Delivering pulsed and phase stable light to atoms of an optical clock

Abstract

In optical clocks, transitions of ions or neutral atoms are interrogated using pulsed ultra-narrow laser fields. Systematic phase chirps of the laser or changes of the optical path length during the measurement cause a shift of the frequency seen by the interrogated atoms. While the stabilization of cw-optical links is now a well-established technique even on long distances, phase stable links for pulsed light pose additional challenges and have not been demonstrated so far. In addition to possible temperature or pressure drift of the laboratory, which may lead to a Doppler shift by steadily changing the optical path length, the pulsing of the clock laser light calls for short settling times of stabilization locks. Our optical path length stabilization uses retro-reflected light from a mirror that is fixed with respect to the interrogated atoms and synthetic signals during the dark time. Length changes and frequency chirps are compensated for by the switching AOM. For our strontium optical lattice clock, we have ensured that the shift introduced by the fiber link including the pulsing acoustooptic modulator is below 2×10^-17.

Appendices

Appendix A: Clock operation requirements

The narrow linewidth of the clock laser light is obtained by a lock of the master laser to an ultra-low expansion glass (ULE) reference cavity (see Fig. 2). A double pass AOM allows for a frequency offset between laser light and cavity mode. A polarization maintaining fiber is used between this AOM and the cavity. The lock to a TEM₀₀ mode of the cavity is done with a Pound–Drever–Hall method, which uses a 14 MHz electro optical modulator (EOM) to create sidebands. The obtained servo signal is fed back to the current of the master diode and at low frequencies to the piezo of the grating for long-term corrections.

As for most ULE cavities, the length of the reference cavity is shrinking slowly [19]. In our case, the frequency drift is around 30 mHz/s. To ensure that the laser keeps the same frequency while staying locked to the cavity, we apply a ramp to the frequency offset AOM. In order to lock the laser to the atomic reference, we also apply frequency corrections to the AOM, which are determined by the control PC. We use a home built frequency generator for the drift (see Appendix B.1) and a synthesizer for the corrections. The AOM is driven with the sum frequency of these two sources, which is obtained from a mixer as indicated in Fig. 2.

To operate the optical clocks, i.e. to servo the laser to the line center of the reference transition, the line is probed at the half maximum points. Because of hyperfine structure in ⁸⁷Sr the clock transition is split into several Zeeman components and the laser needs to be locked to the average of the two extreme Zeeman components [11]. A Zeeman component and the side of the fringe is addressed through altering the frequency at the end of the fiber link by changing the reference frequency of the noise cancellation. This frequency shift of few kHz is applied by the switching AOM, thus the laser itself runs all the time at the same frequency, which is beneficial for the frequency counting or frequency comparison with the frequency comb. Before the actual clock interrogation, a clock laser pulse excites the atoms to a specific m _F state of the ³P₀. During this preparation π-pulse the magnetic field is higher than during the clock laser interrogation in order to split the hyperfine transitions more, which allows spectrally resolving the hyperfine structure even with shorter pulse duration. The frequency driving the switching AOM is altered accordingly within a clock cycle to account for the different magnetic field. After the preparation pulse, undesired atoms in the ¹S₀ level are removed with resonant light and the magnetic field is reduced before the clock laser pulse starts.

Appendix B: Frequency generation

Throughout the experiments, various radio frequencies are generated and sent to AOMs. We have combined a DDS chip (Analog Devices AD9956 [20]) with a micro-controller (Atmel ATmega644) and created a versatile rf source. This source may operate in different modes: firstly, creating a ramp in the frequency, secondly, phase coherent switching of frequency and phase, and thirdly, a mode that allows for using it as a VCO that can be controlled via a phase detector. These modes are discussed in more detail below. The micro-controller is controlled from a PC by a USB interface, which is provided by an on-board USB to RS-232 interface. A set of commands is supported to process requests.

The clock signal of the DDS chip is provided by a low phase noise 400 MHz VCO (Vectron VS-500). Its output signal can be phase locked to a reference with a phase detector and a frequency divider, both provided by the DDS chip. For the first two modes, we lock the 400 MHz VCO to an external 100 MHz reference.

This phase locked loop (PLL) has a unity gain bandwidth of 15 kHz, above which the phase noise is determined by the phase noise of the VCO. For a carrier frequency of 100 MHz, the phase noise at f=15 kHz is at -100 dBc and falls off quickly toward higher frequencies. Below that point, the system inherits the phase noise of the reference and adds inherent noise. In the range 10 Hz <f< 15 kHz, the inherent noise decreases from -90 dBc at 10 Hz approximately as f ^-1. For even lower frequencies, the inherent noise remains constant at -90 dBc.

2.1 B.1 Frequency ramp

The generation of a frequency ramp with a AD9956 is one if its on-chip features. But the resolution of the sweep rate is too coarse for a cavity drift compensation. We therefore generate the frequency ramp of our rf source by changing the output frequency of the DDS by the micro-controller at a rate of about 100 Hz while maintaining the phase coherence. The frequency resolution of the DDS is 48-bit, i.e. 1.4 μHz, while the phase resolution is 14-bit. The sole input to the micro-controller is the start frequency and the rate of the frequency ramp. The micro-controller also allows for the read-out of the instantaneous frequency via the USB link. A frequency generator running in this mode is used to compensate for the linear drift of the reference cavity of the laser via an AOM.

2.2 B.2 Frequency switch

The DDS chip keeps eight profiles with pairs of frequency and phase offset. One may select one of these profiles by three TTL signals. When switching between profiles, the phase is altered by the difference between the two phase offsets and the frequency is changed. If the phase offsets are the same, the frequency switches while the phase of the output remains continuous. In this mode, the micro-controller is used to set the values of the frequencies and phase offsets via the USB port. The selection of the profile (frequency and phase) is done purely by the TTL signals, which allows for μs timing. In our experiment, this mode is used to quickly alter the clock lasers frequency, i.e. between preparation and clock pulse or—less time critical—for addressing the Zeeman components.

2.3 B.3 External phase lock

This mode is used for the rf source driving the AOM of the optical path length stabilization as described in this work. It uses the phase detector and divider stages of the AD9956 to generate a signal that is fed to the tuning input of the 400 MHz VCO. In this mode, the input to the phase detector are two external signals. In our case of the path length stabilization, these are the beat note and the rf reference. The pull range of the VCO is ±5×10^-5, which allows to detune the AOM frequency of 80 MHz by several kHz.

Appendix C: Hyper Ramsey

A method to compensate shifts introduced by the interrogation pulses is the application of a hyper Ramsey scheme [22], where a 3π/2 pulse is used as the second interaction pulse. Similar to this scheme, we propose an interrogation scheme with one π/2 pulse in beginning and, after a long dark time, three individual π/2 pulses. Two short dark times between the three pulses reset the optical path length stabilization to have a similar phase chirp in all four pulses. This sequence has a phase sensitivity function (see Fig. 9) that may help to reduce the influence of the observed phase excursions and the investigated slow phase drifts. If one assumes that the phase behaves exactly the same for each of the four pulses their effects cancel as the integral of the product of phase sensitivity function and assumed phase excursion is zero. The effect from the first pulse is canceled by the third and the second is canceled by the fourth pulse.

Fig. 9

Frequency and phase sensitivity for a hyper Ramsey like excitation scheme. The dark time in this scheme needs to be longer than in a Ramsey scheme to obtain the same sensitivity. This is due to the sign change in g(t) between the second and the third pulse: the additional pulses reduce the sensitivity of a Ramsey scheme (first two pulses only) but allow for an automatic compensation of effects related to the activation of the optical path length stabilization