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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Coherent population trapping with cold atoms

T. Zanon-Willette, Stéphane Guérandel, E. De Clereq, N. Dimareq, Andr  Clairon

Published Jul 8, 2004• 2 citations
Publisher

Abstract

Atomic clocks based on CPT are interesting because of the narrow linewidths achievable at very low intensities. The linewidth of a CPT resonance in a sample of cold atoms mainly depends on the optical saturation by two lasers and the different relaxation terms responsible for destroying the hyperfine coherence. We propose a complete analytical solution for the excited population based on the classical Bloch formalism to determine the line shape of the resonance. Finally we present the future development of a cold atoms clock based on CPT linewidth.

DOI
10.1109/freq.2003.1274985

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Atomic clocks based on CPT are interesting because of the narrow linewidths achievable at very low intensities. The linewidth of a CPT resonance in a sample of cold atoms mainly depends on the optical saturation by two lasers and the different relaxation terms responsible for destroying the hyperfine coherence. We propose a complete analytical solution for the excited population based on the classical Bloch formalism to determine the line shape of the resonance. Finally we present the future development of a cold atoms clock based on CPT linewidth.
We present a coherent population trapping clock system based on laser-cooled 87Rb atoms. The clock consists of a frequency-stabilized CPT interrogation laser and a cooling laser as well as a compact magneto-optical trap, a high-performance microwave synthesizer, and a signal detection system. The resonance signal in the continuous wave regime exhibits an absorption contrast of ∼ 50%. In the Ramsey interrogation method, the linewidth of the central fringe is 31.25 Hz. The system achieves fractional frequency stability of 2.4 × 10 − 11 / τ , which goes down to 1.8 × 10−13 at 20000 s. The results validate that cold atom interrogation can improve the long-term frequency stability of coherent population trapping clocks and holds the potential for developing compact/miniature cold atoms clocks.
An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at <20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two mF=0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5×10-11 τ-1/2(1 s<τ<2000 s). The best stability of 6.4×10-13 is reached at an integration time of τ=2000 s. This stability is sufficient for many high-precision applications. Frequency-shift measurements were made to evaluate the frequency dependencies on the operation parameters.
A compact cold-atom clock based on coherent population trapping (CPT) has been developed. The clock typically demonstrates a short-term fractional frequency stability of 4×10−11/√τ, limited by frequency noise on the interrogation lasers. The clock interrogates a sample of 2×105atoms under free-fall with typical cycle and Ramsey periods of 50 ms and 16 ms, respectively. The largest two systematic frequency shifts that can limit the clock's long-term stability are the light shift and the Doppler shift.
We study the peculiarities of the coherent population trapping (CPT) dark resonance in atomic vapor confined in a finite-size cell. Taking into account the scattering of atoms on anti-relaxation coating of the walls, we analyze the line shape of the CPT resonance in 133 C s depending on various parameters, such as the width of laser radiation spectrum, the type of pumping, and the magnitude of static magnetic field for both lin || lin and l i n ⊥ l i n polarization schemes. We show that for different parameters, the dependence of the line shape on the size of a cell is different, i.e., different factors affect the CPT resonance nonadditively. Thus, in the case when CPT resonance is excited by a narrowband laser, the shape of the resonance weakly depends on the size of a cell due to the laser-induced narrowing effect. We also show that the distortion of the line shape of the CPT resonance caused by nonresonant hyperfine sublevels of atomic excited states is modified with the size of a cell. Our calculation reveals the important role of accounting for the hyperfine and Zeeman structure of atomic levels. We have shown that the contrast of the CPT resonance differs about 5 times from the prediction of the simple three-level Λ model. The obtained results can be used for the optimization of the quantum frequency standards based on the CPT effect. In the final part of the paper, on the basis of the shot noise approximation we estimate the short-term stability of such standards.
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.
Toward the next generations of compact atomic clocks, clocks based on coherent population trapping (CPT) offer a very interesting alternative. Thanks to CPT, a quantum interfering process, this technology has made a decisive step in the miniaturization direction. Fractional frequency stability of 1.5x10-10 at 1 s has been demonstrated in commercial devices of a few cm3. The laboratory prototype presented here intends to explore what could be the ultimate stability of a CPT based device. To do so, an original double-Λ optical scheme and a pulsed interrogation have been implemented in order to get a good compromise between contrast and linewidth. A study of two main sources of noise, the relative intensity and the local oscillator (LO) noise, has been performed. By designing simple solutions, it led to a new fractional frequency limitation lower than 4x10-13 at 1 s integration. Such a performance proves that such a technology could rival with classical ones as double resonance clocks.