Wideband laser locking to an atomic reference with modulation transfer spectroscopy

Laser frequency stabilization by modulation transfer spectroscopy and balanced detection of molecular iodine for laser cooling of 174Yb

We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (127I2), which is used as a new frequency reference for laser trapping and cooling of 174Yb on the 1S0 - 3P1 transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 ×10-13 at 0.17 s of averaging time.

Magnetic-field enhanced modulation transfer spectroscopy: theory and experiment

We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S_1/2 (F = 1) → 5P_3/2 (F' = 0, 1, and 2) transitions of ⁸⁷Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F' = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F' = 1 transition are also examined.

Laser frequency stabilization via bichromatic Doppler-free spectroscopy of an 87Rb D1 line

We demonstrate a bichromatic Doppler-free spectroscopy of an ⁸⁷RbD₁ line by using a dual-frequency, counterpropagating laser field with orthogonal linear polarizations. A reversed Doppler-free resonance dip is observed in the dual-frequency scheme, and a significant improvement of frequency discrimination curve is acquired due to the coherent population trapping (CPT) effect. The influence of the static magnetic field and laser intensity on the spectroscopy is studied in both single- and dual-frequency schemes. After locking the laser frequency to the ⁸⁷RbD₁ line in the dual-frequency stabilization scheme, the beat note fractional frequency stability is at the level of 7×10^-12 at 1 s integration time. This technique can be used in various applications, such as CPT atomic clocks, laser spectroscopy, quantum optics, and laser-cooling experiments.

Magnetic-enhanced modulation transfer spectroscopy and laser locking for 87Rb repump transition

Locking of a laser frequency to an atomic or molecular resonance line is a key technique in applications of laser spectroscopy and atomic metrology. Modulation transfer spectroscopy (MTS) provides an accurate and stable laser locking method which has been widely used. Normally, the frequency of the MTS signal would drift due to Zeeman shift of the atomic levels and rigorous shielding of stray magnetic field around the vapor cell is required for the accuracy and stability of laser locking. Here on the contrary, by applying a transverse bias magnetic field, we report for the first time observation of a magnetic-enhanced MTS signal on the transition of ⁸⁷Rb D₂-line Fg = 1→ Fe = 0 (close to the repump transition of Fg = 1→ Fe = 2), with signal to noise ratio larger than 100:1. The error signal is immune to the external magnetic fluctuation. Compared to the ordinary MTS scheme, it provides a robust and accurate laser locking approach with more stable long-term performance. This technique can be conveniently applied in areas of laser frequency stabilization, laser manipulation of atoms and precision measurement.

Optimization strategies for modulation transfer spectroscopy applied to laser stabilization

We present a general analysis for determining the optimal modulation parameters for the modulation transfer spectroscopy scheme. The results are universally valid and can be applied to spectroscopy of any atomic species requiring only the knowledge of the effective linewidth Γeff. A signal with optimized slope and amplitude is predicted for a large modulation index M and a modulation frequency comparable to the natural linewidth of the spectroscopic transition. As a result of competing practical considerations, a modulation index in the range of 3 ≤ M ≤ 10 has been identified as optimal. This parameter regime is experimentally accessible with a setup based on an acousto-optic modulator. An optimized signal for spectroscopy of the rubidium D2 line is presented. The signal shape and the dependence on the modulation parameters are in very good agreement with the theoretical description given. An experimental procedure for achieving a strong suppression of residual amplitude modulation is presented. Based on the optimized signal, we demonstrate long-term laser stabilization resulting in a laser linewidth of 150 kHz (16 s average) and a frequency stability of 18 kHz (rms) over 15 hours.

A misaligned magneto-optical trap to enable miniaturized atom chip systems

We describe the application of displaced, or misaligned, beams in a mirror-based magneto-optical trap (MOT) to enable portable and miniaturized atom chip experiments where optical access is limited to a single window. Two different geometries of beam displacement are investigated: a variation on the well-known 'vortex-MOT', and the other a novel 'hybrid-MOT' combining Zeeman-shifted and purely optical scattering force components. The beam geometry is obtained similar to the mirror-MOT, using a planar mirror surface but with a different magnetic field geometry more suited to planar systems. Using these techniques, we have trapped around 6 × 10⁶ and 26 × 10⁶ atoms of ⁸⁵Rb in the vortex-MOT and hybrid-MOT respectively. For the vortex-MOT the atoms are directly cooled well below the Doppler temperature without any additional sub-Doppler cooling stage, whereas the temperature of the hybrid-MOT has been measured slightly above the Doppler temperature limit. In both cases the attained lower temperature ensures the quantum behaviour of the trapped atoms required for the applications of portable quantum sensors and many others.

Compact Rb optical frequency standard with 10-15 stability

We achieved a low-cost and small-sized Rb optical frequency standard based on ⁸⁵Rb 5S_1/2 → 6P_3/2 transition with 10^-15 stability, which is comparable with that of the best 532 nm I₂ optical frequency standards. In this system, we directly lock the 420 nm diode laser on the 5S_1/2 F = 3 → 6P_3/2 F^' = 4 hyperfine transition line without an additional Pound-Drever-Hall pre-locking system. The signal-to-noise-ratio reaches as high as 350 000 when the averaging time is at 1 s. Eventually by the fluctuation of the residual error signal after locking, the preliminary stability of the optical frequency standard reaches 1.2×10^-14/τ, decreasing to 2.1 × 10^-15 at 80 s. It shows potential in stability performance, experimental cost, and system volume compared with the 532 nm I₂ optical frequency standard as a wavelength standard. It also opens a door for the achievement of wavelength standards by using higher excited states of alkalies.

Two Step Excitation in Hot Atomic Sodium Vapor

A two step excitation scheme in hot atomic sodium vapor is experimentally investigated. The observed effects reflect a coupling between the 3²S, 3²P and the 3²D states. We present the relative dependence on detuning of the two utilized lasers around λ = 589 nm and 819 nm. Unlike expected, we achieve a higher detuning dependence of the probe and the coupling laser by a factor of approximately three. The presented work aimed for a Rydberg excitation and quantum light storage. Such schemes are usually implemented with a red laser on the D-line transition and a coupling laser of shorter (typically blue) wavelength. Due to the fact that higher P-Rydberg states are approximately two times higher in energy than the 3²D state, a two photon transition from the atomic excited 3²P state to a Rydberg P state is feasible. This might circumvent laser frequency doubling whereby only two lasers might mediate a three photon process. The scheme of adding three k-vectors allows for electromagnetically induced transparency experiments in which the resulting k-vector can be effectively reduced to zero. By measurements utilizing electric fields and an analysis of the emission spectrum of the atomic vapor, we can exclude the excitation of the P-P two photon transition.

Carrier frequency modulation of an acousto-optic modulator for laser stabilization

The stabilization of lasers to absolute frequency references is a fundamental requirement in several areas of atomic, molecular and optical physics. A range of techniques are available to produce a suitable reference onto which one can 'lock' the laser, many of which depend on the specific internal structure of the reference or are sensitive to laser intensity noise. We present a novel method using the frequency modulation of an acousto-optic modulator's carrier (drive) signal to generate two spatially separated beams, with a frequency difference of only a few MHz. These beams are used to probe a narrow absorption feature and the difference in their detected signals leads to a dispersion-like feature suitable for wavelength stabilization of a diode laser. This simple and versatile method only requires a narrow absorption line and is therefore suitable for both atomic and cavity based stabilization schemes. To demonstrate the suitability of this method we lock an external cavity diode laser near the ⁸⁵Rb 5S_1/2 → 5P_3/2, F = 3 → F' = 4 using sub-Doppler pump probe spectroscopy and also demonstrate excellent agreement between the measured signal and a theoretical model.

Sub-kilohertz laser linewidth narrowing using polarization spectroscopy

We identify several beneficial characteristics of polarization spectroscopy as an absolute atomic reference for frequency stabilization of lasers, and demonstrate sub-kilohertz laser spectral linewidth narrowing using polarization spectroscopy with high-bandwidth feedback. Polarization spectroscopy provides a highly dispersive velocity-selective absolute atomic reference based on frequency-dependent birefringence in an optically pumped atomic gas. The pumping process leads to dominance of the primary closed transition, suppressing closely-spaced subsidiary resonances which reduce the effective capture range for conventional atomic references. The locking signal is based on subtraction of two orthogonal polarization signals, reducing the effect of laser intensity noise to the shot noise limit. We measure noise-limited servo bandwidth comparable to that of a high-finesse optical cavity without the frequency limit or complexity imposed by optical modulation normally associated with high bandwidth laser frequency stabilization. We demonstrate narrowing to 600±100 Hz laser linewidth using the beatnote between two similarly locked external cavity diode lasers.

Modulation transfer spectroscopy in a lithium atomic vapor cell

We have investigated modulation transfer spectroscopy of D₂ transitions of ⁷Li atoms in a vapor cell. The role of the intensity of the probe beam in the spectrum is important, we have seen unique characteristics of the signal in the crossover peak. In order to find the best signal for laser locking, the slope and frequency offset of the zero-crossing signal are determined. The dependence of the modulation transfer spectra on polarizations of pump and probe beam is demonstrated. The residual amplitude modulation in the system is also considered, and the distortion of the spectra due to the modulation is analyzed. It was found that the crossover peak is more suitable for frequency stabilization due to its better residual amplitude modulation compensation.

Modulation transfer spectroscopy mediated by spontaneous emission

We report the polarization dependence of the spectrum in modulation transfer spectroscopy for the transitions from the lower ground state (F(g) = 1) of (87)Rb atoms. We measured the spectra for the two polarization configurations where the carrier and probe beams were linearly polarized in parallel or perpendicular directions. The measured spectra were in excellent agreement with calculated results. The spectra were strongly dependent on the polarization configurations. In particular, the signal for parallel polarization configuration was generated via an incoherent process mediated by spontaneous emission.