Extremely sensitive readout of a stable "etalon of length" is achieved with laser frequency-locking techniques. Rotation of the entire electro-optical system maps any cosmic directional anisotropy of space into a corresponding frequency variation. We found a fractional length change $\frac{\ensuremath{\Delta}l}{l}=(1.5\ifmmode\pm\else\textpm\fi{}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, with the expected ${P}_{2}(cos\ensuremath{\theta})$ signature. This null result represents a 4000-fold improvement on the best previous measurement of Jaseja et al.

Improved laser test of the isotropy of space

Frequency combs are optical spectra composed of a set of discrete equally spaced lines. Such spectra can be generated by diverse sources such as mode-locked lasers, resonators, or electro-optic modulators. This last possibility has shown a growing interest in the recent years for its advantageous features in providing high repetition rates, intrinsic mutual coherence, or high power per comb lines. Moreover, applications of electro-optic modulator-based combs have flourished in fundamental physics, spectroscopy, or instrumental calibrations. In this paper, we present the most recent progresses made on frequency combs generated by electro-optic modulators, along with the applications where these combs have shown a particular interest.

Electro-optic frequency combs

Active control and cancellation of residual amplitude modulation (RAM) in phase modulation of an optical carrier is one of the key technologies for achieving the ultimate stability of a laser locked to an ultrastable optical cavity. Furthermore, such techniques are versatile tools in various frequency modulation-based spectroscopy applications. In this Letter we report a simple and robust approach to actively stabilize RAM in an optical phase modulation process. We employ a waveguide-based electro-optic modulator (EOM) to provide phase modulation and implement an active servo with both DC electric field and temperature feedback onto the EOM to cancel both the in-phase and quadrature components of the RAM. This technique allows RAM control on the parts-per-million level where RAM-induced frequency instability is comparable to or lower than the fundamental thermal noise limit of the best available optical cavities.

Reduction of residual amplitude modulation to 1 × 10^-6 for frequency modulation and laser stabilization

Bureau International des Poids et Mesures, Pavillon de Breteuil, 92312 S`evres Cedex, France(Dated: February 6, 2008)We present new results from our test of Lorentz invariance, which compares two orthogonalcryogenic sapphire microwave oscillators rotating in the lab. We have now acquired over 1 yearof data, allowing us to avoid the short data set approximation (less than 1 year) that assumesno cancelation occurs between the ˜κ

Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic

We report on a theoretical study and experimental characterization of coherent-population-trapping (CPT) resonances in buffer-gas-filled vapor cells with push-pull optical pumping (PPOP) on Cs ${D}_{1}$ line. We point out that the push-pull interaction scheme is identical to the so-called $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ polarization scheme. Expressions of the relevant dark states, as well as of absorption, are reported. The experimental setup is based on the combination of a distributed feedback diode laser, a pigtailed intensity Mach-Zehnder electro-optic modulator (MZ EOM) for optical sideband generation and a Michelson-like interferometer. A microwave technique to stabilize the transfer function operating point of the MZ EOM is implemented for proper operation. A CPT resonance contrast as high as 78$%$ is reported in a cm-scale cell for the magnetic-field-insensitive clock transition. The impact of the laser intensity on the CPT-clock signal key parameters (linewidth, contrast, linewidth/contrast ratio) is reported for three different cells with various dimensions and buffer-gas contents. The potential of the PPOP technique for the development of high-performance atomic vapor-cell clocks is discussed.

Coherent-population-trapping resonances in buffer-gas-filled Cs-vapor cells with push-pull optical pumping

Residual amplitude modulation is one of the major sources of instability in ultra-sensitive optical detections based on frequency modulation. Using a MgO·LiNbO3 electro-optic crystal, we systematically measure the temperature and polarization dependence of residual amplitude modulation and our experimental results are in good agreement with a previous theoretical analysis. After optical phase modulation, two independent arms including optical detection and frequency demodulation are employed to closely examine the instability of the residual amplitude modulation. Residual amplitude modulation below 25 ppm is obtained with an active cancellation scheme in which the crystal temperature is varied so as to zero the baseline drifts with different origins. Possible improvements for better suppression and stability are discussed.

Measurement and control of residual amplitude modulation in optical phase modulation.

We theoretically analyze the effects of two primary mechanisms of residual amplitude modulation, estimate the resulting frequency instabilities, and discuss relevant experimental countermeasures, providing useful information that are beneficial for the development of ultrastable optical oscillators as well as many precision experiments relying on stable lasers. A Pound-Drever-Hall signal comprising contributions from the birefringence of the electro-optic crystal is derived and used to examine the birefringence-related amplitude modulation and the resultant frequency offset in terms of various experimental parameters. The combined effect of the crystal birefringence and pararsitic 'etalons is further investigated by dividing the etalons into three representative categories according to their locations in the optical path. The analysis shows that introducing a resonant optical cavity only scales the birefringence-generated amplitude modulation by a constant, thereby lending strong support to the active control scheme using a separate detection path. When a parasitic 'etalon is added, the active control scheme can still suppress the resultant instability except for the parasitic 'etalon that is located closely in front of the optical cavity. In this case the etalon produces rather large frequency instability and therefore should be avoided. In addition, numerical calculations are performed to assess the impact of a special situation where the front and end surfaces of an ultrastable optical cavity are potential sources of the parasitic etalon that can strongly couple with the cavity.

Systematic and quantitative analysis of residual amplitude modulation in Pound-Drever-Hall frequency stabilization

This paper aims at two practical design issues encountered with electro-optic amplitude modulators, namely (1) the long-term optical power drift when a single electro-optic crystal is used and (2) the mechanical resonances of the crystal that limit the control bandwidth. We investigated an active control scheme using a single crystal to offset the drifts of different origins such as polarization, crystal birefringence, and electronics. The control system worked continuously for at least 15 h without interruption and a power instability of 8 x 10(-4) was achieved in a 3-h measurement. This technique can be employed in electro-optic applications where two matched crystals are usually used to compensate the birefringence-related drifts. Meanwhile, mechanical resonances in two crystals (LiNbO3 and KTiOPO4) were mapped out and their influences on the control bandwidth were quantitatively investigated. Residual noises of two intensity-stabilized lasers (a Helium-Neon laser and a dye laser) were analyzed in detail. (c) 2012 Elsevier Ltd. All rights reserved.

Long-term and wideband laser intensity stabilization with an electro-optic amplitude modulator

Residual amplitude modulation is one of the major stability-degrading factors in many precision measurements. Using an electro-optic (EO) crystal with wedged input and output surfaces is an effective way to suppress residual amplitude modulation. Here the mechanism of residual amplitude modulation in this approach is investigated. The residual amplitude modulations measured in standard and wedged EO crystals bear similarities in their temperature and polarization dependences, implying that a mixture of the two orthogonal polarizations in the extraordinary light is responsible for the residual amplitude modulation in the wedged EO crystal. Similar to a standard EO crystal, a non-uniform spatial distribution of residual amplitude modulation is also observed in the extraordinary light emerging from the wedged EO crystal. The optical isolator after the EO crystal is replaced by a Faraday rotator, and an improvement in the long-term stability is observed. With the wedged-crystal approach, residual amplitude modulation as low as 2×10−7 is observed, contributing a frequency instability of 8×10−18 (500 s) in Pound–Drever–Hall frequency stabilization with a discrimination slope of 1×10−4  V/Hz.

Suppressing residual amplitude modulation to the 10-7 level in optical phase modulation.

Two 1,064-nm Nd:YAG lasers frequency stabilized by high-finesse optical cavities are developed to investigate various noise mechanisms in ultra-stable optical oscillators. Active control of residual amplitude modulation using a separate sensing path is implemented and its effectiveness in the presence of a resonant optical cavity is theoretically analyzed and experimentally verified by measuring the rejection ratios in optical heterodyne beat between a perturbed laser and a stable reference. Laser frequency noises originated from vibration, residual amplitude modulation, quantum-limited shot noise, and electronic noise are experimentally analyzed. With active control, residual amplitude modulation is suppressed to below 1 x 10(-6) at 0.02-1,000 s, reaching a minimum of 2 x 10(-7) at similar to 2 s. A frequency stability of 2 x 10(-15) is obtained from 0.1 to 10 s, and the optical heterodyne beat of the two Nd: YAG lasers shows 1-Hz linewidth with a measurement time of 4.096 s. In addition, the experimentally determined linewidths agree well with the calculation according to a simplified relationship between the linewidth and the underlying flicker noise that modulates the laser frequency.

Liufeng Li

Papers

Measurement and control of residual amplitude modulation in optical phase modulation.

Systematic and quantitative analysis of residual amplitude modulation in Pound-Drever-Hall frequency stabilization

Long-term and wideband laser intensity stabilization with an electro-optic amplitude modulator

Suppressing residual amplitude modulation to the 10-7 level in optical phase modulation.

Analysis of frequency noise in ultra-stable optical oscillators with active control of residual amplitude modulation