We consider microwave hyperfine transitions in the ground state of cesium and rubidium atoms which are presently used as the primary and the secondary frequency standards. The atoms are confined in an optical lattice generated by a circularly polarized laser field. We demonstrate that applying an external magnetic field with appropriately chosen direction may cancel dynamic Stark frequency shift making the frequency of the clock transition insensitive to the strengths of both the laser and the magnetic fields. This can be attained for practically any laser frequency which is sufficiently distant from a resonance.
We consider microwave hyperfine transitions in the ground state of cesium and rubidium atoms which are presently used as the primary and the secondary frequency standards. The atoms are confined in an optical lattice generated by a circularly polarized laser field. We demonstrate that applying an external magnetic field with appropriately chosen direction may cancel dynamic Stark frequency shift making the frequency of the clock transition insensitive to the strengths of both the laser and the magnetic fields. This can be attained for practically any laser frequency which is sufficiently distant from a resonance.
We propose a new class of atomic microwave clocks based on the hyperfine transitions in the ground state of aluminum or gallium atoms trapped in optical lattices. For such elements magic wavelengths exist at which both levels of the hyperfine doublet are shifted at the same rate by the lattice laser field, cancelling its effect on the clock transition. A similar mechanism for the magic wavelengths may work in microwave hyperfine transitions in other atoms which have the fine-structure multiplets in the ground state.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb atoms. Recent progress in metrology exploits so-called “magic wavelengths,” whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87Rb atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.
Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias B field along a circularly polarized trapping laser field. We map out these B fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.
The evolution of the populations of the magnetic sublevels of the cesium atom (133Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F g = 3 ↔ F e = 2, 3 and F f = 4 ↔ F e = 3, 4 of lines D1 (62S1/2 → 62P1/2) and D2 (62S1/2 → 62P3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 62S1/2F g = 3 M = 0 of the “clock” microwave transition F g = 3 M = 0 ↔ F f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.
The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10−^16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements. The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10^−16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements.