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Abstract
We report the optical phase-locking of two extended-cavity diode lasers with a frequency difference of 6.9 GHz by serrodyne modulation. The bandwidth of the phase-locking loop is extended up to 9.5 MHz. The residual phase noise of the two phase-locked lasers reaches in the offset frequency range of 1.5 kHz to 9 kHz and below in the range of 150 Hz to 350 kHz, respectively. It is expected that the sensitivity limit of atom interferometers will be enhanced when the phase-locked lasers are used.
© 2019 Optical Society of America
1. INTRODUCTION
The optical phase-locking of two independent lasers is widely used in the fields of frequency metrology [1], microwave-light converters [2], and atomic physics, such as electro-magnetically induced transparency [3], Raman velocity selection [4], coherent population trapping [5], and atom interferometry [6].
Recently, many researchers have paid attention to atom interferometers because they have potential as powerful tools for precise measurements of fundamental constants [7,8], gravity [9], accelerations [10], rotations [11], and so on. Phase-locked lasers have an important role in atom interferometers. Three Raman pulses of pulses are used to divide and recombine a traveling atom wave packet in an atom interferometer. The phase noise between two Raman lasers should be very low to increase the sensitivity of the atom interferometer. It is because the phase noise is directly imprinted on the states of atoms during the stimulated Raman transitions [9,12], which affects the measurement precision of the atom interferometer.
Many studies on a stable optical phase-locking loop (OPLL) with low phase noise have been carried out [13–17]. To enhance the phase noise performance of an OPLL, a wide servo bandwidth and a high feedback loop gain are needed for the OPLL. The bandwidth of the OPLL is hardly over 5 MHz due to the characteristics of the extended-cavity diode laser (ECDL) [3]. To enhance the bandwidth of the OPLL, an intra-cavity electro-optics modulator (EOM) [17] or a field-effect transistor feedback circuit have additionally been used [15]. Recently, we were able to extend the bandwidth of the OPLL up to 8 MHz simply by tuning a phase lead compensation of the fast signal into the injection current of the ECDL [18].
In this paper, we use a different approach to achieve the OPLL of two ECDLs by using serrodyne modulation, for the first time. We prepare an optical serrodyne frequency shifter [19] by using an EOM to which a sawtooth waveform is supplied as part of the fast servo loop of the OPLL. By applying a sawtooth waveform to the EOM, it can be used as an optical frequency shifter with adequate suppression of unwanted sidebands, and another merit is its intrinsic wide bandwidth of several megahertz [20]. As a result, we are able to extend the OPLL bandwidth of the serrodyne modulation up to 9.5 MHz, and the residual phase noise between the two phase-locked ECDLs with a 6.9 GHz frequency offset is reduced to in the offset frequency range from 1.5 to 9 kHz. We discuss the sensitivity limit of an atom interferometer when our OPLL laser system with serrodyne modulation is adopted.
2. EXPERIMENTAL SETUP
The experimental setup for the OPLL laser system using the optical serrodyne frequency shifter is shown in Fig. 1. The two ECDLs with a Littrow configuration are used as the master and slave lasers. The ECDLs used in the experiment are described in our previous paper [18].
Fig. 1. Serrodyne modulation apparatus for the OPLL of two ECDLs. ML, master laser; SL, slave laser; MTS, modulation transfer spectroscopy; EOM, electro-optic modulator; FPD, fast photodiode; DC, directional coupler; APD, analog phase detector; FALF, fast active loop filter; VCO, voltage-controlled oscillator; NLTL, nonlinear transmission line; PNA, phase noise analyzer; SA, spectrum analyzer.
The output frequency of the master ECDL is stabilized to the D2 transition from to with a modulation transfer spectroscopy [21]. The output frequency of the slave ECDL is tuned around the transition from to by monitoring the saturated absorption spectroscopy, which is not shown in Fig. 1. The frequency difference between the two ECDLs is about 6.9 GHz. The output of the slave ECDL is sent to a highly efficient waveguide EOM (Photline NIR-MPX-800), which has pigtailed polarization-maintaining fibers for optical input and output. The modulation bandwidth and optical insertion loss of the EOM are 10 GHz and 4 dB, respectively. Maximum optical input power of the waveguide EOM is about 20 mW. Therefore, the output power we can produce in this experiment is less than 10 mW. However, phase-locked optical power can be easily amplified by a semiconductor amplifier.
The EOM is modulated by a sawtooth wave of 500 MHz, which is generated by a nonlinear transmission line (NLTL, Picosecond Pulse Labs Model 7102). The NLTL has a function of transforming a sinusoidal wave to a sawtooth wave [22]. The sinusoidal wave of a voltage controlled oscillator (VCO, Mini-Circuits ZX95-520+), whose electrical bandwidth is 60 MHz, is supplied to the NLTL after passing through an RF amplifier.
The heterodyne beat signal of 6.9 GHz is detected by a fast photodiode (Hammamatsu G4176-03). The optical power of each laser that impinges on the photodiode is 2 mW. The beat signal of 6.9 GHz is mixed by a microwave mixer (Marki M8-0412L) with a low phase noise 7 GHz signal from a local oscillator. The 7 GHz signal is synthesized from a 100 MHz ultra-low phase noise (ULN) quartz oscillator, which is phase-locked to a 5 MHz ULN quartz oscillator. The downconverted 100 MHz beat signal from the microwave mixer is amplified by a low noise amplifier (Mini-Circuits ZFL-500LN) and sent to a directional coupler (Mini-Circuits ZFDC-10-1). The coupled output of the directional coupler is used to measure the phase noise and monitor the microwave spectrum of the 100 MHz signal by using a phase noise analyzer and a spectrum analyzer, respectively. The output of the directional is sent to an analog phase detector (Mini-Circuits ZRPD-1+). The analog phase detector makes a phase error signal by comparing the phase difference between the downconverted beat signal and the 100 MHz signal from the ULN quartz oscillator. The error signal is divided into two paths for the slow and the fast servo loops of the OPLL. For the fast servo loop, the phase error signal is directly fed back to the control voltage of the VCO after passing through a fast active loop filter (FALF).
The FALF is designed to compensate for the phase delay of the loop and to widen the OPLL bandwidth of the serrodyne modulation. The circuit diagram of the FALF is shown in Fig. 2. An operational amplifier with a gain-bandwidth product of 800 MHz is used in the FALF. The proportional gain is set to 10, which is defined as R4/R2. The first and the second corner frequencies of the proportional-integral (P-I) servo are around 6.6 MHz and 4.8 MHz, respectively. A passive phase lead filter (PLF) with a 5.9 MHz corner frequency is attached to the output of the operational amplifier. The gain and corner frequencies of all P-I servos are tuned to the optimal value to have the lowest phase noise level in the loop bandwidth.
Fig. 2. Circuit diagram of the fast active loop filter. R1: 5 Ω, R2: 91 Ω, R3: 910 k Ω, R4: 1 k Ω, R5: 270 Ω, R6: 47 Ω, R7: 15 Ω, C1: 330 pF, C2: 24 pF, C3: 100 pF.
For the slow servo loop in Fig. 1, the phase error signal from the analog phase detector is integrated by a low-pass filter with a high loop gain in the low-frequency region. The integrated error signal is fed back to the piezo-electric transducer of the slave ECDL to keep the average phase error signal near zero, which enhances the long-term stability of the OPLL.
The total loop length of the OPLL, which includes the optical and microwave path lengths, is reduced as much as possible because a loop delay may cause an additional phase delay and limit the bandwidth of the OPLL. In the experiment, the total loop length is shorter than 4 m.
3. RESULTS AND DISCUSSION
For optimizing the efficiency of the optical serrodyne frequency shifter before running the OPLL, the spectrum of the laser after the EOM is monitored by a confocal optical spectrum analyzer. The observed optical spectra are shown in Fig. 3, when the serrodyne modulation frequency is around 500 MHz. In Fig. 3, the black line and red line show the optical spectrum without and with the application of the serrodyne modulation, respectively. The input RF power of the NLTL is adjusted so that frequency shift efficiency is maximized [19]. The frequency shift efficiency of the serrodyne modulation is over 60%, which is comparable to that of a double-pass acousto-optic modulator (AOM) configuration [16]. The carrier and higher harmonic of the modulated laser, however, are included in the output of the EOM. The carrier and higher harmonics can be easily filtered out by using an optical cavity [16]. In the experiment, an optical cavity for filtering is not adopted.
Fig. 3. Optical spectrum with and without serrodyne modulation normalized to the unmodulated carrier and measured by a confocal spectrum analyzer. The black line shows the optical spectrum with no modulation. The red line is the optical spectrum with a serrodyne modulation of 500 MHz. The small peaks in the red line that are not specified are higher-order optical sidebands.
After running the OPLL, we measured the spectrum of the phase-locked beat signal shown in Fig. 4. The resolution bandwidth of the microwave spectrum analyzer is set to 1 kHz. In contrast with typical OPLL systems [13–15], the OPLL system with serrodyne modulation by the EOM provides a high gain in the medium frequency region and a wide bandwidth. Note that one servo bump appears near 9.5 MHz. By optimizing the corner frequencies of the FALF, the bandwidth of the OPLL can be extended over 10 MHz. The phase noise, however, becomes worse over a 10 MHz bandwidth. It is suspected that the main reason for the noise increasing with a bandwidth over 10 MHz is the limited intrinsic tuning range of the VCO. The frequency tuning range of the VCO in the experiment is from 470 to 530 MHz. When the bandwidth of the OPLL is 9.5 MHz, the overall frequency range of the spectrum covers 30 MHz, which is already half of the tuning range of the VCO. As we increase the bandwidth of the OPLL, the tuning range of the VCO does not support the bandwidth anymore. The frequency components over the tuning range produce a nonlinear effect to the system and finally give rise to large phase noise. The bandwidth of the OPLL with the serrodyne modulation could be further improved by using a VCO with a wide tuning range.
Fig. 4. Microwave spectrum of the downconverted output from the beating signal between the two ECDLs. The resolution bandwidth is set to 1 kHz.
The phase noise of the phase-locked beat signal was measured with a phase noise analyzer (Agilent E5052B), shown in Fig. 5. The phase noise level reaches at a 1.5 kHz offset frequency and below from 150 Hz to 350 kHz.
The OPLL laser system based on serrodyne modulation was developed for its application to atom interferometers. For this reason, the sensitivity of an atom interferometer is estimated on the assumption that the developed laser system is used in an atom gravimeter. In the atom gravimeter, three Raman pulses consisting of one -pulse, one -pulse, and another -pulse are used for the Raman transitions. The fractional measurement sensitivity, which is defined as the ratio between the local gravitational acceleration and its uncertainty , is given by
where is a phase uncertainty, and is an effective wavenumber, which is the sum of the wavenumbers of the Raman pulses [15]. is a time interval between two consecutive Raman pulses.Integrating over the frequency region, we obtain the sensitivity limits of at different pulse lengths of the Raman pulses. The result is shown in Fig. 6. In this calculation, the time interval is set to 150 ms. The sensitivity limits of our OPLL laser system based on serrodyne modulation is 2 times lower than that of our previous report [18]. This result is attributed to the fact that the OPLL laser system based on serrodyne modulation has lower phase noise characteristics in the offset frequency range from 1 kHz to 7 MHz than those of [18]. As the pulse duration increases, the difference between the two results becomes closer because the weighting function acts as a low-pass filter, and its cutoff frequency is similar to the Rabi frequency of the Raman pulses [15]. At a long pulse duration, therefore, the contribution of the phase noise from a high frequency to the sensitivity limit decreases. The measurement sensitivity of an atom gravimeter is limited to in the case of when our OPLL laser system based on serrodyne modulation is applied.
Fig. 6. Sensitivity limits given by the OPLL laser system based on serrodyne modulation for different Raman pulse lengths . For calculation, the time interval between two consecutive Raman pulses is set to 150 ms.
4. CONCLUSION
We achieved a low phase noise optical phase-locking of two ECDLs for cold atom interferometry. The OPLL is based on the optical serrodyne modulation frequency shift using an EOM for the modulation and a fast servo loop for the OPLL. The technique benefits from using an EOM for frequency correction and phase lock, which leads to a wide bandwidth [20]. The bandwidth of the OPLL based on serrodyne modulation reaches up to 9.5 MHz, which is comparable to the bandwidth of the OPLL system using intra-cavity EOM [17]. We have achieved a phase noise below in two phase-locked lasers in an offset frequency range of 150 Hz to 350 kHz. We expect that this OPLL laser system based on serrodyne modulation will enable us to reduce the phase noise and thereby get a lower sensitivity limit in the atom interferometry under development.
Funding
Korea Research Institute of Standards and Science (KRISS) (18011034); Agency for Defense Development (ADD).
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