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Register a new userBroadband, unpolarized repumping and clearout light sources for Sr$^+$ single-ion clocks
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Future transportable optical clocks require compact and reliable light sources. Here, broadband, unpolarized repumper and state clearout sources for Sr+ single-ion optical clocks are reported. These turn-key devices require no frequency stabilization nor external modulators. They are fiber based, inexpensive, and compact. Key characteristics for clock operation are presented, including optical spectra, induced light shifts and required extinction ratios. Tests with an operating single-ion standard show a clearout efficiency of 100%. Compared to a laser-based repumper, the achievable fluorescence rates for ion detection are a few tens of per cent lower. The resulting ion kinetic temperature is 1--1.5 mK, near the Doppler limit of the ion system. Similar repumper light sources could be made for Ca+ (866 nm) and Ba+ (650 nm) using semiconductor gain media.
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Many ion species commonly used for laser-cooled ion trapping studies have a low-lying metastable 2D3/2 state that can become populated due to spontaneous emission from the 2P1/2 excited state. This requires a repumper laser to maintain the ion in the Doppler cooling cycle. Typically the 2D3/2 state, or some of its hyperfine components if the ion has nuclear spin, has a higher multiplicity than the upper state of the repumping transition. This can lead to dark states, which have to be destabilized by an external magnetic field or by modulating the polarization of the repumper laser. We propose using unpolarized, incoherent amplified spontaneous emission (ASE) to drive the repumping transition. An ASE source offers several advantages compared to a laser. It prevents the buildup of dark states without external polarization modulation even in zero magnetic field, it can drive multiple hyperfine transitions simultaneously, and it requires no frequency stabilization. These features make it very compact and robust, which is essential for the development of practical, transportable optical ion clocks. We construct a theoretical model for the ASE radiation, including the possibility of the source being partially polarized. Using 88Sr+ as an example, the performance of the ASE source compared to a single-mode laser is analyzed by numerically solving the eight-level density matrix equations for the involved energy levels. Finally a reduced three-level system is derived, yielding a simple formula for the excited state population and scattering rate, which can be used to optimize the experimental parameters. The required ASE power spectral density can be obtained with current technology.
A frequency-stable, broadband laser is presented for experiments on trapped ions. Since the design is based on widely available semiconductor optical amplifier technology, similar lasers can be realized for virtually any wavelength in the near-infrared, and the coherence properties and output power allow for efficient second harmonic generation. No closed-loop frequency stabilization for addressing Doppler- or naturally-broadened, dipole-allowed transitions is needed, and the light source can be turned on and off during a measurement cycle with sub-microsecond response time. As a case study, a 921.7-nm laser with an output power of 20mW and a linewidth of 10GHz is realized, which is then frequency doubled to 460.9nm for excitation of strontium as the first step in photo-ionization. The excitation efficiency is compared to that achievable with a narrow-linewidth distributed Bragg reflector laser as well as to theory.
The uncertainty of the ac Stark shift due to thermal radiation represents a major contribution to the systematic uncertainty budget of state-of-the-art optical atomic clocks. In the case of optical clocks based on trapped ions, the thermal behavior of the rf-driven ion trap must be precisely known. This determination is even more difficult when scalable linear ion traps are used. Such traps enable a more advanced control of multiple ions and have become a platform for new applications in quantum metrology, simulation and computation. Nevertheless, their complex structure makes it more difficult to precisely determine its temperature in operation and thus the related systematic uncertainty. We present here scalable linear ion traps for optical clocks, which exhibit very low temperature rise under operation. We use a finite-element model refined with experimental measurements to determine the thermal distribution in the ion trap and the temperature at the position of the ions. The trap temperature is investigated at different rf-drive frequencies and amplitudes with an infrared camera and integrated temperature sensors. We show that for typical trapping parameters for $mathrm{In}^{+}$, $mathrm{Al}^{+}$, $mathrm{Lu}^{+}$, $mathrm{Ca}^{+}$, $mathrm{Sr}^{+}$ or $mathrm{Yb}^{+}$ ions, the temperature rise at the position of the ions resulting from rf heating of the trap stays below 700 mK and can be controlled with an uncertainty on the order of a few 100 mK maximum.
Optical frequency comparison of the 40Ca+ clock transition u_{Ca} (2S1/2-2D5/2, 729nm) against the 87Sr optical lattice clock transition u_{Sr}(1S0-3P0, 698nm) has resulted in a frequency ratio u_{Ca} / u_{Sr} = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio u_{Ca} / u_{Sr} to reach 1x10-15 in only 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of u_{Ca} using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We report the absolute frequency of ^{40}Ca+ with a systematic uncertainty 14 times smaller than our previous measurement [1].
Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S_{1/2} and 5D_{3/2} states to 0.1% precision. We find R = Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{S,D} are the light shifts of the m = +/- 1/2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.
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