The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

Resonant nonlinear magneto-optical effects in atoms

The synthesis of optical frequencies from the primary cesium microwave standard has traditionally been a difficult problem due to the large disparity in frequency. Recently this field has been dramatically advanced by the introduction and use of mode-locked lasers. This application of mode-locked lasers has been particularly aided by the ability to generate mode-locked spectra that span an octave. This review article describes how mode-locked lasers are used for optical frequency synthesis and gives recent results obtained using them.

/pdf/optical-frequency-synthesis-based-on-mode-locked-lasers-2mdp2gsl1s.pdf

Optical Frequency Synthesis Based on Mode- Locked Lasers

The merging of continuous wave laser-based precision optical-frequency metrology with mode-locked ultrafast lasers has led to precision control of the visible and near-infrared frequency spectrum produced by mode-locked lasers. Such a phase-controlled mode-locked laser forms the foundation of a "femtosecond optical-frequency comb generator" with a regular comb of sharp lines with well-defined frequencies. For a comb with sufficiently broad bandwidth, it is now straightforward to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical-frequency metrology, synthesis, and optical atomic clocks. Precision femtosecond optical-frequency combs also have a major impact on time-domain applications, including carrier-envelope phase stabilization, synthesis of a single pulse from two independent lasers, nonlinear spectroscopy, and passive amplifiers based on empty external optical cavities. The authors first review the frequency-domain description of a mode-locked laser and the connection between the carrier-envelope phase and the frequency spectrum to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical-frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by discussions of time-domain experiments.

/pdf/optical-frequency-combs-from-frequency-metrology-to-optical-eozl6eyh01.pdf

Optical frequency combs: from frequency metrology to optical phase control

Many-particle entangled states and entanglement between continuous properties are valuable resources for quantum information, but are notoriously difficult to generate. An experiment now entangles the energy and emission times of three photons, creating generalized Einstein–Podolsky–Rosen correlations.

Three-photon energy-time entanglement

We review the techniques used in the design and construction of cryogenic sapphire oscillators at the University of Western Australia over the 18year history of the project. We describe the project from its beginnings when sapphire oscillators were first developed as low-noise transducers for gravitational wave detection. Specifically, we describe the techniques that were applied to the construction of an interrogation oscillator for the PHARAO Cs atomic clock in CNES, in Toulouse France, and to the 2006 construction of four high performance oscillators for use at NMIJ and NICT, in Japan, as well as a permanent secondary frequency standard for the laboratory at UWA. Fractional-frequency fluctuations below 6×10−16 at integration times between 10 and 200s have been repeatedly achieved.

/pdf/invited-article-design-techniques-and-noise-properties-of-4nz214jyyz.pdf

Invited Article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators

The frequencies of AlGaAs laser diodes were stabilized to the F=4→F'=5 component of the Cs-D2 line with the Zeeman modulation method, in which the laser frequency remains unmodulated. Allan variance measurements were made on the beat note between two laser diodes thus stabilized and a frequency stability of 2.4×10-10 was obtained at an averaging time of 1s. By changing the dc magnetic field applied to the Cs cell, the frequency of the laser diodes could be tuned almost linearly in the range of -180 MHz to 180 MHz.

Frequency Stabilization of Laser Diodes to the Cs-D 2 Line with the Zeeman Modulation Method

Phase-locked 3:1 division of an optical frequency was achieved with a continuous-wave monolithic optical parametric oscillator (OPO) pumped by a 532-nm Nd:YAG laser, by use of 5% MgO-doped LiNbO3 as a nonlinear optical crystal. The OPO generated signal light (798 nm) with 4-mW power and idler light (1596 nm) with 3-mW power for a pump power of 68 mW.?Approximately 2 µW of second harmonics (SH’s) of the idler light was produced by external-cavity-enhanced SH generation by use of a periodically poled LiNbO3 crystal. The beat signal between the signal light and the SH of the idler light was observed with a signal-to-noise ratio of 40 dB at a 10-kHz bandwidth and was successfully phase locked to a signal from a synthesizer through the electro-optic effect of the crystal.

Phase-coherent optical frequency division by 3 of 532-nm laser light with a continuous-wave optical parametric oscillator.

Ultra-high short-term frequency stability has been realized in microwave oscillators based on liquid helium cooled sapphire resonators which operate on the same Whispering Gallery mode. Two cryogenic sapphire oscillators were built to evaluate their stability at short averaging times. These oscillators exhibited a fractional frequency stability of 1.1×10-15 at an averaging time of 1 s, which is more than 100 times better than that of a hydrogen maser. For averaging times between 2 and 640 s the measured oscillator fractional frequency instability was below 10-15 with a minimum of 5.5×10-16 at an averaging time of 20 s. The noise floors of the control servos which contribute to the short-term frequency stability are also discussed.

https://iopscience.iop.org/article/10.1143/JJAP.45.9234/pdf

Shin-ichi Ohshima

Papers

Frequency Stabilization of Laser Diodes to the Cs-D 2 Line with the Zeeman Modulation Method

Phase-coherent optical frequency division by 3 of 532-nm laser light with a continuous-wave optical parametric oscillator.

Short Term Frequency Stability Tests of Two Cryogenic Sapphire Oscillators

Accuracy of an optical parametric oscillator as an optical frequency divider

Long-term, mode-hop-free operation of a continuous-wave, doubly resonant, monolithic optical parametric oscillator