Zeeman Shift Research Articles

Effect of antiprotons on hydrogen-like ions in external magnetic fields

In the present work, quasi-molecular compounds consisting of one antiproton ( p ¯ ) and one hydrogen-like ion are investigated: He + − p ¯ , Li 2 + − p ¯ , C 5 + − p ¯ , S 15 + − p ¯ , Kr 35 + − p ¯ , Ho 66 + − p ¯ , Re 74 + − p ¯ , U 91 + − p ¯ . For the calculations, the Dirac equation with two-centre potential is solved numerically using the dual-kinetically balanced finite-basis-set method adapted to systems with axial symmetry (A-DKB). Adiabatic potential curves are constructed for the ground state of the above quasi-molecular compounds in the framework of the A-DKB approach. Calculations were also performed for the case of an external magnetic field (the field is taken into account non-perturbatively). Zeeman shifts of the quasi-molecular terms are obtained for a homogeneous magnetic field with a strength of the laboratory order (up to 100 Tesla) directed along the axis of the molecule.

A new search for the variation of fundamental constants using the rovibrational levels and isotope effects of magnesium fluoride molecule

Abstract The recently demonstrated methods for cooling and trapping diatomic molecules offer new possibilities for precision searches in fundamental physical theories. Here, we propose to study the variations of the fine-structure constant (α=e 2/ħc) and the proton-to-electron mass ratio (μ = mp/me) with time - by taking advantage of the nearly degenerate rovibrational levels in the electronic states of the magnesium fluoride (MgF) molecule. Specifically, due to the cancellation between the fine structure splitting and the rovibrational intervals in the different MgF natural isotopes, a degeneracy occurs for the A 2Π(3/2) (v'=0,J'=18.5,-) and the A2Π(1/2) (v''=0,J''=20.5,-). We find that using the nearly degenerate energy level of such states can be 104 times more sensitive than using a pure rotational transition to measure the variations of α and μ. To quantify the small gap between the A2Π(3/2) (v'=0,J'=18.5,-) and the A2Π(1/2) (v''=0,J''=20.5,-), the special transitions of choice are feasible: the X 2Σ(1/2) + (v=0,J=19.5,+) to the A2Π(3/2) (v'=0,J'=18.5,-) and the X 2Σ(1/2) + (v=0,J=19.5,+) to the A 2Π(1/2) (v''=0,J''=20.5,-). In addition, we estimate the frequency uncertainties caused by the narrow linewidth, Zeeman shift, the Stark shift, Doppler boarding and the Blackbody radiation.

Blackbody-radiation Zeeman shifts in optical clocks: The role of fine-structure intramanifold resonances

Blackbody-radiation Zeeman shifts in optical clocks: The role of fine-structure intramanifold resonances

Electroweak Nuclear Properties from Single Molecular Ions in a Penning Trap.

We present a novel technique to probe electroweak nuclear properties by measuring parity violation (PV) in single molecular ions in a Penning trap. The trap's strong magnetic field Zeeman shifts opposite-parity rotational and hyperfine molecular states into near degeneracy. The weak interaction-induced mixing between these degenerate states can be larger than in atoms by more than 12 orders of magnitude, thereby vastly amplifying PV effects. The single molecule sensitivity would be suitable for applications to nuclei across the nuclear chart, including rare and unstable nuclei.

Optimizing off-axis fields for two-axis magnetometry with point defects

Vector magnetometry is an essential tool for characterizing the distribution of currents and magnetization in a broad range of systems. Point defect sensors, like the nitrogen vacancy center in diamond, have demonstrated impressive sensitivity and spatial resolution for detecting these fields. Measuring the vector field at a single point in space using single defects, however, remains an outstanding challenge. We demonstrate that careful optimization of the static bias field can enable simultaneous measurement of multiple magnetic field components with enhanced sensitivity by leveraging the nonlinear Zeeman shift from transverse magnetic fields, realizing an improvement in transverse sensitivity from >200 μT/Hz (no bias field) to 30 μT/Hz. This work quantifies the trade-off between the increased frequency shift from second-order Zeeman effects with decreasing contrast as off-axis field components increase, demonstrating the measurement of multiple components of the magnetic field from an exemplar antiferromagnet with a complex magnetic texture.

Elementary excitations in a spin–orbit-coupled Floquet spinor Bose–Einstein condensate

We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.

Multiple-quantum-coherence dynamics of spin-1 Bose–Einstein condensate during quantum phase transitions

Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose–Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.

Strong single-photon to two-photon bundles emission in spin-1 Jaynes–Cummings model

High-quality special nonclassical states beyond the strong single atom-cavity coupling regime are fundamental elements in quantum information science. Here, we study strong single-photon blockade to two-photon bundles emission in a single spin-1 atom coupled to an optical cavity by constructing a spin-1 Jaynes–Cummings model (JCM). By tuning the quadratic Zeeman shift, the energy-spectrum anharmonicity can be significantly enhanced, leading to a remarkable increase in the dressed-state splitting of the well-resolved n-photon resonance. The mechanism, which benefits from the internal degrees of freedom in high-spin systems, compensates for the strong coupling condition required by the multi-photon blockade, thereby facilitating the experimental feasibility of engineering special nonclassical states beyond the strong-coupling limit. It is shown that the photon emission from the spin-1 JCM demonstrates high-quality single photon and two-photon bundles with large steady-state photon numbers in the cavity-driven and atom-pump cases, respectively. In particular, compared to the two-level two-photon JCM, the antibunching amplitude of the three-order correlation function for two-photon bundles in the spin-1 JCM is enhanced by 3 orders of magnitude. More interestingly, a multimode transducer, enabling a transition from strong single-photon blockade to two-photon bundles and super-Poissonian photon emission, is achieved and highly controllable by the light-cavity detuning in the presence of both atom and cavity driven fields. This study based on the high-spin JCM broadens the scope of engineering special nonclassical quantum states beyond the standard two-level JCM. Our proposal not only opens up a new avenue for generating high-quality n-photon sources but also provides versatile applications in quantum networks and metrology.

Electronic density of states of a U(1) quantum spin liquid with spinon Fermi surface. II. Zeeman magnetic field effects

This work studies the Zeeman magnetic field effect on a quantum spin liquid with a spinon Fermi surface. In the absence of gauge binding, the quantum spin liquid electronic density of states exhibits no Zeeman shift in the threshold energy. As the gauge binding increases, the band edge resonance peaks exhibit a reduced Zeeman shift and eventually have the Zeeman shift direction reversed for a sufficiently large gauge binding. The authors further suggest to use such anomalous Zeeman response to identify the gapless quantum spin liquid phase.

Optical telecommunications-band clock based on neutral titanium atoms

We propose an optical clock based on narrow, spin-forbidden M1 and E2 transitions in laser-cooled neutral titanium. These transitions exhibit much smaller black body radiation shifts than those in alkaline earth atoms, small quadratic Zeeman shifts, and have wavelengths in the S, C, and L-bands of fiber-optic telecommunication standards, allowing for integration with robust laser technology. We calculate lifetimes; transition matrix elements; dynamic scalar, vector, and tensor polarizabilities; and black body radiation shifts of the clock transitions using a high-precision relativistic hybrid method that combines a configuration interaction and coupled cluster approaches. We also calculate the line strengths and branching ratios of the transitions used for laser cooling. To identify magic trapping wavelengths, we have completed the largest-to-date direct dynamical polarizability calculations. Finally, we identify new challenges that arise in precision measurements due to magnetic dipole-dipole interactions and describe an approach to overcome them. Direct access to a telecommunications-band atomic frequency standard will aid the deployment of optical clock networks and clock comparisons over long distances.

Advances in Two-Dimensional Magnetic Semiconductors via Substitutional Doping of Transition Metal Dichalcogenides.

Transition metal dichalcogenides (TMDs) are two-dimensional (2D) materials with remarkable electrical, optical, and chemical properties. One promising strategy to tailor the properties of TMDs is to create alloys through a dopant-induced modification. Dopants can introduce additional states within the bandgap of TMDs, leading to changes in their optical, electronic, and magnetic properties. This paper overviews chemical vapor deposition (CVD) methods to introduce dopants into TMD monolayers, and discusses the advantages, limitations, and their impacts on the structural, electrical, optical, and magnetic properties of substitutionally doped TMDs. The dopants in TMDs modify the density and type of carriers in the material, thereby influencing the optical properties of the materials. The magnetic moment and circular dichroism in magnetic TMDs are also strongly affected by doping, which enhances the magnetic signal in the material. Finally, we highlight the different doping-induced magnetic properties of TMDs, including superexchange-induced ferromagnetism and valley Zeeman shift. Overall, this review paper provides a comprehensive summary of magnetic TMDs synthesized via CVD, which can guide future research on doped TMDs for various applications, such as spintronics, optoelectronics, and magnetic memory devices.

Electron and nuclear magnetic properties near ZEFOZ region

In the vicinity of spin level anti-crossings, electron-nuclear spin systems reveal characteristic features that have been investigated by electron paramagnetic resonance (EPR) methods, including electron spin echo envelope modulation (ESEEM). The spectral properties depend considerably on the difference, ΔB, between the magnetic field and the critical field at which the zero first-order Zeeman shift (ZEFOZ) occurs. To analyze the characteristic features near the ZEFOZ point, analytical expressions for the behavior of EPR spectra and ESEEM traces as a function of ΔB are obtained. It is shown that the influence of hyperfine interactions (HFI) decreases linearly when approaching the ZEFOZ point. The HFI splitting of the EPR lines is essentially independent of ΔB near the ZEFOZ point, while the depth of the ESEEM signal has an approximately quadratic dependence on ΔB with a small cubic asymmetry due to the Zeeman interaction of the nuclear spin.

Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices

Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimension lower than the bulk have significantly opened a new perspective for understanding of topological quantum matters. Here, we propose to generate two-dimensional topological boundary states for implementing synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices, which includes Chern insulator, Dirac semimetals, and second-order topological phase (SOTP) by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of bulk, Wilson loop spectra, and the spin textures at the higher symmetric points of system. We show that the SOTP exhibits a pair of $0$D boundary states. While the phases of Dirac semimetals and Chern insulator support the conventional $1$D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the emerged boundary states for Dirac semimetals and SOTP are topologically protected by $\cal P T$-symmetry and chiral-mirror symmetry ($\mathcal{\widetilde{M}}_{\alpha}$), respectively. In particular, the location of $0$D corner states for SOTP which are associated with existing $\mathcal{\widetilde{M}}_{\alpha}$-symmetry can be highly manipulated by tuning magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.

Trap-Induced ac Zeeman Shift of the Thorium-229 Nuclear Clock Frequency.

We examine the effect of a parasitic rf magnetic field, attributed to ion trapping, on the highly anticipated nuclear clock based on ^{229}Th^{3+} [C. J. Campbell etal., Phys. Rev. Lett. 108, 120802 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.120802]. The rf magnetic field induces an ac Zeeman shift to the clock frequency. As we demonstrate, this shift threatens to be the dominant systematic frequency shift for the clock, exceeding other systematic frequency shifts and the projected systematic uncertainty of the clock by orders of magnitude. We propose practical means to suppress or eliminate this shift.

Intercombination-line photoassociation spectroscopy of Rb87Yb170

We report on the first observation of photoassociation near the ${}^2 S _\frac 1 2 + {}^3P_1$-asymptote in a mixture of ${}^{87}$Rb and ${}^{170}$Yb. In a search spanning binding energies between 0.1 GHz and 11 GHz, a single pair of interspecies PA resonances is detected around 3.1 GHz. These resonances are characterized by extracting PA rates, binding energies and Zeeman shift coefficients. Using one of these resonances, 2-photon-photoassociaton is performed, improving on previous measurements of the binding energies of the two least bound states in the electronic ground state and demonstrating intercombination line photoassociation as a powerful spectroscopic tool. We discuss implications for pathways towards RbYb molecules in the absolute ground state.

Spin-orbit-coupled spinor gap solitons in Bose-Einstein condensates

Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximating model by replacing the optical lattice with a Harmonic trap, we demonstrate the physical origination of these two families. For a large negative quadratic Zeeman shift, we also find a type of gap solitons that spontaneously breaks the spin-dependent parity symmetry due to the ferromagnetic spinor interactions.

Atomic mixer based on phase control without ac Zeeman shift

Atom-based mixers have been shown to be very useful in performing the absolute measurement of the magnitude of a radio-frequency (rf) field by using Autler-Townes (AT) splitting. However, there has been less success in measuring the phase of a rf field with the AT splitting in a magnetic-resonance system. The phase of the rf magnetic field plays a very important role in imaging applications. Here, we design an atomic mixer for measuring the phase of the rf field by detecting the transmission spectra of a laser-detected magnetic-resonance system based on the interference between Raman and cascade two-photon processes for ${F}_{g}=4$ of the ${D}_{1}$ line of cesium atoms. A scheme of measuring the rf phase can be realized with the elimination of the ac Zeeman shift of the system by adjusting the amplitude ratio of a transverse fundamental-wave field and its third-harmonic field. Theoretical and experimental results show that the scheme with cancellation of the ac Zeeman shift is superior in linear measurement of the longitudinal rf component. Our results provide schemes for a magnetic sensor based on quantum interference of nonlinear processes for the absolute measurement of the relative phase of rf fields.

Precise measurement of 171Yb magnetic constants for 1 S 0–3 P 0 clock transition

We present a precise measurement of 171Yb magnetic constants for 1 S 0–3 P 0 clock transition. The background magnetic field is firstly compensated to < 1 mGs (1 Gs = 10−4 T) through measuring the splitting of two π transitins of 171Yb clock transition at different compensation coils currents. Then, the splitting ratios of the π and σ components of 171Yb clock transition at different bias magnetic fields are measured, and the first-order Zeeman coefficient is determined to be α = 199.49(5) Hz/Gs. The second-order Zeeman shifts at various bias magnetic fields are also measured through interleaved self-comparison in which the bias magnetic fields are modulated between high and low values. The second-order Zeeman coefficient is fitted to be β = –6.09(3) Hz/mT2, which is consistent with the result of NIST group.

Controlling atomic spin mixing via multiphoton transitions in a cavity

We propose to control spin-mixing dynamics in a gas of spinor atoms, via the combination of two off-resonant Raman transition pathways, enabled by a common cavity mode and a bichromatic pump laser. The mixing rate, which is proportional to the synthesized spin-exchange interaction strength, and the effective atomic quadratic Zeeman shift (QZS), can both be tuned by changing the pump laser parameters. Quench and driving dynamics of the atomic collective spin are shown to be controllable on a faster time scale than in existing experiments based on inherent spin-exchange collision interactions. The results we present open a promising avenue for exploring spin-mixing physics of atomic ensembles accessible in current experiments.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce. In this work, the hyperfine-induced Landé g-factors and quadratic Zeeman shift coefficients of the nsnp clock states for 111,113Cd and 25Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory. To obtain accurate values of these parameters, the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the Landé g-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy. Our calculations provide important data for estimating the first- and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.