Tune-out Wavelengths Research Articles

Electric dipole polarizabilities and tune-out wavelengths for 23S1 and 33S1 states of Be2.

The electric dipole polarizabilities and the tune-out wavelengths for the n3S1 (n = 2, 3) states of Be2+ are determined through the application of the relativistic full-configuration-interaction approach. Our calculations directly integrate the mass shift operator into the Dirac-Coulomb-Breit Hamiltonian and further assess the quantum electrodynamics (QED) correction to the dynamic dipole polarizabilities using perturbation theory. The results reveal that the static electric dipole polarizability of the 23S1 and 33S1 states, as well as the 93nm tune-out wavelength of the 23S1 state and the 238nm tune-out wavelength of the 33S1 state, exhibits a high sensitivity to QED correction, which exceeds 80 ppm, providing a sensitive test for atomic structure theory.

Tune-out wavelengths of Rydberg atoms

The atomic polarizability represents the response characteristics of atoms to externally applied electro-magnetic fields. The wavelength (or frequency) at which the dynamic polarizability of an atom is equal to zero is referred to as the tune-out wavelength (or frequency). Spectroscopy technology based on the tune-out effect has potential applications in quantum precision measurement, quantum computation and quantum communication. Related research topics include the measurement of fundamental physical constants and strong interactions. The tune-out wavelengths of atoms in low-lying states primarily fall within the optical band, where the theoretical calculations and experimental measurements have significant progress. However, for Rydberg atoms in highly excited states, theoretical calculations are challenging due to their high density of atomic states. The difficulty of experimental measurement arises from small splitting of adjacent atomic energy levels. In this paper, we demonstrate the tune-out wavelengths measurement for Rydberg atoms in a cesium vapor cell at room temperature. We utilize a two-photon cascade excitation to prepare Rydberg states and employ amplitude-modulation electromagnetically-induced transparency (AM-EIT) spectroscopy to measure the tune-out wavelength. By continuously scanning the microwave frequencies, we obtain AM-EIT signals of Rydberg atoms. At near-resonant microwave transition wavelengths, strong AM-EIT signals are observed due to microwave-atom coupling. Conversely, at tune-out wavelengths, the dynamically polarization-induced destructive interference in neighboring energy states occurs which leads to the weak AM-EIT signals. The AM-EIT provides a spectral resolution of about 10 MHz. We have developed a simplified three-level model to calculate the tune-out wavelength. The results of our theoretical calculations are consistent with the experimental findings within a range of ±90 MHz.

Polarizabilities for the low-lying triplet states of He-like Be III

The nonrelativistic and relativistic full-configuration-interaction calculations are performed for the low-lying triplet states of Be2+ ion. The energies for n3S1, n3PJ and n3DJ states, and the dipole oscillator strengths for the 23S1(33S1)→n3PJ and 23PJ(33PJ)→n3DJ transitions with the main quantum number n up to 5 are determined. We calculate the nonrelativistic dynamic dipole polarizabilities by using the sum rule of intermediate states. In addition, the tune-out wavelengths for the four lowest triplet states and magic wavelengths for the 23S→23P and 23S→33P transitions are obtained.

Tune-out wavelengths for the 2 3S1 state of the Li+ ion

Configuration interaction calculations are performed to determine the dipole polarizabilities and tune-out wavelengths for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state in ${\mathrm{Li}}^{+}$ ion. The finite nuclear mass correction is given by including the mass shift operator in the Dirac-Coulomb-Breit Hamiltonian directly, while the QED correction to dynamic dipole polarizabilities is evaluated by using the perturbation theory. The tune-out wavelengths for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=0)$ and $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ states are 159.620 55(6) nm and 159.631 14(6) nm, respectively. And the QED correction for 159 nm tune-out wavelength is 43 ppm. In addition, we obtain the static dipole polarizability for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ state to be 46.857 03(4) a.u., in which the contribution from QED is 70 ppm. The 159 nm tune-out wavelength and the static dipole polarizability of $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state might provide a test of atomic structure theory.

Realization of space-dependent interactions by an optically controlled magnetic p -wave Feshbach resonance in degenerate Fermi gases

We report experimental realization of the space-dependent interaction by optical controlled narrow $p$-wave magnetic Feshbach resonance in a $^{40}\mathrm{K}$ Fermi gas. A space varied optical field at the tune-out wavelength is applied to illuminate the atomic sample, which drives the bound-to-bound molecular transition to shift the energy of a closed-channel molecule state. Due to the position varied atomic interaction induced by the different laser intensity distribution across the entire Fermi atom cloud, the space-dependent atomic loss rate is observed. This scheme provides a control technique to study the Fermi gas with the space-dependent atomic $p$-wave interaction, and has great potential in quantum simulation.

Magnetic Sublevel Independent Magic and Tune-Out Wavelengths of the Alkaline-Earth Ions

Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths (λTs). Similarly, differential light shift in a transition vanishes at the magic wavelengths (λmagics). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λmagic. Similarly, the λT values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole (α) values of only one state whereas the λmagic values require evaluation of α values for two states. However, both the λmagic and λT values depend on angular momenta and their magnetic components (M) of states. Here, we report the λmagic and λT values of many S1/2 and D3/2,5/2 states, and transitions among these states of the Mg+, Ca+, Sr+ and Ba+ ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations.

Measurement of the Rb87 D -line vector tune-out wavelength

We report a precision measurement of a tune-out wavelength for 87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using $\sigma_-$ polarized light with an an estimated purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.

Measurement of the tune-out wavelength for Cs133 at 880 nm

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

Experimental study of tune-out wavelengths for spin-dependent optical lattice in 87Rb Bose–Einstein condensation

We study the periodic potential of a one-dimensional optical lattice originating from a scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of an optical lattice is measured by Kapitza–Dirac scattering of 87 R b Bose–Einstein condensate, and the characteristics of a spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that the ac Stark shift cancels can be probed by the optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both scalar and vector shifts. Our results provide a clear interpretation for a spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.

Tune-out and magic wavelengths of Ba+ ions

The static and dynamic polarizabilities of the ground state and low-lying excited states of ${\mathrm{Ba}}^{+}$ ions are calculated by using a relativistic semiempirical method: the relativistic configuration interaction plus core polarization (RCICP) method. The tune-out wavelengths of the ground state and magic wavelengths of the $6{s}_{1/2}\ensuremath{\rightarrow}6{p}_{1/2,3/2},5{d}_{3/2,5/2}$ transitions are determined. One visible tune-out wavelength, 480.658(18) nm, is found. High-precision measurements on this tune-out wavelength could be used to determine the ratio of the oscillator strengths of the $6{s}_{1/2}\ensuremath{\rightarrow}6{p}_{1/2,3/2}$ transitions. In addition, we suggest that the measurements on the magic wavelengths corresponding to the $6{s}_{1/2}\ensuremath{\rightarrow}5{d}_{3/2,5/2}$ transitions could be used to determine the oscillator strengths of the $5{d}_{5/2}\ensuremath{\rightarrow}4{f}_{7/2}$ and $5{d}_{3/2}\ensuremath{\rightarrow}4{f}_{5/2}$ transitions, while the measurements of the magic wavelengths near 416 nm for the $6{s}_{1/2}\ensuremath{\rightarrow}6{p}_{3/2}$ transition could be used to determine the ratio of the oscillator strengths of the $6{p}_{3/2}\ensuremath{\rightarrow}6{d}_{3/2,5/2}$ transitions.

Tune-out and magic wavelengths, and electric quadrupole transition properties of the singly charged alkaline-earth metal ions

In this paper, we present the tune-out and magic wavelengths of the Mg+, Ca+, Sr+ and Ba+ alkaline earth-metal ions by determining dynamic E1 polarizabilities. Furthermore, we have evaluated the electric quadrupole (E2) matrix elements of a large number of forbidden transitions using an all-order relativistic many-body method and compare them with the previously reported values for a few selective transitions. Compilation of both the E1 and E2 transition matrix elements, will now provide a more complete knowledge about the transition properties of the considered singly charged alkaline earth-metal ions. Similarly, the listed precise values of tune-out and magic wavelengths due to the dominant E1 polarizabilities can be helpful to conduct experiments using the above ions with reduced systematics. Therefore, all these data will be immensely useful for various applications for carrying out the high-precision experiments and laboratory simulations in atomic physics, and interpreting transition lines in the astrophysical observations. This work is a continuation of our earlier reported data on the electric dipole (E1) matrix elements and lifetimes of the metastable states of the alkaline earth ions in Kaur et al. (2021).

Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular-momentum conservation of the beam. The theory is employed on $^{87}\mathrm{Sr}^{+}$ to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using the relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes a fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and orbital angular momentum of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ atoms.

Tune-out wavelengths of the hyperfine components of the ground level of Cs133 atoms

The static and dynamic electric-dipole polarizabilities and tune-out wavelengths for the ground state of Cs atoms are calculated by using a semiempirical relativistic configuration interaction plus core polarization approach. By considering the hyperfine splittings, the static and dynamic polarizabilities, hyperfine Stark shifts, and tune-out wavelengths of the hyperfine components of the ground level of $^{133}$Cs atoms are determined. It is found that the hyperfine shifts of the first primary tune-out wavelengths are about $-$0.0135 nm and 0.0106 nm, which are very close to the hyperfine interaction energies. Additionally, the contribution of the tensor polarizability to the tune-out wavelengths is determined to be about $10^{-5} \sim 10^{-6}$ nm.

Tune-Out and Magic Wavelengths for Ground-State ^{23}Na^{40}K Molecules.

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of ^{23}Na^{40}K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

Many-body calculations and hyperfine-interaction effect on dynamic polarizabilities at the low-lying energy levels of Y2+

The present work determines the precise values of magic wavelengths corresponding to the clock transitions 5$^2S$-4$^2D$ of Y$^{2+}$ ion both at the levels of fine- and hyperfine-structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine structure splitting.

State-Dependent Optical Lattices for the Strontium Optical Qubit.

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than 4 orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

Measurement of the 671-nm tune-out wavelength of Li7 by atom interferometry

We have measured the tune-out wavelength of lithium isotope $^{7}\mathrm{Li}$ at 671 nm. We have used our atom interferometer to measure the phase shift due to the dynamical Stark effect as a function of the laser frequency when a laser beam was focused on a single interferometer arm. The tune-out wavelength is a function of the hyperfine $F,{m}_{F}$ sublevel, and we have prepared the atoms in the sublevel $F=2,{m}_{F}=+2$ or $\ensuremath{-}2$. We find that the tune-out frequency of the $F=2,{m}_{F}=+2$ sublevel is at $3388(8)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ to the blue of the $^{2}S_{1/2},F=1\ensuremath{\rightarrow}^{2}P_{1/2},{F}^{\ensuremath{'}}=2$ transition, the accuracy of this measurement being limited by imperfect optical pumping. This measurement is in excellent agreement with its theoretical value, and, once corrected for different tensorial contributions, our measurement agrees with the more precise measurement of Copenhaver et al. [Phys. Rev. A 100, 063603 (2019)], who also used atom interferometry but different experimental conditions.

Rayleigh scattering formalism for the tune-out wavelength: Application to the 2 3 S state of helium

SynopsisThe tune-out wavelength for an atom interacting with an incident laser beam is reformulated as a zero in the Rayleigh scattering cross section instead of the dynamic polarizability (or AC Stark shift). The two pictures are equivalent in lowest order, but not when higher-order retardation effects are taken into account. Detailed high-precision calculations in Hylleraas coordinates will be presented for the tune-out wavelength of helium at 413 nm near the 2 3 S – 33 P optical transition, including D-wave retardation corrections, and compared with recent high-precision measurements.

Polarizabilities and tune-out wavelengths of the hyperfine ground states of 133Cs atom

SynopsisThe static and dynamic electric dipole polarizabilities of the ground state and hyperfine ground states of the 133Cs have been calculated by using relativistic configuration interaction plus core polarization (RCICP) approach. The tune-out wavelengths of ground and hyperfine ground states are also determined.

Measurement of a Li7 tune-out wavelength by phase-patterned atom interferometry

Atom interferometers typically use the total populations the interferometer's output ports as the signal, but finer spatial structure can contain useful information. We pattern a matter-wave phase profile onto an atomic sample. An interferometer translates the phase into a measurable pattern in the atomic density that we use perform the first direct precision measurement of the $^7$Li tune-out wavelength near 671 nm. Expressed as a detuning from the $|2S_{1/2},F{=}2\rangle{\rightarrow}|2P_{1/2},F'{=}2\rangle$ transition, we find 3329.3(1.4) MHz for the tensor-shifted tune out of the $|2S_{1/2},F{=}2,m_F{=}0\rangle$ state with $\sigma^\pm$ light polarization and 3310.1(4.9) MHz for the tune out of the the scalar polarizability. This technique may be generalized for directly sensing spatially varying phase profiles.