High-accuracy calculation of the blackbody radiation shift in the 133Cs primary frequency standard

Long-lived quantum coherent dynamics of a Λ-system driven by a thermal environment

We present a theoretical study of quantum coherent dynamics of a three-level Λ-system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving nonsecular Bloch-Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven Λ-system as underdamped and overdamped depending on whether the ratio Δ/[rf(p)] is greater or less than one, where Δ is the ground-state energy splitting, r is the incoherent pumping rate, and f(p) is a function of the transition dipole alignment parameter p. In the underdamped regime, we observe long-lived coherent dynamics that lasts for τ_c ≃ 1/r, even though the initial state of the Λ-system contains no coherences in the energy basis. In the overdamped regime for p = 1, we observe the emergence of coherent quasi-steady states with the lifetime τ_c = 1.34(r/Δ²), which have a low von Neumann entropy compared to conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He* atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular Λ-systems in the absence of coherent driving.

Experimental Evaluation of the Blackbody Radiation Shift in the Cesium Atomic Fountain Clock

The cesium atomic fountain clock is the world’s most accurate microwave atomic clock. The uncertainty of blackbody radiation (BBR) shift accounts for an increasingly large percentage of the uncertainty associated with fountain clocks and has become a key factor in the performance of fountain clocks. The uncertainty of BBR shift can be reduced by improving the system environment temperature. This study examined the mechanism by which the BBR shift of the transition frequency between the two hyperfine energy levels of the 133Cs ground state is generated and the calculation method for the BBR shift in the atomic fountain. Methods used to reduce the uncertainty of BBR shift were also examined. A fountain system structure with uniform temperature and good heat preservation was designed, and related technologies, such as that for measuring the temperature of the cesium fountain system, were studied. The results of 20 days of measurements, in combination with computer simulation results, showed that the temperature uncertainty of the atomic action zone is 0.12 °C and that the resulting uncertainty of BBR shift is 2.4 × 10−17.

High-Precision Time-Frequency Signal Simultaneous Transfer System via a WDM-Based Fiber Link

In this paper, we demonstrate a wavelength division multiplexing (WDM)-based system for simultaneously delivering ultra-stable optical frequency reference, 10 GHz microwave frequency reference, and a one pulse per second (1 PPS) time signal via a 50 km fiber network. For each signal, a unique noise cancellation technique is used to maintain their precision. After being compensated, the transfer frequency instability in terms of the overlapping Allan deviation (OADEV) for the optical frequency achieves 2 × 10−17/s and scales down to 2 × 10−20/10,000 s, which for the 10 GHz microwave reference, approaches 4 × 10−15/s and decreases to 1.4 × 10−17/10,000 s, and the time uncertainty of the 1 PPS time signal along the system is 2.08 ps. In this scheme, specific channels of WDM are, respectively, occupied for different signals to avoid the possible crosstalk interference effect between the transmitted reference signals. To estimate the performance of the above scheme, which is also demonstrated in this 50 km link independent of these signals, the results are similar to that in the case of simultaneous delivery. This work shows that the WDM-based system is a promising method for building a nationwide time and frequency fiber transfer system with a communication optical network.

High accuracy measurement of the ground-state hyperfine splitting in a ¹¹³Cd⁺ microwave clock

A microwave frequency standard based on laser-cooled (113)Cd(+) ions has been developed in recent years, and the short-term frequency instability is measured to be 6.1×10(-13)/√τ. By comparing the Cd(+) clock to a superior frequency reference, the ground-state hyperfine splitting of (113)Cd(+) is measured precisely to be 15199862855.0192(10) Hz with a fractional precision of 6.6×10(-14). This result is consistent with previous results, and the measurement precision is improved by nearly one order more than the best result reported before.

High-accuracy measurement of the blackbody radiation frequency shift of the ground-state hyperfine transition in 133Cs

We report a high-accuracy direct measurement of the blackbody radiation shift of the 133Cs ground-state hyperfine transition. This frequency shift is one of the largest systematic frequency biases encountered in realizing the current definition of the International System of Units (SI) second. Uncertainty in the blackbody radiation frequency shift correction has led to its being the focus of intense theoretical effort by a variety of research groups. Our experimental measurement of the shift used three primary frequency standards operating at different temperatures. We achieved an uncertainty a factor of five smaller than the previous best direct measurement. These results tend to validate the claimed accuracy of the recently calculated values.

Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions

Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.

Progress in atomic fountains at LNE-SYRTE

We give an overview of the work done with the Laboratoire National de Métrologie et d'Essais-Systèmes de Référence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the (87)Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

"Doubly magic" conditions in magic-wavelength trapping of ultracold alkali-metal atoms

In experiments with trapped atoms, atomic energy levels are shifted by the trapping optical and magnetic fields. Regardless of this strong perturbation, precision spectroscopy may be still carried out using specially crafted, "magic" trapping fields. Finding these conditions for particularly valuable microwave transitions in alkali-metal atoms has so far remained an open challenge. Here I demonstrate that the microwave transitions in alkali-metal atoms may be indeed made impervious to both trapping laser intensity and fluctuations of magnetic fields. I consider driving multiphoton transitions between the clock levels and show that these "doubly magic" conditions are realized at special values of trapping laser wavelengths and fixed values of relatively weak magnetic fields. This finding has implications for precision measurements and quantum information processing with qubits stored in hyperfine manifolds.

Cryogenic fountain development at NIST and INRIM: preliminary characterization

This paper describes the new twin laser-cooled Cs fountain primary frequency standards NIST-F2 and ITCsF2, and presents some of their design features. Most significant is a cryogenic microwave interrogation region which dramatically reduces the blackbody radiation shift. We also present a preliminary accuracy evaluation of IT-CsF2.

Black-body radiation shifts and theoretical contributions to atomic clock research

A review of theoretical calculations of black-body radiation (BBR) shifts in various systems of interest to atomic clock research is presented. Calculations for monovalent systems, such as Ca(+), Sr(+), and Rb are carried out using a relativistic all-order single-double method, where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. A recently developed method for accurate calculations of BBR shifts in divalent atoms such as Sr is discussed. This approach combines the relativistic allorder method and the configuration interaction method. The evaluation of uncertainties in theoretical values of BBR shifts is discussed in detail.

Micromagic clock: microwave clock based on atoms in an engineered optical lattice

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.

Magic frequencies for cesium primary-frequency standard

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.

Accurate optical lattice clock with 87Sr atoms

We report a frequency measurement of the 1S0-3P0 transition of 87Sr atoms in an optical lattice clock. The frequency is determined to be 429 228 004 229 879(5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall. The two previous measurements of this transition were found to disagree by about 2 x 10(-13), i.e., almost 4 times the combined error bar and 4 to 5 orders of magnitude larger than the claimed ultimate accuracy of this new type of clocks. Our measurement is in agreement with one of these two values and essentially resolves this discrepancy.

Frequency shift of the cesium clock transition due to blackbody radiation

We perform ab initio calculations of the frequency shift induced by a static electric field on the cesium clock hyperfine transition. The calculations are used to find the frequency shifts due to blackbody radiation. Our result [deltanu/E2=-2.26(2)x10(-10) Hz/(V/m)2] is in good agreement with early measurements and ab initio calculations performed in other groups. We present arguments against recent claims that the actual value of the effect might be smaller. The difference (approximately 10%) between ab initio and semiempirical calculations is due to the contribution of the continuum spectrum in the sum over intermediate states.