Optical Clock Transition Research Articles

State-dependent interactions in ultracold 174Yb probed by optical clock spectroscopy

We report on the measurement of the scattering properties of ultracold 174Yb bosons in a three-dimensional optical lattice. Site occupancy in an atomic Mott insulator is resolved with high-precision spectroscopy on an ultranarrow, metrological optical clock transition. Scattering lengths and loss rate coefficients for 174Yb atoms in different collisional channels involving the ground state 1S0 and the metastable 3P0 states are derived. These studies set important constraints for future experimental studies of two-electron atoms for quantum-technological applications.

Collisional frequency shift of a trapped-ion optical clock

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a non-perturbative framework based on a quantum channel description of the scattering process, and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr$^+$ optical atomic clock transition due to elastic collisions with helium.

Quantum lock-in force sensing using optical clock Doppler velocimetry

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator, thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single-trapped 88Sr+ ion as a force sensor. The ion is electrically driven at a frequency much lower than the trap resonance frequency. We measure small amplitude of motion by measuring the periodic Doppler shift of an atomic optical clock transition, enhanced using the quantum lock-in technique. We report frequency force detection sensitivity as low as 2.8 × 10−20 NHz−1/2.

Spin-orbit-coupled fermions in an optical lattice clock.

Engineered spin-orbit coupling (SOC) in cold-atom systems can enable the study of new synthetic materials and complex condensed matter phenomena. However, spontaneous emission in alkali-atom spin-orbit-coupled systems is hindered by heating, limiting the observation of many-body effects and motivating research into potential alternatives. Here we demonstrate that spin-orbit-coupled fermions can be engineered to occur naturally in a one-dimensional optical lattice clock. In contrast to previous SOC experiments, here the SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states in 87Sr atoms. We use clock spectroscopy to prepare lattice band populations, internal electronic states and quasi-momenta, and to produce spin-orbit-coupled dynamics. The exceptionally long lifetime of the excited clock state (160 seconds) eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in situ probing of the SOC band structure and eigenstates. We use these capabilities to study Bloch oscillations, spin-momentum locking and Van Hove singularities in the transition density of states. Our results lay the groundwork for using fermionic optical lattice clocks to probe new phases of matter.

Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition.

We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron ^{173}Yb atoms. By mapping the electronic states onto effective sites along a synthetic "electronic" dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.

Space-borne frequency comb metrology

Precision time references in space are of major importance to satellite-based fundamental science, global satellite navigation, earth observation, and satellite formation flying. Here we report on the operation of a compact, rugged, and automated optical frequency comb setup on a sounding rocket in space under microgravity. The experiment compared two clocks, one based on the optical D2 transition in Rb, and another on hyperfine splitting in Cs. This represents the first frequency comb based optical clock operation in space, which is an important milestone for future satellite-based precision metrology. Based on the approach demonstrated here, future space-based precision metrology can be improved by orders of magnitude when referencing to state-of-the-art optical clock transitions.

Superradiance on the millihertz linewidth strontium clock transition

Laser frequency noise contributes a significant limitation to today's best atomic clocks. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. We demonstrate and characterize superradiant emission from the millihertz linewidth clock transition in an ensemble of laser-cooled 87Sr atoms trapped within a high-finesse optical cavity. We measure a collective enhancement of the emission rate into the cavity mode by a factor of more than 10,000 compared to independently radiating atoms. We also demonstrate a method for seeding superradiant emission and observe interference between two independent transitions lasing simultaneously. We use this interference to characterize the relative spectral properties of the two lasing subensembles.

Particle-hole configuration interaction and many-body perturbation theory: Application toHg+

The combination of configuration interaction and many-body perturbation theory methods (CI+MBPT) is extended to non-perturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes play an important role. For example, the method can treat valence-hole systems like Ir$^{17+}$, particle-hole excitations in noble gases, and difficult transitions such as the $6s \rightarrow 5d^{-1}6s^2$ optical clock transition in Hg$^+$. We take the latter system as our test case for the method and obtain very good accuracy (~1%) for the low-lying transition energies. The $\alpha$-dependence of these transitions is calculated and used to reinterpret the existing best laboratory limits on the time-dependence of the fine-structure constant.

Actinide ions for testing the spatial α -variation hypothesis

Testing the spatial variation of fine-structure constant $\alpha$ indicated in [Webb et al., Phys. Rev. Lett. 107, 191101 (2011)] with terrestrial laboratory atomic measurements requires at least $\dot{\alpha}/\alpha \sim 10^{-19}~\textrm{y}^{-1}$ sensitivity. We conduct a systematic search of atomic systems for such a test that have all features of the best optical clock transitions leading to possibility of the frequency measurements with fractional accuracy on the level of $10^{-18}$ or better and have a factor of 100 extra enhancement of $\alpha$-variation in comparisons to experimental frequency ratio measurement accuracy. We identify the pair of actinide Cf$^{15+}$ and Es$^{16+}$ ions as the best system for a test of spatial $\alpha-$variation hypothesis as it satisfies both of these requirements and have sufficiently simple electronic structure to allow for high-precision predictions of all atomic properties required for rapid experimental progress.

Optical clock transition in a rare-earth-ion-doped crystal: coherence lifetime extension for quantum storage applications

Atomic clock transitions are desirable for quantum information storage and processing thanks to the protection from decoherence they provide. In the context of rare- earth-ion-doped crystals for quantum information storage, clock Zeeman or hyperfine transitions have been identified and exploited for long-lived storage in spin degrees of freedom. We present a theoretical and experimental analysis on the existence of an optical clock transition in Tm3+:YAG, in view of storage in optical coherences. The combination of a Zeeman-like term and a quadratic electronic Zeeman term in the Hamiltonian, lead to the existence of a magnetic field amplitude (12 mT) for which the derivative of the optical transition energy with respect to the field amplitude vanishes, regardless of the magnetic field orientation. We have verified this prediction through hole-burning spectroscopy experiments. In addition to that, a study of the behavior of the Hamiltonian as a function of the magnetic field orientation yields the direction for which both derivatives with respect to the magnetic field angular coordinates also vanish. The condition for an optical clock transition with three vanishing partial derivatives is met.

Magic Wavelengths of the Optical Clock Transition at 1107 nm of Barium**Supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 14JK1402.

Magic wavelengths for laser trapping of barium atoms in the optical lattices are calculated with considering the optical clock transition at 1107 nm between the 6s2 1S0 state and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated. Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.

Doppler spectroscopy of an ytterbium Bose-Einstein condensate on the clock transition

We describe Doppler spectroscopy of Bose-Einstein condensates of ytterbium atoms using a narrow optical transition. We address the optical clock transition around 578 nm between the ${}^{1}{S}_{0}$ and the ${}^{3}{P}_{0}$ states with a laser system locked on a high-finesse cavity. We show how the absolute frequency of the cavity modes can be determined within a few tens of kilohertz using high-resolution spectroscopy on molecular iodine. We show that optical spectra reflect the velocity distribution of expanding condensates in free fall or after release inside an optical waveguide. We demonstrate subkilohertz spectral linewidths, with long-term drifts of the resonance frequency well below 1 kHz/h. These results open the way to high-resolution spectroscopy of many-body systems.

Frequency noise processes in a strontium ion optical clock

A recent comparison of the frequencies of a pair of optical clocks based on the 674 nm 2S1/2–2D5/2 optical clock transition in 88Sr+ has highlighted the need to understand factors affecting frequency instability. We have developed statistical models to show that our clock is capable of reaching the quantum projection noise limit; for our clock using 100 ms probe pulses, this is ∼3 × 10−15/√τ. However, this optical clock uses atomic transitions with a linear Zeeman shift, which can lead to a degradation in stability in the presence of magnetic field noise. We show that this generally leads to an increase in white frequency noise, even in cases dominated by magnetic field flicker or random walk noise. By taking into account both the quantum projection and magnetic field noise we are able to explain our observed frequency instabilities. This analysis will relate to any optical clock with a linear Zeeman shift where cancellation of this shift is achieved by interrogating pairs of components. Furthermore, implementing automatic control of lasers and minimization of micromotion requires pausing of the frequency servo occasionally; this leads to only a small degradation of frequency stability.

Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level

Results are presented from a series of comparisons between two independent femtosecond frequency comb systems at NPL, which were carried out in order to assess their systematic uncertainty. Simultaneous measurements with the two systems demonstrate agreement at the level of 5 × 10−18 when measuring an optical frequency against a common microwave reference. When simultaneously measuring the ratio of two optical frequencies, agreement at the 3 × 10−21 level is observed. The results represent the highest reported level of agreement to date between Ti:Sapphire and Er-doped femtosecond combs. The limitations of the combs when operating in these two different manners are discussed, including traceability to the SI second, which can be achieved with an uncertainty below 1 × 10−16. The technical details presented underpin recent absolute frequency measurements of the 88Sr+ and 171Yb+ optical clock transitions at NPL, as well as a frequency ratio measurement between the two optical clock transitions in 171Yb+.

Frequency Ratio of Two Optical Clock Transitions inYb+171and Constraints on the Time Variation of Fundamental Constants

Singly ionized ytterbium, with ultranarrow optical clock transitions at 467 and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of 6×10(-16). Combining our results with those from other experiments, we report a threefold improvement in the constraint on the time variation of the proton-to-electron mass ratio, μ/μ=0.2(1.1)×10(-16) yr(-1), along with an improved constraint on time variation of the fine structure constant, α/α=-0.7(2.1)×10(-17) yr(-1).

A transportable strontium optical lattice clock

We report on a transportable optical clock, based on laser-cooled strontium atoms trapped in an optical lattice. The experimental apparatus is composed of a compact source of ultra-cold strontium atoms including a compact cooling laser setup and a transportable ultra-stable laser for interrogating the optical clock transition. The whole setup (excluding electronics) fits within a volume of <2 m3. The high degree of operation reliability of both systems allowed the spectroscopy of the clock transition to be performed with 10 Hz resolution. We estimate a relative uncertainty of the clock of 7 × 10−15.

Magic wavelengths of the optical clock transition at 877 nm of barium

Magic wavelengths for laser trapping of barium atoms in the optical lattices are investigated while considering the optical clock transition at 877 nm between the 6s21S0 state and 6s5d 1D2 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also discussed and analyzed. Some of these magic wavelengths are selected and recommended for the optical lattice trapping laser.

An Active Ion Optical Clock

We propose a scheme for an active ion optical clock with a detailed description of the pumping method, lasing states, output power, linewidth and light shift. Considering 171Yb+ ions in a Paul trap, we propose utilizing a Fabry—Perot resonator to realize the lasing of active optical frequency standards. The quantum-limited linewidth of an active 171Yb+ ion optical clock is narrower than 1 mHz. Based on the mechanism and the advantages of an active optical clock at the ion optical clock transition frequency, this new laser light source as a stable local oscillator will be beneficial to the single-ion optical clock, which currently is one of the most accurate clocks.

A superradiant clock laser on a magic wavelength optical lattice.

An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Nevertheless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke superradiant linewidth enhancement will broaden the laser line and nearest neighbor couplings will induce shifts and fluctuations of the laser frequency. We estimate the magnitude and scaling of these effects by direct numerical simulations of few atom systems for different geometries and densities. For Strontium in a regularly filled magic wavelength configuration atomic interactions induce small laser frequency shifts only and collective spontaneous emission weakly broadens the laser. These interactions generally enhance the laser sensitivity to cavity length fluctuations but for optimally chosen operating conditions can lead to an improved synchronization of the atomic dipoles.

Absolute frequency measurement of 1S0(F = 1/2)–3P0(F = 1/2) transition of 171Yb atoms in a one-dimensional optical lattice at KRISS

We measured the absolute frequency of the optical clock transition 1S0(F = 1/2)–3P0(F = 1/2) of 171Yb atoms confined in a one-dimensional optical lattice and it was determined to be 518 295 836 590 863.5(8.1) Hz. The frequency was measured against Terrestrial Time (TT; the SI second on the geoid) using an optical frequency comb of which the frequency was phase-locked to an H-maser as a flywheel oscillator traceable to TT. The magic wavelength was also measured as 394 798.48(79) GHz. The results are in good agreement with two previous measurements of other institutes within the specified uncertainty of this work.