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arXiv:0912.4231 · APS

A Compact Microchip-Based Atomic Clock Based on Ultracold Trapped Rb Atoms

Daniel Farkas, Alex A. Zozulya, Dana Z. Anderson

Published Dec 21, 2009• 9 citations
arXivHTMLPDF

Abstract

We propose a compact atomic clock based on ultracold Rb atoms that are magnetically trapped near the surface of an atom microchip. An interrogation scheme that combines electromagnetically-induced transparency (EIT) with Ramsey's method of separated oscillatory fields can achieve atomic shot-noise level performance of 10^{-13}/sqrt(tau) for 10^6 atoms. The EIT signal can be detected with a heterodyne technique that provides noiseless gain; with this technique the optical phase shift of a 100 pW probe beam can be detected at the photon shot-noise level. Numerical calculations of the density matrix equations are used to identify realistic operating parameters at which AC Stark shifts are eliminated. By considering fluctuations in these parameters, we estimate that AC Stark shifts can be canceled to a level better than 2*10^{-14}. An overview of the apparatus is presented with estimates of duty cycle and power consumption.

DOI
10.48550/arxiv.0912.4231

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We propose a compact atomic clock based on ultracold Rb atoms that are magnetically trapped near the surface of an atom microchip. An interrogation scheme that combines electromagnetically-induced transparency (EIT) with Ramsey's method of separated oscillatory fields can achieve atomic shot-noise level performance of 10^{-13}/sqrt(tau) for 10^6 atoms. The EIT signal can be detected with a heterodyne technique that provides noiseless gain; with this technique the optical phase shift of a 100 pW probe beam can be detected at the photon shot-noise level. Numerical calculations of the density matrix equations are used to identify realistic operating parameters at which AC Stark shifts are eliminated. By considering fluctuations in these parameters, we estimate that AC Stark shifts can be canceled to a level better than 2*10^{-14}. An overview of the apparatus is presented with estimates of duty cycle and power consumption.
We present a compact atomic clock interrogating ultracold 87Rb magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5 s Ramsey time. The clock exhibits a fractional frequency stability of 5.8×10−135.8\times 10^{-13}5.8×10−13 at 1 s and is likely to integrate into the 1×10−151\times10^{-15}1×10−15 range in less than a day. A detailed analysis of 7 noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field (5×10−65\times10^{-6}5×10−6 relative fluctuations shot-to-shot) are the main noise sources together with the local oscillator, which is degraded by the 30% duty cycle. The analysis suggests technical improvements to be implemented in a future second generation set-up. The results demonstrate the remarkable degree of technical control that can be reached in an atom chip experiment.
Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in a variety of applications ranging from network synchronization and secure communications to GPS hold-over and inertial navigation. A cold-atom coherent population trapping (CACPT) clock featuring laser-cooled 87RB atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the principal frequency shifts can be controlled and the performance degradation associated with miniaturization can be overcome. In this thesis, research focused on the development of this type of compact atomic clock is presented. To address the low atom numbers obtained in small cold-atom sources, experiments were performed in which an atomic beam was decelerated with bichromatic stimulated laser forces and loaded into a mm-scale magneto-optical trap, increasing the atom number by a factor of 12.5x. A CACPT clock using the high-contrast lin||lin optical interrogation technique was developed and achieved a stability of 7 × 10-13 after one hour of integration. Doppler shifts in the clock are explained using a simple kinematic model and canceled by interrogating the atoms with a counter-propagating CPT configuration. Finally, a thorough characterization of the AC-stark effect in lin||lin CPT was performed. Observed shifts are explained in terms of contributions from coherent CPT-generating couplings and population transfer effects caused by optical pumping from incoherent light. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that reduces clock drift from light shifts to less than 10-14 for the current system.
Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 → 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 − 13 / τ ( s ) -level, with integration time τ in seconds, and a relative accuracy of ∼ 10 − 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than 2×10−172\times10^{-17}2×10−17 is feasible, which is of the same accuracy as the expected best optical atomic clock.
A scheme is investigated for a coherent population trapping (CPT) atomic clock, wherein the polarization of a beam produced by a vertical-cavity surface-emitting laser is converted to an elliptically polarized beam that interacts with alkali atoms, where the CPT signal is extracted by differentially detecting the magneto-optically rotated light within the transmitted beam. The scheme eliminates the spin-polarized trap state of the atoms and the unwanted background signal, and suppresses in the CPT signal the noise converted from the laser noise. This result reveals the promise of this scheme for realizing a compact CPT atomic clock possessing a significantly improved frequency stability compared to current compact CPT atomic clock devices, coupled with similar power consumption, volume, and cost therewith.
We present a demonstration of a cold-atom optical-microwave double resonance (DR) Ramsey clock utilising an additively manufactured loop-gap-resonator cavity and grating magneto-optical trap (GMOT). The use of additive manufacturing allows for complex cavity structures, more difficult to produce with traditional machining techniques, while the GMOT architecture significantly simplifies the optical system required to trap and cool the atomic sample. In the current demonstration a single laser is used to trap < 3 × 106 87Rb atoms, cool them to below 10 µK, optically pump and read-out state populations of the atoms after microwave interrogation. A Ramsey-type interrogation scheme is employed with an empirically evaluated optimum free evolution time of 10 ms, limited by the loss of signal due to atoms falling out of the read-out beam. We demonstrate a short-term stability of < 2×10−11τ−1/2, in reasonable agreement with the predicted short-term stability based on the signal to noise ratio of the measured Ramsey fringes. Excellent field homogeneity of the cavity microwave field is demonstrated though Rabi oscillations, while almost complete optical pumping and good field orientation is evidenced by Zeeman spectroscopy of the ground-state hyperfine energy levels. This work is a novel approach towards more compact and portable cold-atom microwave clocks with significant potential for further miniaturization of the system.