Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancelation at the ten parts per billion level. Theory and empirical measurements can be used at varying levels of precision to determine the magic wavelength where shift cancelation occurs. However, lasers exhibit background spectra from amplified spontaneous emission or other lasing modes that can easily contaminate measurement of the magic wavelength and its reproducibility in other experiments or conditions. Indeed, residual light shifts from laser background have plagued optical lattice clock measurements for years. In this work, we develop a simple theoretical model allowing prediction of light shifts from measured background spectra. We demonstrate good agreement between this model and measurements of the background light shift from an amplified diode laser in a Yb optical lattice clock. Additionally, we model and experimentally characterize the filtering effect of a volume Bragg grating bandpass filter, demonstrating that application of the filter can reduce background light shifts from amplified spontaneous emission well below the ${10}^{\ensuremath{-}18}$ fractional clock frequency level. This demonstration is corroborated by direct clock comparisons between a filtered amplified diode laser and a filtered titanium:sapphire laser.
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancelation at the ten parts per billion level. Theory and empirical measurements can be used at varying levels of precision to determine the magic wavelength where shift cancelation occurs. However, lasers exhibit background spectra from amplified spontaneous emission or other lasing modes that can easily contaminate measurement of the magic wavelength and its reproducibility in other experiments or conditions. Indeed, residual light shifts from laser background have plagued optical lattice clock measurements for years. In this work, we develop a simple theoretical model allowing prediction of light shifts from measured background spectra. We demonstrate good agreement between this model and measurements of the background light shift from an amplified diode laser in a Yb optical lattice clock. Additionally, we model and experimentally characterize the filtering effect of a volume Bragg grating bandpass filter, demonstrating that application of the filter can reduce background light shifts from amplified spontaneous emission well below the 10\ensuremath−18 fractional clock frequency level. This demonstration is corroborated by direct clock comparisons between a filtered amplified diode laser and a filtered titanium:sapphire laser.
Recent assessments have enhanced the evaluation of the lattice ac Stark shift in optical clocks to a fractional frequency level below ${10}^{\ensuremath{-}18}$. With this level of accuracy, meticulous attention is required to address shifts from the background spectrum of the lattice laser. Therefore, it is essential for the lattice laser to exhibit a minimal background spectrum. In this investigation, we employ a system based on sum-frequency generation (SFG) of the fiber-amplified lasers as the source for the strontium optical-clock lattice laser. The spectrum purity of this laser system has been confirmed through a heterodyne measurement involving a titanium:sapphire (Ti:Sa) laser. Consequently, we have characterized the background light shift resulting from its background spectrum, which is more than one order of magnitude lower than that of a tapered amplifier (TA). Through the implementation of carefully selected spectral filtering, the background light shift can be suppressed to a level of mid-${10}^{\ensuremath{-}20}$. Additionally, the suitability of the SFG laser is also experimentally verified in a strontium clock.
Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an ^{171}Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the 10^{-18} level and beyond.
Master thesis in physics at University of Torino. ABSTRACT :Optical lattice clocks occupy a very important position in metrological research. Diffused worldwide, they are a strong candidate for a future redefinition of the second of the International System of Units (SI) and thanks to their extremely small fractional uncertainty about 10−18 they are involved in fundamental physics experiments, for example in the field of general relativity. In a optical clock, the lattice is used to trap ultracold atoms and it is realized with a retro-reflected laser tuned on magic wavelength to reduce perturbations on the clock transition. An optical lattice is generated usually starting by a titanium:sapphire laser: its main qualities are high output power and narrow linewidth, but it is delicate and difficult to use so its application in new kinds of atomic clocks, such as transportable or spacial, is not strongly recommended. Replacing it with an amplified laser diode would be preferable because these instruments are better for cost, reliability, size and weight, so suitable for applications out of laboratory, but at the same time present the problem of spectral purity as they have a not negligible amplified spontaneous emission (ASE): this phenomenon produces a broad spectrum detuned from magic wavelength inducing a perturbation on the clock transition. In my thesis I investigated experimentally the possibility to generate an optical lattice starting from an amplified laser diode emitting at 759.35 nm, ytterbium magic wavelength, and I applied the laser system that I developed on the atomic clock IT-Yb1 at Istituto Nazionale di Ricerca Metrologica (INRiM) located in Torino. The target of this work is to achieve fractional uncertainty due to ASE below 10−18, making the performances of the two different lasers sources equivalent. First, I calculated the theoretical model of the light shift induced by the lattice on the clock transition between ytterbium atomic states 1S0 →3 P0, comparing it with experimental results and I applied it to estimate ASE contribution to lattice shift. In the experimental part of this work I realized an optical system to study amplified laser diode emission and manipulate laser beam to obtain a good lattice from this laser source, filtering ASE with a volume Bragg grating and controlling power with an acousto optic modulator. Moreover I studied ASE spectral distribution in different conditions and its interaction with optical elements. Next studies foresee to measure experimentally with IT-Yb1 the shift induced by the laser system that I realized to calculate its uncertainty contribution and compare this result with the one obtained with a titanium:sapphire laser. This work will be useful to the development of compact or transportable atomic clocks based exclusively on semiconductor lasers with applications in the generation of optical timescales, travelling optical standards and the measurements of Earth gravitational redshift.
State-of-the-art optical clocks based on neutral atoms have already surpassed the world's best microwave atomic clocks in both accuracy and stability, paving the way to high-precision measurements of elementary aspects of nature, like the search for the drift of fundamental constants or the application of relativistic geodesy.These clocks operate with ensembles trapped in an optical lattice.Normally, high-power trapping laser fields induce a large AC Stark shift on the clock's transition frequency, as the clock states have different polarizabilities.A key feature of lattice clocks is the magic wavelength, for which the atomic polarizabilities of the clock states are equal, therefore compensating a differential frequency shift on the clock transition.In the periodic potential of the optical lattice, the energy spectrum of motional states features a band structure, analogous to electrons in a crystalline structure well-known from solid state physics.Within this band structure, atoms can tunnel between adjacent lattice sites.As a consequence from tunneling motion, the clock transition experiences a frequency shift and a broadening, which becomes pronounced in the shallow lattice regime.This work presents the first demonstration of a 24 Mg optical lattice clock including the precise determination of the frequency of the clock transition, its magic wavelength and its second-order Zeeman shift.Furthermore, the effect of tunneling in an optical lattice for magnesium has been extensively studied via optical spectroscopy of Bloch bands and substantiated with theoretical models, that were initially developed for a strontium optical lattice clock.Measuring lattice light induced frequency shifts of the clock transition for various lattice wavelengths and intensities, yielded a value of the magic wavelength of the 1 S 0 → 3 P 0 clock transition in 24 Mg of 468.463(207) nm.This value is in well agreement with a recent theoretical calculation of 468.45(23) nm, using a refined atomic structure model.The experimental value for the magic wavelength was independently verified with optical spectroscopy of Bloch bands carried out on the clock transition.Here, the AC Stark modified band structure is directly probed by a single frequency scan of the carrier resonance, featuring an asymmetric line shape, that is strongly dependent on the lattice wavelength.This technique demonstrates a novel method for the determination of the magic wavelength and could also be applied to other atomic species.In bosonic isotopes of alkaline earth(-like) elements, like 24 Mg, optical dipole excitation of the spin-forbidden 1 S 0 → 3 P 0 clock transition can be enhanced, e.g. by applying an external magnetic field.While these bosons are insensitive to first-order Zeeman shifts, the second-order Zeeman effect displays a dominant contribution to the clock's error budget.In this thesis, the magnetic polarizability β is measured to be -206.6(2.0)MHz/T 2 , consistent with a theoretical calculation, and the clock transition frequency was found to be 655 058 646 691(101) kHz.
After being pumped from the 5 s 1/2 ground state to the 6 p 1/2 state, the population inversion between 6 s 1/2 and 5 p 1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10 −18 .
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.