Phase-Locking Lasers of Different Colors with the Transfer-Lock Scheme
The experimental control of a trapped Al+-ion relies on precise control of the frequency of many lasers, but residual environmental (temperature, air pressure, humidity) and intrinsic influences (aging) cause the lasers to drift in frequency. To overcome this problem the lasers must be stabilized by comparing their frequency to a stable reference and correcting the detected fluctuations. This is usually done by transferring the length stability of a cavity or the frequency stability of an atomic resonance to the laser which shall be stabilized. Given one such stabilized laser, other slave lasers at approximately the same wavelength can be locked to it by measuring the frequency difference between lasers using a beat note. However, since the frequency of detectable beat notes is limited to a few GHz, a separate frequency reference and master laser is generally required at each wavelength. For an experiment, such as the Al+ clock, involving over a half-dozen laser wavelengths, this becomes very cumbersome, expensive and time-consuming.
The transfer-lock technique overcomes this problem, since it needs just one master laser for as many slave lasers as you wish. The heart of our transfer-lock setup is a commercially available frequency comb. Frequency-combs are mode-locked pulsed lasers whose spectrum consists of equally-spaced frequency peaks, the comb teeth.
In consequence the frequency of the n-th comb tooth can be written as
fn = fceo + n·frep
where n is an integer and fceo and frep are the offset frequency and the repetition rate. Since the spectrum of a frequency comb covers a wide range of wavelengths, it includes comb teeth near the frequencies of both master and slave lasers. The beat notes between each laser and the corresponding comb tooth can be detected with photodiodes, yielding signals with the following frequencies:
fslave = fceo + nslave · frep - fbeat,slave
fmaster = fceo + nmaster · frep - fbeat,master
In the next step the measured offset frequency is electronically subtracted from slave and master beat with an rf mixer. This also removes the noise of the offset frequency. The noise of the repetition rate scales with the frequency, and thus with the integer index, of the comb tooth, e.g. nslave. In order to get rid of this noise the master beat must be multiplied by the factor
nslave / nmaster
before mixing slave and master beat. This results in a so-called virtual beat
fvirtual = fbeat,slave - fbeat,master · nslave / nmaster
which is independent of the frequency comb parameters and their frequency fluctuations. Finally, a PID controller transforms the virtual beat into a feedback signal which corrects the frequency of the slave laser.