Zeeman Shift Research Articles

Determination of Zeeman Shifts of Spectral Structures in a Nonuniform Magnetic Field

The variation in the shift of spectral structures due to the Zeeman effect in a spatially nonuniform magnetic field has been studied. It has been found that this shift can be varied by changing the width and shape of spectral structures, their forms, and methods and conditions of recording. A method of accounting for magnetic-field nonuniformity for optically thin and thick media has been proposed.

Measuring the Rydberg constant using circular Rydberg atoms in an intensity-modulated optical lattice

A method for performing a precision measurement of the Rydberg constant, $R_{\infty}$, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantum-electrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice, and transitions are driven using a recently-demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition frequency yields $R_{\infty}$. Laser wavelengths and beam geometries are selected such that the lattice-induced transition shift is minimized. The selected transitions have no first-order Zeeman and Stark corrections, leaving only manageable second-order Zeeman and Stark shifts. For Rb, the projected relative uncertainty of $R_{\infty}$ in a measurement under the presence of the Earth's gravity is $10^{-11}$, with the main contribution coming from the residual lattice shift. This could be reduced in a future micro-gravity implementation. The next-important systematic arises from the Rb$^+$ polarizability (relative-uncertainty contribution of $\approx 3 \times10^{-12}$).

Entanglement-Based dc Magnetometry with Separated Ions

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As \textit{sensor states}, we use Bell states of the type $\left|\uparrow\downarrow\right>+\text{e}^{\text{i}\varphi}\left|\downarrow\uparrow\right>$ encoded in two $^{40}$Ca$^+$ ions stored at different locations. Due to the linear Zeeman effect, the relative phase $\varphi$ serves to measure the magnetic field difference between the constituent locations, while common-mode fluctuations are rejected. Consecutive measurements on sensor states encoded in the $\text{S}_{1/2}$ ground state and in the $\text{D}_{5/2}$ metastable state are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We measure magnetic field differences over distances of up to $6.2~\text{mm}$, with accuracies of around 300~fT, sensitivities down to $12~\text{pT} / \sqrt{\text{Hz}}$, and spatial resolutions down to $10~\text{nm}$. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.

Interplay of valley polarization and dynamic nuclear polarization in 2D transition metal dichalcogenides

The interplay of Ising spin-orbit coupling and non-trivial band topology in transition metal dichalcogenides (TMDs) produces anomalous transport and optical properties that are very different from a regular 2D electron gas. The spin-momentum locking of optically excited carriers near a valley point can give rise to an anomalous spin-valley Hall current under the application of an in-plane electric field. TMDs also exhibit strong electron-nuclear hyperfine interactions, but their effect on spin-valley-locked currents remains unknown. Here, we show that hyperfine interactions can create a feedback mechanism in which spin-valley currents generate significant dynamical nuclear polarization which in turn Zeeman shifts excitonic transitions out of resonance with an optical driving field, saturating the production of spin-valley polarization. We propose an experimental signature of dynamic nuclear polarization which can be detected via measurements of the anomalous Hall current. Our results help to elucidate the interplay of valley polarization and nuclear spin dynamics in TMDs.

Zeeman effect in sulfur monoxide: A tool to probe magnetic fields in star forming regions.

Magnetic fields play a fundamental role in star formation processes and the best method to evaluate their intensity is to measure the Zeeman effect of atomic and molecular lines. However, a direct measurement of the Zeeman spectral pattern from interstellar molecular species is challenging due to the high sensitivity and high spectral resolution required. So far, the Zeeman effect has been detected unambiguously in star forming regions for very few non-masing species, such as OH and CN. We decided to investigate the suitability of sulfur monoxide (SO), which is one of the most abundant species in star forming regions, for probing the intensity of magnetic fields via the Zeeman effect. We investigated the Zeeman effect for several rotational transitions of SO in the (sub-)mm spectral regions by using a frequency-modulated, computer-controlled spectrometer, and by applying a magnetic field parallel to the radiation propagation (i.e., perpendicular to the oscillating magnetic field of the radiation). To support the experimental determination of the g factors of SO, a systematic quantum-chemical investigation of these parameters for both SO and O2 has been carried out. An effective experimental-computational strategy for providing accurate g factors as well as for identifying the rotational transitions showing the strongest Zeeman effect has been presented. Revised g factors have been obtained from a large number of SO rotational transitions between 86 and 389 GHz. In particular, the rotational transitions showing the largest Zeeman shifts are: N, J = 2, 2 ← 1, 1 (86.1 GHz), N, J = 4, 3 ← 3, 2 (159.0 GHz), N, J = 1, 1 ← 0, 1 (286.3 GHz), N, J = 2, 2 ← 1, 2 (309.5 GHz), and N, J = 2, 1 ← 1, 0 (329.4 GHz). Our investigation supports SO as a good candidate for probing magnetic fields in high-density star forming regions.

Inverted crossover resonance within one Zeeman manifold

We carry out investigations of inverted crossover resonances (ICRs) in π-driven four-level systems where can be zero. Through the use of sub-Doppler frequency modulation spectroscopy of the − transition in 171Yb the resonance becomes manifest. The centre frequency is inherently insensitive to first-order Zeeman shifts and equates to the two-level resonance frequency in the absence of a magnetic field. A rate equation model is used to help validate the nature of the resonance. Optical frequency measurements of the hyperfine line recorded over two months demonstrate a statistical uncertainty of 2 × 10−11. The ICR found with the line is used for 556 nm laser frequency stabilisation, which is an alternative means when applied to magneto-optical trapping of 171Yb.

Paramagnetic and diamagnetic pair-breaking effect in electric-field-induced surface superconductivity under parallel magnetic fields

Electric-field-induced surface superconductivity is studied by Bogoliubov-de Gennes equation under magnetic fields parallel to the surface. We estimate the pair-breaking effects by the paramagnetic Zeeman shift and by diamagnetic screening current. We find that the depth dependences of pair potential, screening current, spin current, and paramagnetic moment under the magnetic fields reflect the multi-gap superconductivity in the sub-band structure.

Precise determination of the isotope shift of 88Sr–87Sr optical lattice clock by sharing perturbations

We report on the isotope shift between 88Sr and 87Sr on the 1S0–3P0 clock transitions. The interleaved operation of an optical lattice clock with two isotopes allows the canceling out of common perturbations, such as the quadratic Zeeman shift, the clock-light shift, and the blackbody radiation shift. The isotope shift is determined to be 62 188 134.004(10) Hz, where the major uncertainty is introduced by the collisional shift that is distinct for each isotope. Our result allows us to determine the frequency of 88Sr–87Sr optical lattice clocks with a fractional uncertainty of 2 × 10−17. The scheme is generally applicable for measuring the isotope shift with significantly reduced uncertainty.

Measurement of the magnetic field profile in the atomic fountain clock FoCS-2 using Zeeman spectroscopy

We report the evaluation of the second-order Zeeman shift in the continuous atomic fountain clock FoCS-2. Because of its continuous operation and geometrical constraints, the methods used in pulsed fountains are not applicable. We use here time-resolved Zeeman spectroscopy to probe the magnetic field profile in the clock. Pulses of ac magnetic excitation allow us to spatially resolve the Zeeman frequency and to evaluate the Zeeman shift with a relative uncertainty smaller than .

Accuracy estimation of the O216+ transition frequencies targeting the search for the variation in the proton-electron mass ratio

The precise measurement of molecular vibrational transition frequencies is useful in the search for variation in the proton-to-electron mass ratio {\mu}. Homonuclear diatomic molecules are particularly advantageous for precise measurement because of the small Stark shift. This paper discusses the Stark and Zeeman shifts in the 16O2+ vibrational transition frequencies.To search for the variation {\mu}(<10-17/yr), the X2{\Pi}1/2(v,J)=(0,1/2)-(v',1/2)(v'>1)in transition frequencies are much more advantageous than the transition frequencies between the X2{\Pi}1/2 v=21 and a4{\Pi}1/2 v=0 states, whose sensitivity to the variation in {\mu} is high because of the accidental degeneracy.

Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates

We have experimentally investigated the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition at zero quadratic Zeeman shift $q$. The rate of instability shows good agreement with predictions based upon solutions to the Bogoliubov de-Gennes equations. A key feature of this work was removal of magnetic field inhomogeneities, resulting in a steep change in behavior near the transition point. The quadratic Zeeman shift at the transition point was resolved to 250 milliHertz uncertainty, equivalent to an energy resolution of $k_B \times 12$ picoKelvin. To our knowledge, this is the first demonstration of sub-Hz precision measurement of a phase transition in quantum gases. Our results point to the use of dynamics, rather than equilibrium studies for high precision measurements of phase transitions in quantum gases.

Structure, branching ratios, and a laser-cooling scheme for theBaF138molecule

For laser cooling considerations, we have theoretically investigated the electronic, rovibrational and hypefine structures of BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between metastable A'2{\Delta} and A2{\Pi} states and further the lifetime of the {\Delta} state have been estimated since the loss procedure via {\Delta} state would like fatally destroy the main quasi-cycling {\Sigma}-{\Pi} transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational states in X2{\Sigma}+ state provide benchmarksfor sideband modulations of cooling and repumping lasers and remixing microwaves to address all necessary levels. The calculated Zeeman shift and g-factors for both X and A states serve as benchmarks for selections of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.

Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring

The spin-change dynamics of a model with ultra-cold hyperfine-spin-1 atoms confined in an optical superlattice is discussed. First, the disturbance of the two-site dynamics by coupling the dimer to a spin-1 ancilla is analyzed. When the dimer is coupled to the ancilla, even by a weak coupling, the significant changes in the system’s time-evolution processes are observed. Next, we show that for the two-particle case the total hyperfine-spin-singlet state is generated by exploiting a quadratic Zeeman shift with realistic values of the strength of external magnetic field and evolution period of time. Moreover, even in a weak coupling regime, the proper choice of the additional ancilla–dimer interaction results in generating the wave function which is characteristic of the homogeneous three-site ring. In consequence, such wave function exhibits translational invariance symmetry despite the strong asymmetry of the lattice. Furthermore, we present our proposal for extracting various kinds of maximally entangled states (MES) for three-site spin-1 systems, starting from initial product states. In particular, we show that the type of generated MES can be unambiguously recognized by the measurement performed on the ancilla.

Ultracold metastable helium: Ramsey fringes and atom interferometry

We report on interference studies in the internal and external degrees of freedom of metastable triplet helium atoms trapped near quantum degeneracy in a \( 1.5\kern0.166667em \upmu \mathrm{m} \) optical dipole trap. Applying a single \( \pi /2 \) rf pulse we demonstrate that 50% of the atoms initially in the \( m=+1 \) state can be transferred to the magnetic field insensitive \( m=0 \) state. Two \( \pi /2 \) pulses with varying time delay allow a Ramsey-type measurement of the Zeeman shift for a high precision measurement of the \( {2}^3{S}_1 \)–\( {2}^1{S}_0 \) transition frequency. We show that this method also allows strong suppression of mean-field effects on the measurement of the Zeeman shift, which is necessary to reach the accuracy goal of 0.1 kHz on the absolute transition frequencies. Theoretically the feasibility of using metastable triplet helium atoms in the \( m=0 \) state for atom interferometry is studied demonstrating favorable conditions, compared to the alkali atoms that are used traditionally, for a non-QED determination of the fine structure constant.

Giant Zeeman shifts in the optical transitions of yttrium iron garnet thin films

We report the observation of giant Zeeman shifts in the optical transitions of high-quality very thin films of yttrium iron garnet (YIG) grown by rf sputtering on gadolinium gallium garnet substrates. The optical absorption profile measured with magneto-optical absorption spectroscopy shows dual optical transition in the UV-visible frequency region attributed to transitions from the O-2p valence band to the Fe-3d conduction band and from the O-2p valence band to Fe-2p53d6 excitonic states at the Γ-symmetry point of the YIG band structure. The application of a static magnetic field of only 0.6 kOe produces giant Zeeman shifts of ∼100 meV in the YIG band structure and ∼60 meV in the excitonic states corresponding to effective g-factors on the order of 104. The giant Zeeman effects are attributed to changes in energy levels by the large exchange fields of the Fe-3d orbitals during the magnetization process.

Evaluation of variation in $$\left( m_\mathrm{p}/m_\mathrm{e}\right)$$ m p / m e from the frequency difference between the $${{}^{15}\hbox {N}_{2}}^{+}$$ 15 N 2 + and $${}^{87}\hbox {Sr}$$ 87 Sr transitions

The uncertainty of the $${}^{87}\hbox {Sr}\, {}^{1}\hbox {S}_{0}-{}^{3}\hbox {P}_{0}$$ transition frequency (429 THz) has been reduced to the level of $$10^{-18}$$ . Also, the $${{}^{15}\hbox {N}_{2}}^{+}\, \hbox {Q}(0)$$ vibrational transition frequency is expected to be measured with an uncertainty of $$10^{-17}$$ , and the v = 0–7 transition frequency (422 THz) is close to the $${}^{87}\hbox {Sr}$$ transition frequency. In this paper, we propose a test for the variation in the proton-to-electron mass ratio $$\mu$$ via precise measurement of the difference $$(f_\mathrm{d}=7 \hbox { THz})$$ between these transition frequencies. By measuring $$f_\mathrm{d}$$ within the uncertainty of $$10^{-16}$$ , a variation in $$\mu$$ of $$4 \times 10^{-18}$$ can be detected. The $${{}^{15}\hbox {N}_{2}}^{+}\, v =0 -7\, \hbox {Q}(0)$$ transition frequency is free from Zeeman and electric quadrupole shifts. The dc Stark coefficient is about $$0.2 \hbox { mHz}/(\hbox {V}/\hbox {cm})^{2}$$ , and the measurement of $$f_\mathrm{d}$$ with an uncertainty lower than $$10^{-16}$$ appears to be attainable using molecular ions in a string crystal. The $${{}^{15}\hbox {N}_{2}}^{+}$$ transition frequency is observed via the two-photon excitation of a laser with a wavelength of 1422 nm (laser A). Another laser with a wavelength of 1396 nm (laser B) is used as a $${}^{87}\hbox {Sr}$$ clock laser after frequency doubling. The frequency difference between lasers A and B (3.5 THz) should be measured using a frequency comb. Lasers A and B can be transferred to another laboratory via an optical fiber. Therefore, a sensitive test of the variation in $$\mu$$ can be performed in cooperation between two distant laboratories.

Research progress of Al$^{+}$ ion optical frequency standard based on quantum logic technique

Optical atomic clocks have many applications in the definition of the time and the length, measurement of fundamental constants and their potential variations with time, testing of relativity, very long baseline interferometry, geodesy, and global navigation satellite systems. An optical clock consists of three parts: ultra-stable laser, frequency comb and trapped ions or atoms. The accuracy of optical atomic clocks can be affected by Doppler shift, Zeeman shift, Stark shift, collision shift, blackbody radiation (BBR) shift, etc. The BBR shift is very difficult to be characterized and controlled. Among all optical atomic clocks under current development, Al$^+$ optical clock has the smallest BBR shift at a level of $4.0\times10^{-19}$, therefore the Al$^+$ is a promising ion for high-accuracy optical frequency standard. In this article we give a review on the three parts of optical frequency standards, the basic working principle of Al$^+$ ion optical frequency standard based on quantum logic technique, and research progress of an Al$^+$ optical clock under development at Huazhong University of Science and Technology.

Automatic compensation of magnetic field for a rubidium space cold atom clock**Project supported by the Ministry of Science and Technology of China (Grant No. 2013YQ09094304), the Youth Innovation Promotion Association, Chinese Academy of Sciences, and the National Natural Science Foundation of China (Grant Nos. 11034008 and 11274324).

When the cold atom clock operates in microgravity around the near-earth orbit, its performance will be affected by the fluctuation of magnetic field. A strategy is proposed to suppress the fluctuation of magnetic field by additional coils, whose current is changed accordingly to compensate the magnetic fluctuation by the linear and incremental compensation. The flight model of the cold atom clock is tested in a simulated orbital magnetic environment and the magnetic field fluctuation in the Ramsey cavity is reduced from 17 nT to 2 nT, which implied the uncertainty due to the second order Zeeman shift is reduced to be less than 2×10−16. In addition, utilizing the compensation, the magnetic field in the trapping zone can be suppressed from 7.5 μT to less than 0.3 μT to meet the magnetic field requirement of polarization gradients cooling of atoms.

Resonantly enhanced spin-lattice relaxation ofMn2+ions in diluted magnetic (Zn,Mn)Se/(Zn,Be)Se quantum wells

The dynamics of spin-lattice relaxation in the magnetic ${\mathrm{Mn}}^{2+}$ ion system of (Zn,Mn)Se/(Zn,Be)Se quantum-well structures are studied using optical methods. Pronounced cusps are found in the giant Zeeman shift of the quantum-well exciton photoluminescence at specific magnetic fields below 10 T, when the Mn spin system is heated by photogenerated carriers. The spin-lattice relaxation time of the Mn ions is resonantly accelerated at the cusp magnetic fields. Our theoretical analysis demonstrates that a cusp occurs at a spin-level mixing of single ${\mathrm{Mn}}^{2+}$ ions and a quick-relaxing cluster of nearest-neighbor Mn ions, which can be described as intrinsic cross-relaxation resonance within the Mn spin system.

Structure of magnetic resonance in 87Rb atoms

Magnetic resonance at the Fg = 1 \( \rightleftarrows \)Fe = 1 transition of the D1 line in 87Rb has been studied with pumping and detection by linearly polarized radiation and detection at the double frequency of the radiofrequency field. The intervals of allowed values of the static and alternating magnetic fields in which magnetic resonance has a single maximum have been found. The structure appearing beyond these intervals has been explained. It has been shown that the quadratic Zeeman shift is responsible for the three-peak structure of resonance; the radiofrequency shift results in the appearance of additional extrema in resonance, which can be used to determine the relaxation constant Γ2. The possibility of application in magnetometry has been discussed.