Rodolphe Boudot

Ultra-low-noise microwave extraction from fiber-based optical frequency comb

In conclusion, we have used two FOFC based optical to microwave division frequency synthesizers referenced to a common optically source to create 11.55 GHz microwave signals with a relative frequency stability of 1.6×10-16 at 1 s. The relative phase noise spectral density at a 1 Hz offset from the 11.55 GHz carrier is measured at 111 dBrad2/Hz, limited by the readout system noise floor. Long term stability and accuracy down to 3×10-19 at 65536 s was also demonstrated from a set of 3 days continuous measurement. These results are obtained with classical double balanced mixers measurement scheme. By using a noise measurement system based on the carrier suppression method and advanced noise reduction techniques we are able to improve the results down to a phase noise spectral density at a 1 Hz of 117 dBrad2/Hz and a FFS is of 1.5×10-19 at 1000s (for a single system).

Sub-100 attoseconds stability optics-to-microwave synchronization

We use two fiber-based femtosecond frequency combs and a low-noise carrier suppression phase detection system to characterize the optical to microwave synchronization achievable with such frequency divider systems. By applying specific noise reduction strategies, a residual phase noise as low as −120 dBc/Hz at 1 Hz offset frequency from a 11.55 GHz carrier is measured. The fractional frequency instability from a single optical-to-microwave frequency divider is 1.1×10−16 at 1 s averaging down to below 2×10−19 after only 1000 s. The corresponding rms time deviation is lower than 100 attoseconds up to 1000 s averaging duration.

Investigations on continuous and pulsed interrogation for a CPT atomic clock

We investigated the influence of some critical parameters and operating conditions such as cell temperature, laser intensity, and interrogation technique affecting the performances of a gas cell Cs frequency standard based on coherent population trapping (CPT). Thanks to an original experimental setup, the atoms can be trapped in the dark state and interrogated using continuous wave (CW) or pulsed coherent optical radiations. Using a double-lambda scheme, a signal contrast as high as 52% has been measured in the continuous regime for an optimum cell temperature of 35degC. Compared with the conventional continuous CPT interrogation, the pulsed interrogation technique reduces the light shift by a factor of 300 and allowed it to reach high-frequency stability for higher laser intensities. The frequency stability has been measured to be 9 x 10-13 for a 1 s integration time. Main noise contributions limiting the short-term and medium-term frequency stability are reviewed and estimated.

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

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 lin perpendicular to 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. DOI: 10.1103/PhysRevA.87.013416

Phase noise in RF and microwave amplifiers

Understanding amplifier phase noise is a critical issue in many fields of engineering and physics, such as oscillators, frequency synthesis, telecommunication, radar, and spectroscopy; in the emerging domain of microwave photonics; and in exotic fields, such as radio astronomy, particle accelerators, etc. Focusing on the two main types of base noise in amplifiers, white and flicker, the power spectral density of the random phase φ(t) is Sφ(f) = b0 + b-1/f. White phase noise results from adding white noise to the RF spectrum in the carrier region. For a given RF noise level, b0 is proportional to the reciprocal of the carrier power P0. By contrast, flicker results from a near-dc 1/f noise-present in all electronic devices-which modulates the carrier through some parametric effect in the semiconductor. Thus, b-1 is a parameter of the amplifier, constant in a wide range of P0. The consequences are the following: Connecting m equal amplifiers in parallel, b-1 is 1/m times that of one device. Cascading m equal amplifiers, b-1 is m times that of one amplifier. Recirculating the signal in an amplifier so that the gain increases by a power of m (a factor of m in decibels) as a result of positive feedback (regeneration), we find that b-1 is m2 times that of the amplifier alone. The feedforward amplifier exhibits extremely low b-1 because the carrier is ideally nulled at the input of its internal error amplifier. Starting with an extensive review of the literature, this article introduces a system-oriented model which describes the phase flickering. Several amplifier architectures (cascaded, parallel, etc.) are analyzed systematically, deriving the phase noise from the general model. There follow numerous measurements of amplifiers using different technologies, including some old samples, and in a wide frequency range (HF to microwaves), which validate the theory. In turn, theory and results provide design guidelines and give suggestions for CAD and simulation. To conclude, this article is intended as a tutorial, a review, and a systematic treatise on the subject, supported by extensive experiments.

The effect of AM noise on correlation phase-noise measurements

We analyze the phase-noise measurement methods in which correlation and averaging is used to reject the background noise of the instrument. All the known methods make use of a mixer, used either as a saturated-phase detector or as a linear-synchronous detector. Unfortunately, AM noise is taken in through the power-to-dc-offset conversion mechanism that results from the mixer asymmetry. The measurement of some mixers indicates that the unwanted amplitude-to-voltage gain is of the order of 5-50 mV, which is 12-35 dB lower than the phase-to-voltage gain of the mixer. In addition, the trick of setting the mixer at a sweet point - off the quadrature condition - where the sensitivity to AM nulls, works only with microwave mixers. The HF-VHF mixers do not have this sweet point. Moreover, we prove that if the AM noise comes from the oscillator under test, it cannot be rejected by correlation. At least not with the schemes currently used. An example shows that at some critical frequencies the unwanted effect of AM noise is of the same order - if not greater - than the phase noise. Thus, experimental mistakes are around the corner

Coherent population trapping resonances in Cs–Ne vapor microcells for miniature clocks applications

We report the characterization of dark line resonances observed in Cs vapor microcells filled with a unique neon (Ne) buffer gas. The impact on the coherent population trapping (CPT) resonance of some critical external parameters such as laser intensity, cell temperature, and microwave power is studied. We show the suppression of the first-order light shift by proper choice of the microwave power. The temperature dependence of the Cs ground state hyperfine resonance frequency is shown to be canceled in the 77–80 °C range for various Ne buffer gas pressures. The necessity to adjust the Ne buffer gas pressure or the cell dimensions to optimize the CPT signal height at the frequency inversion temperature is pointed out. Based on such Cs–Ne microcells, we preliminary demonstrate a 852 nm vertical cavity surface emitted laser (VCSEL)-modulated based CPT atomic clock exhibiting a short term fractional frequency instability σy(τ)=1.5×10−10τ−1/2 until 30 s. These results, similar to those published in the literat...

Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs

We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120 dBc/Hz at 1 Hz offset from an 11.55 GHz carrier frequency. Furthermore, we report a detailed investigation into the fundamental noise sources which affect the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects, we implement an ultra-low noise carrier-suppression measurement system, which avoids the detection and amplification noise of more conventional techniques. This technique suppresses these unwanted sources of noise to very low levels. In the Fourier frequency range of ~200 Hz to 100 kHz, a feed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented to reduce the relative intensity noise which causes unwanted phase noise through power-to-phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements of the relative intensity noise of the fiber comb.

Ramsey spectroscopy of high-contrast CPT resonances with push-pull optical pumping in Cs vapor

We report on the detection of high-contrast and narrow Coherent Population Trapping (CPT) Ramsey fringes in a Cs vapor cell using a simple-architecture laser system. The latter allows the combination of push-pull optical pumping (PPOP) and a temporal Ramsey-like pulsed interrogation. An originality of the optics package is the use of a single Mach-Zehnder electro-optic modulator (MZ EOM) both for optical sidebands generation and light switch for pulsed interaction. Typical Ramsey fringes with a linewidth of 166 Hz and a contrast of 33 % are detected in a cm-scale buffer-gas filled Cs vapor cell. This technique could be interesting for the development of high-performance and low power consumption compact vapor cell clocks based on CPT.

High-Performance Coherent Population Trapping Clock with Polarization Modulation

We demonstrate a vapor cell atomic clock prototype based on continuous-wave (CW) interrogation and double-modulation coherent population trapping (DM-CPT) technique. The DM-CPT technique uses a synchronous modulation of polarization and relative phase of a bi-chromatic laser beam in order to increase the number of atoms trapped in a dark state, i.e. a non-absorbing state. The narrow resonance, observed in transmission of a Cs vapor cell, is used as a narrow frequency discriminator in an atomic clock. A detailed characterization of the CPT resonance versus numerous parameters is reported. A short-term frequency stability of