Zeeman Shift Research Articles

Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing

We demonstrate that the differential ac-Stark shift of a Zeeman-sensitive ground hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the |2S1/2,F=2,mF=-2> to the |2S1/2,F=1,mF=-1> state of 7Li to observe 0.59±0.02 Hz linewidth with interrogation time of 2 s and 0.82±0.06 s coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed.

Nonadiabatic Effects in Ultracold Molecules via Anomalous Linear and Quadratic Zeeman Shifts

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

Spin-Orbit Coupling and Quantum Spin Hall Effect for Neutral Atoms without Spin Flips

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.

Cold-atom double-Λcoherent population trapping clock

Miniature atomic clocks based on coherent population trapping (CPT) states in thermal atoms are an important component in many field applications, particularly where satellite frequency standards are not accessible. Cold-atom CPT clocks promise improved accuracy and stability over existing commercial technologies. Here we demonstrate a cold-atom CPT clock based on ${}^{87}$Rb using a high-contrast double-$\ensuremath{\Lambda}$ configuration. Doppler frequency shifts are explained using a simple model and canceled by interrogating the atoms with counterpropagating light beams. We realize a compact cold-atom CPT clock with a fractional frequency stability of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$, thus demonstrating the potential of these devices. We also show that the long-term stability is currently limited by the second-order Zeeman shift to $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1000 s.

Orthogonality parameter associated with a magnetic field gradient for single-site addressing in a 1D optical lattice

We investigate the possibility of detecting atoms in a 1D optical lattice with the nearest-site resolution by using a magnetic resonance technique. A superimposed magnetic field gradient introduces a position-dependent Zeeman shift to label each site. Among the line-broadening mechanisms, we focus on sideband transitions between the motional states of the lower and the upper hyperfine levels. In addition to the sidebands of the axial motion induced by the field gradient itself, we consider those of the transverse motion induced by field misalignments with respect to the optical lattice. Parameters that determine the sideband strengths are identified in a manner analogous to the Lamb-Dicke parameter. The analysis shows that it is advantageous to use light and cold atoms in a deep optical potential well. An explicit expression for the lineshape of the hyperfine transition is obtained. We use it to calculate lineshapes for a cesium and a lithium atom in a typical optical lattice as well as those for the previously reported experiments using cesium atoms.

Influence of exciton spin relaxation on the photoluminescence spectra of semimagnetic quantum dots

We present a comprehensive experimental and theoretical studies of photoluminescence of single CdMnTe quantum dots with Mn content x ranging from 0.01 to 0.2. We distinguish three stages of the equilibration of the exciton-Mn ion spin system and show that the intermediate stage, in which the exciton spin is relaxed, while the total equilibrium is not attained, gives rise to a specific asymmetric shape of the photoluminescence spectrum. From an excellent agreement between the measured and calculated spectra we are able to evaluate the exciton localization volume, number of paramagnetic Mn ions, and their temperature for each particular dot. We discuss the values of these parameters and compare them with results of other experiments. Furthermore, we analyze the dependence of average Zeeman shifts and transition linewidths on the Mn content and point out specific processes, which control these values at particular Mn concentrations.

Antiferromagnetic Spatial Ordering in a Quenched One-Dimensional Spinor Gas

We have experimentally observed the emergence of spontaneous antiferromagnetic spatial order in a sodium spinor Bose-Einstein condensate that was quenched through a magnetic phase transition. For negative values of the quadratic Zeeman shift, a gas initially prepared in the F=1, m(F)=0 state collapsed into a dynamically evolving superposition of all three spin projections, m(F)=0, ±1. The quench gave rise to rich, nonequilibrium behavior where both nematic and magnetic spin waves were generated. We characterized the spatiotemporal evolution through two particle correlations between atoms in each pair of spin states. These revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations.

Spin mixing in spinor Fermi gases

We study a spinor fermionic system under the effect of spin-exchange interaction. We focus on the interplay between the spin-exchange interaction and the effective quadratic Zeeman shift. We examine the static and the dynamic properties of both two- and many-body system. We find that the spin-exchange interaction induces coherent Rabi oscillation in the two-body system, but the oscillation is quickly damped when the system is extended to the many-body case.

Vector magnetic field sensing by a single nitrogen vacancy center in diamond

In this letter, we proposed and experimentally demonstrated a method to detect the vector magnetic field with a single nitrogen vacancy (NV) center in diamond. The magnetic field in parallel with the axis of the NV center can be obtained by detecting the electron Zeeman shift, while the Larmor precession of an ancillary nuclear spin close to the NV center can be used to measure the field perpendicular to the axis. Experimentally, both the Zeeman shift and Larmor precession can be measured through the fluorescence from the NV center. By applying additional calibrated magnetic fields, complete information on the vector magnetic field can be achieved with such a method. This vector magnetic-field detection method is insensitive to temperature fluctuation and it can be applied to nanoscale magnetic measurements.

Radio-frequency dressed atoms beyond the linear Zeeman effect

We evaluate the impact that nonlinear Zeeman shifts have on resonant radio-frequency (RF) dressed traps in an atom-chip configuration. The degeneracy of the resonance between Zeeman levels is lifted at large intensities of a static field, modifying the spatial dependence of the atomic adiabatic potential. In this context, we find effects that are important for the next generation of atom chips with tight trapping: in particular, that the vibrational frequency of the atom trap is sensitive to the RF frequency and, depending on the sign of the Landé factor, can produce significantly weaker, or tighter trapping when compared to the linear regime of the Zeeman effect. We take 87Rb as an example and find that it is possible for the trapping frequency on F = 1 to exceed that of the F = 2 hyperfine manifold.

Zeeman shift of two-dimensional optical signals of Mg-porphyrin dimers with circularly polarized beams

Two-dimensional (2D) electronic spectra of Mg-porphyrin dimers with circularly polarized laser pulses are simulated for two molecular geometries. The Zeeman shift of the non-chiral 2D spectra induced by a magnetic field highlights spectral regions that are dominated by exciton states with large total angular momentum, and are particularly sensitive to the geometry. These 2D shifts show much higher sensitivity to the molecular array than the absorption spectrum shifts. For different molecular geometries, only the intensity of the 2D spectrum peaks changes while the form of the Zeeman shifts in the 2D frequency space is modified.

Quantum Dynamics in Atomic-Fountain Experiments for Measuring the Electric Dipole Moment of the Electron with Improved Sensitivity

An improved measurement of the electron electric dipole moment (EDM) appears feasible using ground-state alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable electron dipole moment (EDM), is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a facto mu~100. We expand the complete time evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin F=3, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent states), potential systematic errors enter only as even powers of 1/mu, making the expansion rapidly convergent. The remaining EDM mimicking effects are further suppressed in a proposed double-differential setup, where the final state is interrogated in a differential laser configuration, and the direction of the strong electric field also is inverted. Estimates of the signal available at existing accelerator facilities indicate that the proposed apparatus offers the potential for a drastic improvement in EDM limits over existing measurements, and for constraining the parameter space of supersymmetric (SUSY) extensions of the Standard Model.

Measurement of Energy Level Shift of Ultracold Cesium Atoms by Raman Pump–Probe Spectroscopy

AC Stark shift and Zeeman shift of ultracold atoms are measured by a simple Raman pump–probe spectroscopy. We systematically investigate the relationship between these energy level shifts and the experimental parameters of trapping beam intensity, trapping beam detuning and magnetic gradient. The experimental results agree with theoretical values predicted by F ¼ 1 $ F 0 ¼ 2 model, which is developed from a multi-level cesium atom interacting

Magneto-optical studies of ensembles of semimagnetic self-organized Cd(Mn)Se/Zn(Mn)Se quantum dots

Ensembles of Cd(Mn)Se/Zn(Mn)Se semimagnetic self-organized quantum dots with different Mn content have been studied by photoluminescence and Raman scattering under strong magnetic fields in Faraday and Voigt geometries and with selective excitation. Electron spin-flip transitions have been observed in Voigt geometry in the structures with large Mn content, characterized by a large magnetic shift of photoluminescence bands. Narrow exciton peaks completely ${\ensuremath{\sigma}}^{\ensuremath{-}}{\ensuremath{\sigma}}^{+}$ polarized have been observed under selective excitation in the Faraday geometry in the structures with medium and small Mn content. A number of effects due to s,p-d exchange interaction and exciton magnetic polaron formation manifested themselves in the structures with the smallest Mn content, where no Zeeman shift of the photoluminescence bands was observed.

Observation of Andreev Bound States at Spin-active Interfaces

We report on high-resolution differential conductance experiments on nanoscale superconductor-ferromagnet tunnel junctions with ultrathin oxide tunnel barriers. We observe subgap conductance features that are symmetric with respect to bias and shift according to the Zeeman energy with an applied magnetic field. These features can be explained by resonant transport via Andreev bound states induced by spin-active scattering at the interface. From the energy and Zeeman shift of the bound states, both the magnitude and sign of the spin-dependent interfacial phase shifts between spin-up and spin-down electrons can be determined. These results contribute to the microscopic insight into the triplet proximity effect at spin-active interfaces.

Coherent, Mechanical Control of a Single Electronic Spin

We demonstrate coherent quantum control of a single spin driven by the motion of a mechanical resonator. The motion of a mechanical resonator is magnetically coupled to the electronic spin of a single nitrogen-vacancy center in diamond. Synchronization of spin-addressing protocols to the motion of the driven oscillator is used to fully exploit the coherence of this hybrid mechanical-spin system. We demonstrate applications of this coherent mechanical spin-control technique to nanoscale scanning magnetometry.

Preparation of two-particle total-hyperfine-spin-singlet states via spin-changing dynamics

We present our proposals for generating a total-hyperfine-spin-zero state for two $f=1$ or two $f=2$ particles, starting from initial unentangled states. We show that our goal can be achieved by exploiting spin-changing dynamics and quadratic Zeeman shifts with realistic choices of external magnetic fields and evolution time intervals.

Peierls Substitution in an Engineered Lattice Potential

Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.

The Zeeman effect in the [17.6]7.5–X18.5 transition of holmium monoxide

The high resolution molecular beam laser induced fluorescence (LIF) spectrum of the (0,0) band of the [17.6]7.5–X18.5 system of holmium monoxide, HoO, has been recorded field free and in the presence of a variable magnetic field. The Zeeman shifts and splittings in the LIF spectra of several hyperfine lines of the R(8.5) and P(8.5) transitions were analyzed to produce values for the magnitude of the effective magnetic g-factors, geff, of 9.86(2), 10.04(2) and 11.04(2) for [17.6]7.5, v=0, J=7.5 and 9.5 and X18.5, v=0, J=8.5 respectively. Comparison with calculated values of geff indicated that, in a Hund’s case (a) description, the transition was primarily 6H7.5–6I8.5.

Controlled Production of Subradiant States of a Diatomic Molecule in an Optical Lattice

We report the successful production of subradiant states of a two-atom system in a three-dimensional optical lattice starting from doubly occupied sites in a Mott insulator phase of a quantum gas of atomic ytterbium. We can selectively produce either a subradiant 1(g) state or a superradiant 0(u) state by choosing the excitation laser frequency. The inherent weak excitation rate for the subradiant 1(g) state is overcome by the increased atomic density due to the tight confinement in a three-dimensional optical lattice. Our experimental measurements of binding energies, linewidth, and Zeeman shift confirm the observation of subradiant levels of the 1(g) state of the Yb(2) molecule.