![]() In addition, two vibrational levels ( | 0 ⟩ n, | 1 ⟩ n) of a common motional mode of the ions in the trap are shown. ![]() Shown are the clock ground ( S 1 0) and excited ( P 3 0) clock states and an auxiliary metastable state ( P 3 1) together with the logic ion (qubit states | ↓ ⟩ L, | ↑ ⟩ L). Measurement of the frequency of a poorly known optical frequency source (e.g., previously measured at the resolution of a wave meter) can be determined by measuring the heterodyne beat between the frequency source and the frequency comb. Thus, by stabilizing f CEO and f rep to a well-known frequency reference, each comb mode frequency is well known. In this interferometer, one comb mode ν n is frequency doubled and heterodyne beat with the comb mode at twice the frequency ν 2 n. f CEO is given by the frequency of one mode of the comb (e.g., ν n) modulo f rep, and can be measured and stabilized with a f − 2 f interferometer. The relative carrier-envelope phase in the time domain is related to the offset frequency f CEO in the frequency domain. Each tooth in the comb, a particular single-frequency mode, is separated from its neighbor by f rep. ![]() (b) By Fourier transformation to the frequency domain, the corresponding frequency comb spectrum is revealed. Another important degree of freedom is the phase difference between the envelope maximum and the underlying electric field oscillating at the carrier optical frequency. (a) In the time domain, the laser output generates femtosecond pulse-width envelopes separated in time by 1 / f rep.
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