Hyperpolarizability and Operational Magic Wavelength in an Optical Lattice Clock

A lab-based test of the gravitational redshift with a miniature clock network

Einstein's theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of [ - 12.4 ± 0. 7(stat) ± 2. 5(sys)] × 10-19/cm, consistent with the expected redshift gradient of - 10.9 × 10-19/cm. Our results can also be viewed as relativistic gravitational potential difference measurements with sensitivity to mm scale changes in height on the surface of the Earth. These results highlight the potential of local-oscillator-independent differential clock comparisons for emerging applications of optical atomic clocks including geodesy, searches for new physics, gravitational wave detection, and explorations of the interplay between quantum mechanics and gravity.

Subrecoil Clock-Transition Laser Cooling Enabling Shallow Optical Lattice Clocks

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the μK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ^{1}S_{0}-^{3}P_{0} clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10^{-19} level.

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

Quantum walks provide a framework for designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. We do this by combining the fast, programmable control provided by optical tweezers with the scalable, homogeneous environment of an optical lattice. With these tools we study continuous-time quantum walks of single atoms on a square lattice and perform proof-of-principle demonstrations of spatial search with these walks. When scaled to more particles, the capabilities demonstrated can be extended to study a variety of problems in quantum information science, including performing more effective versions of spatial search using a larger graph with increased connectivity.

Dipole-Dipole Frequency Shifts in Multilevel Atoms

Dipole-dipole interactions lead to frequency shifts that are expected to limit the performance of next-generation atomic clocks. In this work, we compute dipolar frequency shifts accounting for the intrinsic atomic multilevel structure in standard Ramsey spectroscopy. When interrogating the transitions featuring the smallest Clebsch-Gordan coefficients, we find that a simplified two-level treatment becomes inappropriate, even in the presence of large Zeeman shifts. For these cases, we show a net suppression of dipolar frequency shifts and the emergence of dominant nonclassical effects for experimentally relevant parameters. Our findings are pertinent to current generations of optical lattice and optical tweezer clocks, opening a way to further increase their current accuracy, and thus their potential to probe fundamental and many-body physics.

Multi-reference ab initio calculations of Hg spectral data and analysis of magic and zero-magic wavelengths

We have identified magic wavelengths for ¹S₀ ↔ ³P_1,2 (m_J = 0) transitions and zero-magic wavelengths for the ³P_1,2 (m_J = 0) states of ²⁰⁰Hg atoms, analysed the robustness of the magic conditions with respect to wavelength and polarization imperfections. We show that the most experimentally feasible magic wavelength for the ¹S₀ ↔ ³P₂ transition is 351.8 nm of π polarized light. Relevant transition wavelengths and transition strengths are calculated using the state-of-the-art Complete Active Space Self-Consistent-Field (CASSCF) method with a perturbative inclusion of spin-orbit coupling. The transition wavelengths are a posteriori corrected for the dynamical energy using the second-order perturbation theory.

Frequency ratio measurements at 18-digit accuracy using an optical clock network

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics¹. Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10^-18 level, two orders of magnitude beyond their microwave predecessors². Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained largely unchanged for more than a decade^3-5. Here we operate a network of optical clocks based on ²⁷Al⁺ (ref. ⁶), ⁸⁷Sr (ref. ⁷) and ¹⁷¹Yb (ref. ⁸), and measure their frequency ratios with fractional uncertainties at or below 8 × 10^-18. Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields^9,10. Our optical clock network utilizes not just optical fibre¹¹, but also a 1.5-kilometre free-space link^12,13. This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws¹, perform relativistic geodesy¹⁴ and substantially improve international timekeeping¹⁵.

Inner-shell clock transition in atomic thulium with a small blackbody radiation shift

One of the key systematic effects limiting the performance of state-of-the-art optical clocks is the blackbody radiation (BBR) shift. Here, we demonstrate unusually low sensitivity of a 1.14 μm inner-shell clock transition in neutral Tm atoms to BBR. By direct polarizability measurements, we infer a differential polarizability of the clock levels of -0.063(30) atomic units corresponding to a fractional frequency BBR shift of only 2.3(1.1) × 10^-18 at room temperature. This amount is several orders of magnitude smaller than that of the best optical clocks using neutral atoms (Sr, Yb, Hg) and is competitive with that of ion optical clocks (Al⁺, Lu⁺). Our results allow the development of lanthanide-based optical clocks with a relative uncertainty at the 10^-17 level.

Operational Magic Intensity for Sr Optical Lattice Clocks

We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.

Uncertainty Evaluation of an 171Yb Optical Lattice Clock at NMIJ

We report an uncertainty evaluation of an ¹⁷¹Yb optical lattice clock with a total fractional uncertainty of 3.6×10^-16 , which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the 6s^{2 1}S₀-6s6p ³P₀ clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift d incorporated in a widely used light shift model by RIKEN and the second-order Zeeman shift a_Z are improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient d is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions 6s6p³P₀-6s8p³P₀, 6s8p³P₂, and 6s5f³F₂. The obtained values are d=-1.1(4) μ Hz and a_Z=-6.6(3) Hz/mT². These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

Evaluation of laser frequency offset locking using an electrical delay line

Frequency offset locking between two Nd:YAG lasers is performed using frequency locking with an electrical delay line. The relative frequency instability of the offset locking is measured to be 3.5×10^-12 for an averaging time of 1 s, which is approximately 77 times smaller than that of the free-running case. The frequency instability of the frequency locking is compared to that of the phase locking between the two Nd:YAG lasers. Furthermore, a compact solid-state laser is frequency locked to an optical frequency comb with a frequency instability of 8.2×10^-11 for an averaging time of 1 s, which is improved by approximately 20 times, with respect to the free-running case. The offset-locking scheme using a delay line is useful for various applications including a research on quantum optics, interferometric measurements, and experiments involving laser cooling, such as an optical lattice clock.

Dual-Mode Operation of an Optical Lattice Clock Using Strontium and Ytterbium Atoms

We have developed an optical lattice clock that can operate in dual modes: a strontium (Sr) clock mode and an ytterbium (Yb) clock mode. Dual-mode operation of the Sr-Yb optical lattice clock is achieved by alternately cooling and trapping ⁸⁷Sr and ¹⁷¹Yb atoms inside the vacuum chamber of the clock. Optical lattices for Sr and Yb atoms were arranged with horizontal and vertical configurations, respectively, resulting in a small distance of the order of between the trapped Sr and Yb atoms. The ¹S₀-³P₀ clock transitions in the trapped atoms were interrogated in turn and the clock lasers were stabilized to the transitions. We demonstrated the frequency ratio measurement of the Sr and Yb clock transitions by using the dual-mode operation of the Sr-Yb optical lattice clock. The dual-mode operation can reduce the uncertainty of the blackbody radiation shift in the frequency ratio measurement, because both Sr and Yb atoms share the same blackbody radiation.

Atomic clocks for geodesy

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10^-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10^-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.

Systematic evaluation of a 171Yb optical clock by synchronous comparison between two lattice systems

Optical clocks are the most precise measurement devices. Here we experimentally characterize one such clock based on the ¹S₀-³P₀ transition of neutral ¹⁷¹Yb atoms confined in an optical lattice. Given that the systematic evaluation using an interleaved stabilization scheme is unable to avoid noise from the clock laser, synchronous comparisons against a second ¹⁷¹Yb lattice system were implemented to accelerate the evaluation. The fractional instability of one clock falls below 4 × 10⁻¹⁷ after an averaging over a time of 5,000 seconds. The systematic frequency shifts were corrected with a total uncertainty of 1.7 × 10⁻¹⁶. The lattice polarizability shift currently contributes the largest source. This work paves the way to measuring the absolute clock transition frequency relative to the primary Cs standard or against the International System of Units (SI) second.

Faraday-Shielded dc Stark-Shift-Free Optical Lattice Clock

We demonstrate the absence of a dc Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the dc Stark shift at the 10^{-20} level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel nonzero dc Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of dc Stark shifts in optical lattice clocks.

Two Clock Transitions in Neutral Yb for the Highest Sensitivity to Variations of the Fine-Structure Constant

We propose a new frequency standard based on a 4f^{14}6s6p ^{3}P_{0}-4f^{13}6s^{2}5d (J=2) transition in neutral Yb. This transition has a potential for high stability and accuracy and the advantage of the highest sensitivity among atomic clocks to variation of the fine-structure constant α. We find its dimensionless α-variation enhancement factor to be K=-15, in comparison to the most sensitive current clock (Yb^{+}  E3, K=-6), and it is 18 times larger than in any neutral-atomic clocks (Hg, K=0.8). Combined with the unprecedented stability of an optical lattice clock for neutral atoms, this high sensitivity opens new perspectives for searches for ultralight dark matter and for tests of theories beyond the standard model of elementary particles. Moreover, together with the well-established ^{1}S_{0}-^{3}P_{0} transition, one will have two clock transitions operating in neutral Yb, whose interleaved interrogations may further reduce systematic uncertainties of such clock-comparison experiments.

Imaging Optical Frequencies with 100 μHz Precision and 1.1 μm Resolution

We implement imaging spectroscopy of the optical clock transition of lattice-trapped degenerate fermionic Sr in the Mott-insulating regime, combining micron spatial resolution with submillihertz spectral precision. We use these tools to demonstrate atomic coherence for up to 15 s on the clock transition and reach a record frequency precision of 2.5×10^{-19}. We perform the most rapid evaluation of trapping light shifts and record a 150 mHz linewidth, the narrowest Rabi line shape observed on a coherent optical transition. The important emerging capability of combining high-resolution imaging and spectroscopy will improve the clock precision, and provide a path towards measuring many-body interactions and testing fundamental physics.

Multipolar Polarizabilities and Hyperpolarizabilities in the Sr Optical Lattice Clock

We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar M1 and E2 atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We develop an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows us to effectively and accurately carry out complete summations over intermediate states. We apply our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carry out an accurate calculation of the multipolar polarizabilities for these states at the magic frequency. Understanding these Stark shifts in optical lattice clocks is crucial for further improvement of the clock accuracy.