Fig. 1. Schematic setup of the waveform generation system. The spectrum of the optical waveform is illustrated at each stage of the amplified modulation. (a) Schematic diagram of fEOM modulation and first optical filtering. CW laser from ECDL is modulated by fEOM with a programmable microwave signal. The fEOM output is collimated into a suitable size and filtered by grating diffraction before being coupled into a single-mode fiber. (b) High-gain optical amplification. TSA₁ is seeded from the side port of an optical isolator for double-pass amplification. Optional Filter₂ serves to remove the optical carrier from the final output. ECDL, external cavity diode laser; OI, optical isolator; PBS, polarization beamsplitter; BS, beamsplitter.

Fig. 2. Characterization of chirped pulses from TSA₂ output without Filter₂. The frequency sweep range Δf is 1 GHz and 4 GHz for data in (a) and (b), respectively. The heterodyning beat notes are given in (i), from which we derive the (ii) spectrogram and (iv) in-phase quadrature Re(E₋₁). As in (iii), due to the self-balanced amplification, the total output power stays approximately unchanged, with a fractional deviation <15% during the full-pulse modulation.

Fig. 3. Accurate phase modulation of TSA₂ output. The heterodyning beat notes in (a) are digitally demodulated as described in the text to obtain the time-dependent phase ϕ(t) in (b). The complex data is presented in (c) the phasor diagram.

Fig. 4. (a) Level diagram and cooling related transitions on the ⁸⁷Rb (left) and ⁸⁵Rb (right) D2 line. (b) Spectragraphs derived from heterodyning beat notes of interleaved nanosecond pulses with τ = 5 ns (left) and τ = 50 ns (right) on log-scale. Fluorescence counts versus τ for ⁸⁵Rb and ⁸⁷Rb are shown in (c) and (d), respectively. Red arrows mark the expected location of τ, where multiple square pulses with T_rep = 2τ period and coherent phases resonantly drive hyperfine depumping transitions to degrade the MOT performance.