Differential Polarizability Research Articles

Differential polarizability of the strontium intercombination transition at 1064.7 nm

Differential polarizability of the strontium intercombination transition at 1064.7 nm

Demonstration of a tunable interface between Rydberg atoms and superconducting microwave circuits with differential polarizability nulling

Microwave-dressed Rydberg atoms in pairs of states that are optically accessible and engineered so that the frequency of the transition between them is tunable while exhibiting a low sensitivity to stray electric fields have been interfaced with a superconducting coplanar waveguide (CPW) microwave resonator. This was achieved with helium atoms in triplet Rydberg states with principal quantum numbers n=55 and 56. The atoms were dressed with two strong microwave fields—a control field and a differential polarizability nulling field. The control field allowed the atoms to be coupled to the resonator using the two-color two-photon transition between the equal parity 1s55sS13≡|55s〉 and 1s56sS13≡|56s〉 Rydberg states, with one photon supplied by it and the other provided by the resonator. The nulling field was detuned from the field-free 1s55sS13→1s55pPJ3≡|55p〉 transition to admix |55p〉 character into the |55s〉 state and eliminate the differential static electric dipole polarizability of the |55s〉 and |56s〉 states. The experiments were performed with atoms located ∼300µm above a λ/4 niobium nitride superconducting CPW resonator operated at temperatures between 3.59 and 3.73K. The measured ac and dc Stark shifts of the Rydberg states at this atom-circuit interface in the presence of the dressing fields are in good quantitative agreement with the results of Floquet calculations. The differential polarizability nulling fields used in the experiments allowed the difference in the Stark shifts of the |55s〉 and |56s〉 states over the range of dc fields offset from the residual stray field by ±65 mV/cm to be reduced from 2π×2.1 MHz to 2π×125 kHz. Published by the American Physical Society 2024

Improved Measurement of the Differential Polarizability Using Co-Trapped Ions.

We present a novel approach for measuring the differential static scalar polarizability of a target ion utilizing a "polarizability scale" scheme with a reference ion co-trapped in a linear Paul trap. The differential static scalar polarizability of the target ion can be precisely extracted by measuring the ratio of the ac Stark shifts induced by an add-on infrared laser shed on both ions. This method circumvents the need for the calibration of the intensity of the add-on laser, which is usually the bottleneck for measurements of the polarizability of trapped ions. As a demonstration, ^{27}Al^{+} (the target ion) and ^{40}Ca^{+} (the reference ion) are used in this work, with an add-on laser at 1068nm injected into the ion trap along the trap axis. The differential static scalar polarizability of ^{27}Al^{+} is extracted to be 0.416(14)a.u. by measuring the ratio of the ac Stark shifts of both ions. Compared to the most recent result [Phys. Rev. Lett. 123, 033201 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.033201], the relative uncertainty of the differential static scalar polarizability of ^{27}Al^{+} is reduced by approximately a factor of 4, to 3.4%. This improvement is expected to be further enhanced by using an add-on laser with a longer wavelength.

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10−19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

Compensation of the multipolar polarizability shift in optical lattice clocks.

In neutral atom optical clocks, the higher-order atomic polarizability terms lead to the clock transition frequency shift that is motion-state dependent and nonlinear with the optical lattice depth. We propose to use an auxiliary optical lattice to compensate the influence of the E2-M1 differential polarizability or tune the associated coefficient to a favorable value. We show that by applying this method to Sr and Hg optical lattice clocks, the low or even sub-10-19 clock transition frequency uncertainty from the optical lattice becomes feasible. Finally, the proposed scheme is simple for experimental realization, is compatible with the use of an enhancement cavity, and can be implemented and tested in the existing setups.

Measurement of infrared magic wavelength for an all-optical trapping of 40Ca+ ion clock

For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4s2S1/2→3d2D5/2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.

Scheme for Quantum-Logic Based Transfer of Accuracy in Polarizability Measurement for Trapped Ions Using a Moving Optical Lattice.

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.

Tunable Rydberg–Rydberg transitions in helium with reduced sensitivity to dc electric fields by two-colour microwave dressing

The difference in the static electric dipole polarizabilities of the and Rydberg levels in helium has been eliminated by dressing the atom with a microwave field near resonant with the single-photon transition. For an amplitude dressing field, detuned by from the zero-field transition frequency, the dc Stark shift of the two-photon transition between these states remained within for electric fields up to . This transition was probed by single-color two-photon microwave spectroscopy, and by two-color two-photon spectroscopy with one strong additional dressing field and a weak probe field. For all measurements, the transition frequencies and Stark shifts were compared, and found to be in excellent quantitative agreement with the results of Floquet calculations of the energy-level structure of the Rydberg states in the presence of the dressing fields and applied dc electric fields. The two-color microwave dressing scheme demonstrated, with one field applied to null the differential polarizability of the Rydberg–Rydberg transition, and the second exploited to allow the two-photon transition to be employed to achieve tunable absorption of single-photons from a weak probe field, will facilitate improved coherence times and tunable single-photon absorption in hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.

New designed helical resonator to improve measurement accuracy of magic radio frequency

Based upon the new designed helical resonator, the resonant radio frequency (RF) for trapping ions can be consecutively adjusted in a large range (about 12 MHz to 29 MHz) with high Q-factors (above 300). We analyze the helical resonator with a lumped element circuit model and find that the theoretical results fit well with the experimental data. With our resonator system, the resonant frequency near magic RF frequency (where the scalar Stark shift and the second-order Doppler shift due to excess micromotion cancel each other) can be continuously changed at kHz level. For 88Sr+ ion, compared to earlier results, the measurement accuracy of magic RF frequency can be improved by an order of magnitude upon rough calculation, and therefore the net micromotion frequency shifts can be further reduced. Also, the differential static scalar polarizability Δα 0 of clock transition can be experimentally measured more accurately.

Liquid-Nitrogen-Cooled Ca + Optical Clock with Systematic Uncertainty of 3×10−18

We present a liquid-nitrogen-cooled $\mathrm{Ca}$${}^{+}$ optical clock with an overall systematic uncertainty of $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. In contrast to the room-temperature $\mathrm{Ca}$${}^{+}$ optical clock that we have reported previously, the cryogenic black-body radiation (BBR) shield in vacuum is cooled to $82\ifmmode\pm\else\textpm\fi{}5$ K using liquid nitrogen. We also implement an ion trap with a reduced heating rate and improved laser cooling. This allows the ion temperature to fall to the Doppler-cooling limit during the clock operation and the systematic uncertainty associated with the secular (thermal) motion of the ion is reduced to $<1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. The uncertainty arising from the probe laser light shift and the servo error is also reduced to $<1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ and $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ with the hyper-Ramsey method and the higher-order servo algorithm, respectively. By comparing the output frequency of the cryogenic clock to that of a room-temperature clock, the differential BBR shift between the two is determined with a fractional statistical uncertainty of $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. The differential BBR shift is used to calculate the static differential polarizability and the result is found to be in excellent agreement with our previous measurement using a different method. This work suggests that the BBR shift of optical clocks can be suppressed well in a liquid-nitrogen environment. Systems similar to what is presented here can also be used to suppress the BBR shift significantly in other types of optical clocks, such as $\mathrm{Yb}$${}^{+}$, $\mathrm{Sr}$${}^{+}$, $\mathrm{Yb}$, Sr, etc.

Dynamic polarizabilities of the clock states of Al+

The dynamic polarizabilities of and states of Al+ are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac–Hartree–Fock method in this work. Five ultraviolet magic wavelengths for the Al+ clock transition – are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al+ clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al+ clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al+ clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can.

Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation.

We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}Yb^{+} that is coupled to the ^{2}S_{1/2} ground state via an electric octupole transition. The radiative lifetime is determined to be 4.98(25)×10^{7} s, corresponding to 1.58(8)yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

Rotational Coherence Times of Polar Molecules in Optical Tweezers.

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7)ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

Spectral induced polarization: frequency domain versus time domain laboratory data

SUMMARY Spectral information obtained from induced polarization (IP) measurements can be used in a variety of applications and is often gathered in frequency domain (FD) at the laboratory scale. In contrast, field IP measurements are mostly done in time domain (TD). Theoretically, the spectral content from both domains should be similar. In practice, they are often different, mainly due to instrumental restrictions as well as the limited time and frequency range of measurements. Therefore, a possibility of transition between both domains, in particular for the comparison of laboratory FD IP data and field TD IP results, would be very favourable. To compare both domains, we conducted laboratory IP experiments in both TD and FD. We started with three numerical models and measurements at a test circuit, followed by several investigations for different wood and sandstone samples. Our results demonstrate that the differential polarizability (DP), which is calculated from the TD decay curves, can be compared very well with the phase of the complex electrical resistivity. Thus, DP can be used for a first visual comparison of FD and TD data, which also enables a fast discrimination between different samples. Furthermore, to compare both domains qualitatively, we calculated the relaxation time distribution (RTD) for all data. The results are mostly in agreement between both domains, however, depending on the TD data quality. It is striking that the DP and RTD results are in better agreement for higher data quality in TD. Nevertheless, we demonstrate that IP laboratory measurements can be carried out in both TD and FD with almost equivalent results. The RTD enables a good comparability of FD IP laboratory data with TD IP field data.

Raman Tensor of Layered SnS2.

Recently, tin disulfide (SnS2) has become a hot research focus in various fields due to its advantages of a high transistor switching ratio, an adjustable band gap in visible light range, excellent Li storage performance, sensitive gas recognition, and efficient photocatalytic capability. However, at present, studies of its basic structure mostly stay on the regulation related to the number of layers. To maximize the value of SnS2 in the application design, this paper analyzes the angle-resolved polarized Raman spectra of SnS2 crystals grown under high-temperature sealing systems. Under the parallel scattering configuration test of both the sample basal plane and the cross plane, we observed that how the Raman scattering intensity of the two test planes varies with the polarization angle is different. Combining this experimental result with theory support allows us to reach a conclusion that the differential polarizability of the phonon vibration mode along the z-axis of the cross plane of SnS2 is proven to be the strongest. This finding is expected to provide favorable support for the application of structural regulation of SnS2 and work as a reference for studying other van der Waals layered materials with greater potential.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Raman tensor of layered black phosphorus

Black phosphorus has a strong Raman anisotropy on the basal and cross planes due to its orthorhombic crystal structure. However, almost all the studies on black phosphorus’ anisotropy focus on basal plane with the cross plane neglected. Here, we performed a systematic angle-resolved polarized Raman scattering on both the basal and cross planes of black phosphorus and obtained its integral Raman tensors. It is discovered that when the polarization direction of excitation light is along different crystal axes, the Raman intensity ratio (Ixx : Iyy: Izz) of {A}_g^1 mode is 256:1:5. Besides, via calculation, it is confirmed that the strong Raman anisotropy mainly comes from different differential polarizability alone different directions. This phenomenon is also observed when it comes to the {A}_g^2 mode.

Raman tensor of layered black arsenic

AbstractDue to the similar atom arrangement with black phosphorus, black arsenic also has obvious Raman anisotropy at both the base and cross planes. However, the polarization characteristics of black arsenic have been rarely reported so far with most relevant studies devoted to the base plane. Here, to compensate for the blank of the anisotropy in cross plane, we implemented a systematical angle‐resolved polarized Raman measurement on both planes of layered black arsenic and observed that the Raman intensity ratios (Ixx : Iyy : Izz) of optical phonons and modes along different axes are 1:4.8:2.76 and 6.9:1:5.7, respectively. Based on the definition of Raman intensity, we abstracted integral Raman tensors of black arsenic. In addition, according to density functional theory, it can be affirmed that the Raman anisotropy of Ag mode is sourced from the anisotropy of differential polarizability along different crystal axes.

Magic wavelength of the Ba+138 6s S1/22–5d D5/22 clock transition

The zero crossing of the dynamic differential scalar polarizability of the $S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be $459.1614(28)\,$THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\gtrsim 700\,$nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

Raman tensor of layered MoS2.

Raman tensors, one of the basic physical properties of ${{\rm MoS}_2}$MoS2, are rarely reported. Here, angle-resolved polarized Raman scatterings on basal and cross planes of layered ${{\rm MoS}_2}$MoS2 were carried out using the geometry configuration of parallel polarization, and the Raman tensors of three optical vibration modes were systematically studied. As a polar vibration mode, the differential polarizability of the ${{\rm A}_{1{\rm g}}}$A1g mode corresponding to the Raman tensor along the $c$c direction is larger than that along the $a$a direction. In addition, it is also larger than that formed by ${{\rm E}_{2{\rm g}}}$E2g and ${{\rm E}_{1{\rm g}}}$E1g modes. All the experimental results above are beneficial to the understanding of inelastic light-scattering process of ${{\rm MoS}_2}$MoS2.