$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
$$\longrightharp{xx}$$,
Measuring and manipulating the quantum state of atoms is at the heart of atomic physics and requires the ability to address specific transitions between atomic electronic states. For example consider rubidium, a typical and much used alkali atom. Here, the wavelength of light coupling the ground and first excited electronic state is ~780 nm (384 THz) and the excited state lifetime due to spontaneous emission is ~26 nsec giving an absorption linewidth of 6 MHz 4. Thus, a light source with frequency stability of at least one part in 108 is required to reliably address this transition.
Before the development of ECDLs, dye lasers and Titanium Sapphire lasers were typically used for atomic physics. These are large, expensive, complex systems that offer optical gain over a large bandwidth and thus can be tuned to overlap an atomic transition. The potential to replace these gain media with a cheap, simple diode laser engineered with a bandgap matching the desired wavelength was recognized in the early 1980s1,2. Simple, easy to build designs which achieve 100 kHz linewidths were well understood and common place by the early 1990s3,5,6. Many different configurations and designs have been demonstrated each with advantages and disadvantages. Probably the most common configurations are the Littrow3,5,7,8 and Littman 9 configurations. This discussion focuses on the simplest, the Littrow configuration shown in Figure 1A.
A number of tuning mechanisms are simultaneously used to achieve a high precision in the laser frequency. Firstly, a diode is required with a bandgap producing sufficient gain at the desired wavelength at an achievable operating temperature. The typical laser diode will have gain over several nanometers (THz). Secondly, a reflective diffraction grating is angle tuned to provide optical feedback into the diode at the desired wavelength. Depending on the grating, the diode, the focusing lens used and their alignment, the grating will select a frequency range of typically 50-100 GHz. The laser will oscillate at a wavelength resonant with the external laser cavity (between the diode rear facet and the grating). Tuning this cavity length across a wavelength allows the laser to be tuned across a free spectral range (c/(2L)) around the grating gain peak where c, is the speed of light and L, is the cavity length, typically 1-5 cm (FSR 3-15 GHz). When two cavity modes are a similar wavelength from the peak grating feedback wavelength the laser may run multimode. As the oscillating cavity mode is tuned further from the gain peak than its neighboring mode the laser will mode hop limiting the tuning range. The behavior of the cavity modes with respect to the grating mode can be seen in Figure 3. The mode hop free tuning range is a key performance metric for an ECDL. By simultaneously tuning the grating angle and the cavity length it is possible to continuously tune across many free spectral ranges without mode hops, making locating and locking to spectral features much easier8. Electronic tuning of the optical path length of the cavity for locking may be achieved by a combination of tuning the grating angle/position using a piezo actuator (Figure 1A) (scanning bandwidth ~1 kHz) and tuning the diode current which primarily modulates the refractive index of the diode (scanning bandwidth ≥100 kHz). Using laser diodes rather than anti-reflection (AR) coated gain chips for the gain medium adds the additional complication of adding the laser diode internal cavity response which may have a typical free spectral range of 100-200 GHz. In this case the cavity must be temperature tuned to match the response from the grating. Using a laser diode rather than an AR coated gain chip will dramatically reduce the mode hop free tuning range unless there is a means to synchronously tune the diode current or temperature. Finally, to achieve a linewidth better than 100 kHz careful attention must be paid to eliminate other noise sources. This requires careful mechanical design of the mounts to minimize acoustic vibration, mK level temperature stabilization, rms current stability of the diode at the ≤30 nA level and careful tuning of the gain of all locking loops10. Selecting the proper electronics for the application is just as important as the laser and optics design. A list of diode controllers and specifications can be found in Table 1.
Once stable lasing has been achieved, the next requirement is to lock the laser frequency to a reference such as an atomic transition, an optical cavity or another laser. This removes the effects of slow drifts such as small temperature fluctuations, essentially eliminating noise for frequencies within the bandwidth of the locking loop. There are a myriad of locking techniques that have been developed for obtaining an error signal, each suited for a particular reference system. An error signal for phase locking two lasers can be obtained by mixing the two lasers on a beam splitter. Pound-Drever hall11 or tilt-locking12 can be used to lock to a cavity. To lock to an atomic absorption line DAVLL13 or saturated absorption spectroscopy3,14 in combination with current modulation10, Zeeman modulation10, or tilt-locking15 may be used.
The locking of an ECDL to a rubidium transition using Zeeman modulation of saturated absorption in a vapor cell will be described here. If a low intensity beam passes through a rubidium vapor cell at room temperature and the frequency is tuned in the vicinity of the 780 nm atomic transition a number of Doppler broadened absorption features ~500 MHz wide will be observed rather than the 6 MHz wide natural linewidth (calculations for natural and Doppler linewidths can be found in Foot16). If, however, this beam is retro reflected, the second pass will have less absorption on resonance as atoms with a zero longitudinal velocity have already been partially excited by the first pass17. Other frequencies will be absorbed by different velocity populations on each pass and therefore absorption will not be saturated. In this way an apparent transmission feature overlaid on the Doppler broadened absorption at transitions with a width about the natural linewidth can be obtained. This provides a sharp absolute frequency reference to lock to. The frequency of the atomic transition may be modulated using the Zeeman effect by dithering the magnitude of a magnetic field in the reference cell. A suitable homogeneous magnetic field may be produced using a solenoid setup as shown in Figure 5. Electronically mixing the modulated waveform with the saturated absorption transmission generates an error signal which can be used to adjust the diode current and integrated to adjust the piezo voltage. Thus, the laser may be locked to the transition without needing to modulate the laser frequency.
The linewidth of an ECDL is generally measured by interfering two frequency locked lasers of the same type on a beam splitter18. The beat frequency between the lasers is then measured using a fast photodiode and an RF spectrum analyzer. The noise spectrum beyond the locking loop bandwidth is then fitted to a Voigt (convolution of a Gaussian and Lorentzian) profile. The noise from the different lasers add in quadrature. In the case of two equivalent lasers this gives a fitted linewidth of √(2) times the single laser linewidth. If a laser is available with a known linewidth significantly smaller than that expected from the ECDL and it is within the tuning range of the ECDL, then that could be used instead. Another method commonly used for measuring linewidth is the delayed self homodyne technique19,20 where part of the beam is sent along an optical delay line such as a fiber and then mixed on a beam splitter with the laser. This technique relies on the delay being longer than the coherence length of the laser under measurement. This works well for noisy lasers but for a 100 kHz linewidth laser the coherence length is around 3 km, which begins to become impractical. Alternatively, an atomic transition in a saturated absorption cell or a Fabry-Perot cavity can be used to provide a frequency reference for laser linewidth measurement. In this system the laser frequency will need to sit at a linear portion of ether a saturated absorption or Fabry-Perot resonance rather than allowed to scan in frequency. By measuring the signal noise on a photo diode and knowing the resonance linewidth, the frequency noise can be found. The lower limit of the linewidth measurement is then limited by the slope of the transmission resonance.
The presence of higher order lasing modes may be checked for by looking at intensity noise at the frequency of the free spectral range using an RF spectrum analyzer or by using a scanning Fabry-Perot or an optical spectrum analyzer with a resolution better than the free spectral range of the ECDL. The coarse tuning range may be measured by measuring the power as a function of wavelength (using a wavemeter, monochromator, or optical spectrum analyzer) while tuning the laser across its limits using the grating. The mode hop free tuning range is generally measured using a scanning Fabry-Perot cavity where a mode hop can be detected as a discontinuous jump in frequency.