Ramsey Spectroscopy with Displaced Frequency Jumps.

Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.

Dynamic regime of coherent population trapping and optimization of frequency modulation parameters in atomic clocks.

We theoretically investigate the dynamic regime of coherent population trapping (CPT) in the presence of frequency modulation (FM). We have formulated the criteria for quasi-stationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by this FM. Using the density matrix formalism for Λ system, the error signal is exactly calculated and optimized. It is shown that the optimal FM parameters correspond to the dynamic regime of atomic-field interaction, which significantly differs from conventional description of CPT resonances in the frame of quasi-stationary approach (under small modulation frequency). Obtained theoretical results are in good qualitative agreement with different experiments. Also we have found CPT-analogue of Pound-Driver-Hall regime of frequency stabilization.

Magnetic-dipole transitions in highly charged ions as a basis of ultraprecise optical clocks.

We evaluate the feasibility of using magnetic-dipole (M1) transitions in highly charged ions as a basis of an optical atomic clockwork of exceptional accuracy. We consider a range of possibilities, including M1 transitions between clock levels of the same fine-structure and hyperfine-structure manifolds. In highly charged ions these transitions lie in the optical part of the spectra and can be probed with lasers. The most direct advantage of our proposal comes from the low degeneracy of clock levels and the simplicity of atomic structure in combination with negligible quadrupolar shift. We demonstrate that such clocks can have projected fractional accuracies below the 10^{-20}-10^{-21} level for all common systematic effects, such as blackbody radiation, Zeeman, ac-Stark, and quadrupolar shifts.

Generalized Ramsey excitation scheme with suppressed light shift.

We experimentally investigate a recently proposed optical excitation scheme V. I. Yudin et al. [Phys. Rev. A 82, 011804(R) (2010)] that is a generalization of Ramsey's method of separated oscillatory fields and consists of a sequence of three excitation pulses. The pulse sequence is tailored to produce a resonance signal that is immune to the light shift and other shifts of the transition frequency that are correlated with the interaction with the probe field. We investigate the scheme using a single trapped ^{171}Yb^{+} ion and excite the highly forbidden (2)S(1/2) - (2)F(7/2) electric-octupole transition under conditions where the light shift is much larger than the excitation linewidth, which is in the hertz range. The experiments demonstrate a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations.

Atomic clocks with suppressed blackbody radiation shift.

We develop a concept of atomic clocks where the blackbody radiation shift and its fluctuations can be suppressed by 1-3 orders of magnitude independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies ν1 and ν2) which are exposed to the same thermal environment, there exists a "synthetic" frequency ν(syn) ∝ (ν1 - ε12ν2) largely immune to the blackbody radiation shift. For example, in the case of 171Yb+ it is possible to create a synthetic-frequency-based clock in which the fractional blackbody radiation shift can be suppressed to the level of 10(-18) in a broad interval near room temperature (300±15 K). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies ν1 and ν2, where the frequency ν(syn) is generated as one of the components of the comb spectrum.

Frequency shifts in an optical lattice clock due to magnetic-dipole and electric-quadrupole transitions.

We report a hitherto undiscovered frequency shift for forbidden J = 0-->J = 0 clock transitions excited in atoms confined to an optical lattice. These shifts result from magnetic-dipole and electric-quadrupole transitions, which have a spatial dependence in an optical lattice that differs from that of the stronger electric-dipole transitions. In combination with the residual translational motion of atoms in an optical lattice, this spatial mismatch leads to a frequency shift via differential energy level spacing in the lattice wells for ground state and excited state atoms. We estimate that this effect could lead to fractional frequency shifts as large as 10(-16), which might prevent lattice-based optical clocks from reaching their predicted performance levels. Moreover, these effects could shift the magic wavelength in lattice clocks in three dimensions by as much as 100 MHz, depending on the lattice configuration.

Optical lattice induced light shifts in an yb atomic clock.

We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).

Optical lattice polarization effects on hyperpolarizability of atomic clock transitions.

The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, J = 0 --> J = 0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.

Experimental preparation of pure superposition states of atoms via elliptically polarized bichromatic radiation.

We propose a simple and effective way of creating pure dark superposition states. The generation of pure states is carried out by using bichromatic radiation with controllable polarization ellipticity. We experimentally confirm analytic formulas for polarization ellipticity to obtain m-m pure dark states in the system of Zeeman sublevels of alkali atoms. For 87Rb we experimentally accumulated 60% of the atoms in the 0-0 dark state and 50% into the (+/-1) - (+/-1) dark states.

Magnetic field-induced spectroscopy of forbidden optical transitions with application to lattice-based optical atomic clocks.

We develop a method of spectroscopy that uses a weak static magnetic field to enable direct optical excitation of forbidden electric-dipole transitions that are otherwise prohibitively weak. The power of this scheme is demonstrated using the important application of optical atomic clocks based on neutral atoms confined to an optical lattice. The simple experimental implementation of this method--a single clock laser combined with a dc magnetic field--relaxes stringent requirements in current lattice-based clocks (e.g., magnetic field shielding and light polarization), and could therefore expedite the realization of the extraordinary performance level predicted for these clocks. We estimate that a clock using alkaline-earth-like atoms such as Yb could achieve a fractional frequency uncertainty of well below 10(-17) for the metrologically preferred even isotopes.

Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice.

We report direct single-laser excitation of the strictly forbidden (6s2)1S0 <--> (6s6p)3P0 clock transition in 174Yb atoms confined to a 1D optical lattice. A small (approximately 1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FWHM) with high contrast were observed, demonstrating a resonance quality factor of 2.6 x 10(13). The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35 +/- 0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks and can create new clock possibilities in other alkaline-earth-like atoms such as Mg and Ca.