as simultaneous perturbations on a Pr³⁺ ion in a crystal field with site symmetryC _3h .Project of the Sonderforschungsbereich Festkörperspektroskopie SFB65, Darmstadt—Frankfurt, supported by the Deutsche Forschungsgemeinschaft.     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h ₀ (h ₀ is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.     

Doppler-free two-photon absorption spectroscopy of trans-glyoxal under magnetic fields up to 6T

In order to measure the Doppler-free two-photon absorption (DFTPA) spectrum in the presence of a strong magnetic field, a sample cell placed in an optical resonator was installed at the centre of the bore of a superconducting magnet capable of generating a magnetic field of up to 6T. Changes in spectra of the A ¹A_u ← X ¹A_g transition of trans-glyoxal were measured as a function of magnetic field strength. Level crossings induced by Zeeman energy shifts were observed. The perturbing level, which shows hyperfine splitting, was identified as the ³A_u(nπ?) state, because the hyperfine splitting is small in the ³B_u(^ππ?) state and large in the ³A_u(nπ?) state. The perturbation between the A ¹A_u(nπ?) and ³A_u(nπ?) states was shown to take place by either vibronic interaction or Zeeman interaction between the ³A_u(nπ?) state and the ³B_u(ππ?) component mixed to the A ¹A_u(nπ?) state by spin-orbit interaction. The magnetic moment of the A ¹A_u state was determined to be approximately 0.0028μ_B, and the magnitude of the mixing coefficients 〈1 ³B_u|H _so|1 ¹A_u〉/[E(1 ¹A_u) ? E(1 ³B_u)] was evaluated to be 0.026.     

Influence of light on the magnetoelectric effect in Fe-doped Bi<Subscript>12</Subscript>SiO<Subscript>20</Subscript>

We report an extraordinary oxidation state of iron in the Fe-doped Bi₁₂SiO₂₀ single crystal. Magnetoelectric effect and changes of this effect under illumination of the sample were investigated in magnetic fields up to 32 T. Moreover, an absorption line and its shift to higher energy caused by magnetic field (the Zeeman effect) were seen in the optical measurements. Obtained results show that the iron dopant is in unexpected, +4 oxidation state and it changes to +5 after illumination with blue light.     

Magnetic excitations and phase transition of CsFeBr3 in an external magnetic field

In CSFeBr₃ the Fe²⁺ ion with effective spin one has locally a singlet ground state (m=0). The antiferromagnetic interactions between neighbouring Fe-ions are too weak as compared with the anisotropy constant to introduce long range order in the absence of an external field. By inelastic neutron scattering we studied the magnetic excitations in an external magnetic field up to 5 Tesla applied along thec-axis. A linear Zeeman splitting was observed with a Landé factorg=2.4. The field renormalizes the dispersion curves in such a way that the exchange interaction has decreasing influence with increasing field. Theoretical calculations according to the excitonic model of Lindgård describe the experimental results very well. At 4.1 Tesla a phase transition appears to a commensurate long range order with a 120° arrangement of the spins in the hexagonal plane. Within the limits of experimental observation this phase transition has no influence on the dynamical behaviour. No critical phenomena could be observed. The dynamical structure factor |G _j()|² of the lower Zeeman split modes decreases with increasing field.     

Magnetism-Related Properties of CdSb Revealed by the Zeeman 121Sb NQR Spectra

The ¹²¹Sb NQR spectra of CdSb single crystal were measured in the presence of weak (up to 500 Oe) external magnetic fields. As the analysis of the ¹²¹Sb EFG symmetry showed, two magnetically nonequivalent Sb sites exist in the CdSb crystal lattice. An upper limit of the local magnetic field, which may exist in CdSb characterized with the observed ¹²¹Sb NQR spectra, was estimated by modeling the Zeeman perturbed patterns. This amounted to H _loc ∼10 G, hence being much less than earlier found local fields H _loc ∼30–200 G in bismuth-based compounds.     

Zeeman effect in the luminescence spectra of terbium-yttrium-aluminum garnet

The Zeeman effect is investigated in the green luminescence band corresponding to the 4f→4f radiative transition ⁵D₄ → ⁷F₅ of Tb ³⁺ ions in Tb _0.2 Y _2.8 A _l5 O ₁₂ terbium-yttrium-aluminum garnet at the temperature T = 85 K. It is demonstrated that an external field causes not only the Zeeman shifts of the resonant frequencies of radiative transitions in the luminescence spectra but also changes in the emission line intensities caused by modification of the optical transition probabilities in the σ₋ and σ₊ opposite circular polarization states. Special features of field dependences of the Zeeman effect for the emission lines are qualitatively explained based on the results of numerical energy spectrum calculations for the ⁵D₄ and ⁷F₅ multiplets of the Tb ³⁺ ion in yttrium-aluminum garnet in the geometry of the longitudinal and transverse Zeeman effects. The possibility of nonequilibrium population of sublevels of the (Γ₁, Γ₄) quasi-doublet state of the ⁵D₄ multiplet with energy of ∼20585 cm⁻¹ is demonstrated in an external magnetic field. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–45, June, 2008.     

The excitonic and zero-field splittings of the first triplet state of toluquinone single crystals

The pure electronic S ₀ → T ₁ transition of toluquinone has been studied in absorption using single crystals at 6 K and polarized light. The theory of the Zeeman effect on the crystal exciton levels is developed and compared with the experimental results. High-field measurements show that the factor group splitting is 0·32 cm^-1 and that the orbital plus state lies at higher energy. The ordering and energy separation of the magnetic substates of the factor group levels is also obtained. The latter results are confirmed by low field measurements and the following molecular zero-field splitting parameters are obtained: Y = +0·12, X = -0·02 and Z = -0·09 cm^-1.     

Analysis of the Zeeman effect on the energy spectrum in graphenes

An analysis of the Zeeman effect with a strong external magnetic field on the energy spectrum in graphene is presented. In general, the Hamiltonian of graphene in applied electric and magnetic fields is not of SO(1, 2) invariance even in the nearest-neighbor approximation because of the Zeeman coupling. But an approximate SO(1, 2) invariance can be obtained when the applied magnetic field is very strong. This approximate invariance can be used to relate the energy structure of graphene in the presence of both electric and magnetic fields to that when there is only magnetic field. Therefore, it can help explain the recently found quantum Hall conductance (4q ²/h)L for L = 0.1.     

The effect of the crystal-field ground-state splitting on the electrical resistivity of dilute (La,Pr)B6

We have measured the resistivity and the magnetoresistivity of some dilute (La, Pr)B₆ single crystals. At temperatures below 1 K a pronounced step in the resistivity occurs which shifts to higher temperatures with increasing Pr concentration as well as with increasing external magnetic fields. The observed resistance anomaly is caused by Pr–Pr interactions which remove the degeneracy of the ₅ crystal field ground state of Pr³⁺ in LaB₆. The resistance step reflects the temperature-dependent probability that conduction electrons are scattered from the ₅ crystal field sublevels of the Pr³⁺ ions. The shift of the resistance step in a magnetic field can be simply explained as Zeeman effect of the ₅ triplet.     

Magnetic Resonance and Optical Spectroscopy of Yb<Superscript>3+</Superscript> in CsCaF<Subscript>3</Subscript> Single Crystal: an Analysis of Distortions of the Crystal Lattice near Yb<Superscript>3+</Superscript>

A trigonal Yb³⁺ paramagnetic center in the CsCaF₃ single crystal was studied by magnetic resonance and optical spectroscopy methods. The structural model of the complex and the empirical energy level scheme were established. The transferred hyperfine interaction parameters and the crystal field ones were determined. The crystal field parameters were used to analyze the lattice distortions in the vicinity of Yb³⁺ using the superposition model.     

Laser cooling and trapping of ytterbium atoms

The experiments on the laser cooling and trapping of ytterbium atoms are reported, including the two-dimensional transversal cooling, longitudinal velocity Zeeman deceleration, and a magneto-optical trap with a broadband transition at a wavelength of 399 nm. The magnetic field distributions along the axis of a Zeeman slower were measured and in a good agreement with the calculated results. Cold ytterbium atoms were produced with a number of about 10⁷ and a temperature of a few milli-Kelvin. In addition, using a 556-nm laser, the excitations of cold ytterbium atoms at ¹S₀-³P₁ transition were observed. The ytterbium atoms will be further cooled in a 556-nm magneto-optical trap and loaded into a three-dimensional optical lattice to make an ytterbium optical clock.      

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature T_c, the regionT _c⪯ T ⪯ T* is a vast fluctuation regime.T _c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field H_c2 bounding the superconducting response and the pseudogap closing field H_pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi₂Sr₂CaCu₂O_8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field H_c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.     

Effect of a strong magnetic field on the quadrupole and magnetic orders and crossover in the Jahn-Teller magnet DyVO<Subscript>4</Subscript>

The effect of a strong magnetic field H||[001] on magnetic properties of the Jahn-Teller compound DyVO₄ is studied. New phase transitions discovered and investigated experimentally and theoretically include the breaking of quadrupole order (enhancement of the crystal symmetry) and breaking of antiferromagnetic order as well as the effect of convergence of energy levels of the Dy³⁺ ion (crossover). The differential magnetic susceptibility of a DyVO₄ crystal is measured in fields up to 36 T in the temperature interval 1.4?15 K. The observed magnetic susceptibility anomalies and phase transitions are described using a unified theoretical approach.     

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er³⁺ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ₈ states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμ_BBJ+ uμ_BBJ³ with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g_∥ and g_⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g_∥ + 2g_⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g_∥| + 2|g_⊥| is not always equal to their real trace g_∥ + 2g_⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values g_x, g_y and g_z. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.     

Level splitting in semimagnetic semiconductors under spin-magnetophonon resonance conditions

The splitting of electronic levels in quantum wells of semimagnetic semiconductors typically characterized by large effective g factors is analyzed theoretically. They are found to be capable of supporting resonance, provided the Zeeman spin-level splitting is equal to the energy of the longitudinal optical phonon ?ω_‖. The resonance condition can be written as ?ω_‖ = gμ_B B. This condition can be satisfied by choosing the magnetic field Bsuch that the sum of the energies of the lowest spin level and the optical phonon coincides with the energy of the highest level. It is shown that these two degenerate energy levels should experience mutual repulsion. The magnitude of the corresponding splitting depends on both the electron-phonon and spin-orbit interactions in semiconductors; moreover, it turns out substantially lower than the Zeeman energy gμ_B B. Resonant passage of light through and its reflection from a quantum well are considered as one of possible ways to observe this energy level splitting.     

Doppler-free high resolution spectroscopy of carbon disulphide and the effects of a magnetic field

A single-mode autoscan laser spectrometer operating in the ultraviolet in combination with a collimated molecular beam was used to measure high resolution fluorescence excitation spectra of the CS₂ V ¹B₂ ← X ¹Σ⁺ _g transition under collision-free conditions, and the effects of a magnetic field were measured. Rotational and vibrational levels were fully resolved, and Zeeman splittings were observed in many of the perturbed lines. The Zeeman interaction was observed to induce new perturbation, which induces new transitions, level splitting, and energy shift. When the magnetic field strength was changed, the magnitude of the interaction, which was observed in the absence of a magnetic field, changed dramatically depending on the energy shifts of the Zeeman components. It is shown that the V ¹B₂(¹Δ_u) state is mixed with the B₂(³A₂) component by first-order spin-orbit interaction, and through the mixed component, the Zeeman interaction between the V ¹B₂(¹Δ_u) and ³A₂(³Δ_u) states is induced. Large Zeeman splittings were observed for most of the background lines of weak intensity, and this demonstrates that the background levels are levels of the ³A₂(³Δ_u) state. The fluorescence decays of single Zeeman components were observed to be single exponential. The lifetimes of the perturbing ³A₂(³Δ_u) levels were determined by deperturbation analysis. Triplet-triplet ³A₂(³Δ_u) → ³B₂(³Σ⁺ _u) emission was confirmed. It was demonstrated that the quenching of the V ¹B₂ → X ¹Σ⁺ _g fluorescence by a magnetic field was caused by mixing of the ³A₂ state with the V ¹B₂ state and the resulting increase of triplet-triplet emission. In a time-dependent picture, the intersystem crossing from the ¹B₂(¹Δ_u) and ³A₂(³Δ_u) states is enhanced by the magnetic field.     

Local investigation of the energy gap within the incompressible strip in the quantum Hall regime

We experimentally study the energy gap within the incompressible strip at local filling factor ν _c = 1 at the quantum Hall edge for samples of very different mobilities. The obtained results indicate strong enhancement of the energy gap in comparison to the single-particle Zeeman splitting. We identify the measured gap as a mobility gap, so a pronounced experimental in-plane magnetic field dependence can both be attributed to the spin effects as well as to the change in the energy levels broadening.