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Abstract
A simple and compact design of the laser system is important for realization of compact atom interferometers (AIs). We design and realize a simple fiber bench-based 780-nm laser system used for 85Rb AI-based gravimeters. The laser system contains only one 780 nm seed laser, and the traditional frequency-doubling-module is not used. The Raman beams are shared with one pair of the cooling beams by using a liquid crystal variable retarder based polarization control technique. This laser system is applied to a compact AI-based gravimeter, and a best gravity measurement sensitivity of 230 μGal/Hz1/2 is achieved. The gravity measurements for more than one day are also performed, and the long-term stability of the gravimeter is 5.5 μGal.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Atom interferometers (AIs) have been used to measure gravity [1–9], gravity gradient [10–13] and rotation [14–16]. High-precision AIs have potential applications in technology [17] and fundamental physics [18–24]. Laser system is an important subsystem for AIs. Usually, the laser system is complex and bulky. Compact, robust and portable AIs are useful for both field and space applications, thus a simple and compact design of the laser system is necessary for portable AIs.
In recent years, many efforts have been taken to develop compact laser systems for AIs. On the one hand, integrated laser systems in free space were designed [25,26], where optical components were designed and integrated in a stable optical module, and all lasers needed in AIs are supplied by this module. This well designed optical module is extremely stable and compact [27, 28], however, it is difficult to adjust when some of the optical components are damaged or needed to be replaced. On the other hand, laser systems based on a fiber bench were also proposed [29–34]. There are several advantages for these laser systems. First, the optical module and fiber bench are less sensitive to ambient temperature and vibration, therefore they can work in a worse environment. Second, the fiber components at 1.5 μm are mature due to the development of optical communication, and many high-performance components can be used. However, laser frequencies matching the transition of alkali atoms should be obtained from 1.5 μm fiber laser by frequency doubling technique.
At the same time, several techniques have been used to reduce the number of components contained in the laser systems. Laser systems with only two laser sources were designed by using the frequency beat-note locking method [26,33,34]. And by using the offset sideband locking technique [35], laser systems with a single 1.5 μm laser source have been proposed [36,37]. In these laser systems, the output laser is alternately used for laser cooling, the Raman transition and detection. The reduced number of laser sources or optical amplifiers makes the laser system more compact. In addition, a laser system for Cs AI with only one diode laser was realized for the first time by Wu et al [38]. All functions such as atom trapping, interferometry and detection can be achieved and multiple axes of acceleration, rotation and inclination measurement can be realized by using this simple laser system. The multi axis atom interferometers can find important applications in field of geodesy, geology and navigation.
In this paper, we realize a very simple and compact one-seed 780-nm laser system for an 85Rb AI. There is no frequency doubling module, which makes the laser system compact and lower energy consumption. This paper and [38] both present a one-seed laser system for AIs, but the principle and design of the laser systems are quite different. First, we design and use several homemade and commercial 780-nm fiber components to form an all fiber-component based laser system, the utilization of fiber components makes the laser system compact and easy to maintain. Second, we utilize the electro-optic modulator (EOM) based offset sideband locking technique to stabilize and control the laser frequency, benefiting from the high bandwidth of the fiber-coupled EOM, the frequency of the seed laser is shifted fast and flexibly over more than 500 MHz. The laser beams for cooling, repumping, state preparation, Raman operation and detection are all realized by the combine usage of the offset sideband locking and phase modulation by another EOM. Third, in the laser system, the lasers needed for AI pass in a straight line without split and combine beside the final beam splitter which sends lasers into the physics package. Only one acousto-optic modulator (AOM) is used for laser intensity control. Though there is only one laser output from the AOM, the laser power at every stage can be easily stabilized, as will be shown in section 2.4. Fourth, a liquid crystal variable retarder (LCVR) is used to dynamically adjust the polarization of laser, which makes sharing the cooling and Raman beams possible. Our laser system can also realize very general purpose. For example, without replacing any component of the laser system and only changing the frequency locking point and some frequency drivers of the EOM, the laser system could be used for an 87Rb AI. We believe that the laser systems in [38] and in this paper have their own characteristics and advantages, both are important steps forward a compact, robust and reliable AI in the future.
The paper is organized as follows. In section 2, we describe the configuration of laser system and the experimental results of frequency stabilization, laser intensity stabilization and polarization control. In section 3, we introduce the time sequence and experimental results of gravity measurements. In section 4, the conclusion and outlook are given.
2. Design of the one-seed laser system
Figure 1 is a schematic of an AI-based gravimeter. The laser system is shown in Fig. 1(a). It consists of several homemade and commercial fiber components, and has only one 780-nm seed laser. All of the components are connected by polarization maintaining (PM) fibers. Figure 1(b) is the control system, which is used to drive the laser system. Two main fibers are used to connect the optical module and the physics system of the AI, which is placed on a passive vibration isolation platform, as shown in Fig. 1(c). The vertical laser beam in the physics system is alternatively used for the Raman beams and one pair of the cooling beams. Benefiting from the compact design, the laser system fits in a cabinet with a size of 40 × 30 × 10 cm3. This laser system can supply all laser beams needed for the AIs.
Fig. 1 The schematic of an AI-based gravimeter. (a) Laser system; (b) Control system; (c) Physics system. DAQ-card, data acquisition card; LCC, laser diode current controller; PID, proportional integral differential circuit; LIA, lock-in amplifier; VCO, voltage controlled crystal oscillator; FDL, fiber-coupled diode laser module; FOI, fiber-coupled optical isolator module; FBS, fiber-coupled beam splitter module; FEOM, fiber-coupled electro-optic modulator module; SAS, saturated absorption spectrum module; FTA, fiber-coupled optical tapered amplifier module; FAOM, fiber-coupled acousto-optic modulator module; FC, fiber coupler; LCVR, liquid crystal variable retarder; PBS, polarization beam splitter; QWP, quarter-wave plate; DDS, direct digital synthesizer; LPS, laser power supply.
2.1. Frequency stabilization
The seed laser is a homemade fiber-coupled diode laser module (FDL) based on a commercial distributed feedback laser diode (DFB-LD) emitting at 780 nm in free space. The laser beam from the DFB-LD passes through an optical isolator and a half-wave plate, then is coupled into a PM fiber. The linewidth of the FDL is about 2 MHz and the maximum output power is about 50 mW. The laser beam from the FDL goes through an additional commercial fiber optical isolator (FOI) for better isolation. Then the laser beam is split into two parts by a 95/5 fiber-coupled beam splitter module (FBS). The 5% beam passes through a commercial fiber-coupled electro-optic modulator module (FEOM (a), 780 nm) to generate sidebands. The bandwidth of the FEOM is 10 GHz. Then the frequency is stabilized and controlled by a homemade fiber-coupled Rb saturated absorption spectrum module (SAS) where a pure 87Rb isotopic vapor cell is used to avoid crosstalk and a fast photo detection circuit (up to 100 MHz) is used to monitor the absorption signal.
By scanning the injection current of the DFB-LD, the laser frequency of the carrier and sidebands varies and the Rb saturated absorption spectrum induced by the carrier and sidebands are obtained, as shown in Fig. 2(b). The saturated absorption spectrum of 87Rb F=2 → F′ and 85Rb F=3 → F′ transition of D2 line is also displayed in Fig. 2(a) for comparison. In order to get the demodulated signal of the spectrum, we need to modulate the frequency of the laser. Instead of modulating the current of the DFB-LD directly, we modulate the driving microwave of the FEOM (a) in Fig. 1(a) by adding a 6.25 MHz sinusoidal signal to the voltage controlled oscillator (VCO). With this method, the frequencies of the sidebands are modulated at the same frequency, but the carrier is not affected. Then we demodulate the saturated absorption signal by a lock-in amplifier (LIA). The demodulated error signal is shown in Fig. 2(c). By processing this error signal with a proportional integral differential (PID) circuit and feeding it back to the current of the DFB-LD, we can lock the frequency of the sidebands to any of the saturated absorption peaks.
Fig. 2 Frequency stabilization and control signal. (a) Saturated absorption spectrum of 87Rb F=2 → F′ and 85Rb F=3 → F′ transition of D2 line. Natural abundance rubidium vapor cell is used. (b) Saturated absorption spectrum of 87Rb F=2 → F′ transition of D2 line induced by the carrier and the ±1-order sidebands. Pure 87Rb isotopic vapor cell is used. (c) Error signal of b for the frequency stabilization.
There are two advantages of this frequency lock method. (1) because we do not modulate the current of the DFB-LD, the frequency of the laser emitting from the DFB-LD is without modulation; (2) the modulation bandwidth of the VCO is high (up to 50 MHz), thus the bandwidth of the error signal feeding back to the DFB-LD can be very high too, which is helpful to narrow the linewidth of the DFB-LD. The typical linewidth of the frequency-locked laser is about 1.4 MHz, which is estimated from the noise of the error signal.
We lock the −1-order sideband of the laser to the cross peak of F=2 → F′ = CO 2, 3 transition of 87Rb D2 line as displayed in Fig. 2(b). The frequency of the carrier is then detuned to the blue side of this transition. For the AI application, because only one seed laser is employed in the laser system, the frequency of the laser has to be shifted rapidly in a large range. We realize this by scanning the frequency of the microwave of the FEOM (a) and keeping the −1-order sideband locked during the scanning, then the frequency of the carrier shifts correspondingly. During the frequency shift, the current of the DFB-LD is changed passively to follow the shift. The frequency of the sideband will be out of lock if the scanning rate of the microwave frequency is too high. An active feedback is appended to the current of the DFB-LD to avoid losing lock. Figure 3 shows that we can realize the frequency shift of 578 MHz in 10 ms, which is fast enough for the AI operation.
2.2. Phase modulation and laser power amplification
The rest 95% of the laser from the FBS goes through another FEOM (b). This FEOM is used to create sidebands for the repumping laser and Raman beams. A 2.9-GHz VCO and a 3.035-GHz direct digital synthesizer (DDS) are used to drive this FEOM (b) in cooling (detection) and Raman operation stage, respectively. Then the laser beam passes through another FOI and injects into a homemade fiber-coupled optical tapered amplifier module (FTA), which is used to amplify the laser power for the cooling and Raman operating stages for the AI. Next, the laser beam passes through an 80 MHz fiber-coupled acousto-optic modulator module (FAOM) for intensity stabilization and pulse modulation. The output laser power of the FAOM can be adjusted smoothly from 0–100% of its maximum. The power extinction ratio of the FAOM is about 40 dB when the FAOM is off, and the switch time is less than 200 ns. The laser from the FAOM is split into two parts equally by a 50/50 FBS and then sent to the physics system by two PM fibers. One part is split and distributed by a polarization beam splitter (PBS) and four mirrors in the physics system to create two pairs of mutually perpendicular beams for 3 dimensional magneto-optical trap (3D-MOT). The other part goes through a half-wave LCVR and a quarter-wave plate (QWP) for polarization control, and then passes through the vacuum tube of the physics system and another QWP, and is reflected from a reflector to create a pair of counter-propagated beams, as shown in Fig. 1(c). This pair of beams is alternately used for laser cooling, state preparation, the Raman transition and detection. A detection module is mounted at the bottom of the physics system recording the fluorescence of the cold atom cloud.
The FTA for laser power amplification is based on a tapered amplifier and its size is 6×6.5×18.2 cm3. The reliability of the tapered amplifier is a problem both in the power stability and the mode stability aspects. For the power stability problem, the FTA can work stably for more than 1 year. The output laser power from the FTA decays to some extent during its usage. However, we can use the laser intensity stabilization technique to stabilize the laser power to a given level, which will be shown in section 2.4. For the mode stability problem, in our laser system, the modulated lasers are fed into the FTA, the carrier and sidebands lasers both exist. Mode competition does exist in the power amplification process. The ratio of the sidebands to carrier varies with time, and affects the accuracy of the AI. However, an ac Stark shift locking technique is implemented to control the ratio of the sidebands to carrier in the FTA, and this effect is suppressed greatly.
2.3. Polarization control
The LCVR and the following QWP are used to change the polarization of the laser beam. At the 3D-MOT stage, the counter-propagated beams should be circularly polarized in a same direction. But at the Raman operating stage, in order to address the Doppler sensitive Raman transition, the counter-propagated beams should be circularly polarized at opposite direction or linearly polarized in a line ⊥ line configuration [1]. The polarization at the two stages is not the same. If the laser beam after the LCVR and the following QWP is circularly polarized, then the counter-propagated beams are circularly polarized in the same direction. If the laser beam is linearly polarized, then the counter-propagated beams are linearly polarized at vertical directions.
The LCVR is made of birefringent liquid crystal. When light passes though the retarder, it will suffer birefringence and induce a phase difference δ on the two axis of the liquid crystal. By changing the applied voltage for the LCVR, the phase retardance for our LCVR (Thorlabs, LCC1221-B) can be varied from 0.077π to π. The QWP introduces a fixed phase retardance of π/2. The light initially incident on the LCVR is linearly polarized. By properly setting the angles between the incident polarization direction, the axis of the LCVR and the axis of the QWP and changing the voltages for the LCVR, the polarization of laser travelling through the LCVR and the following QWP can be flexibly switched from perfect linear polarization to perfect circular polarization. For example, consider that the axis of the QWP is parallel to the axis of the LCVR and that the angle between the axis of the LCVR and the direction of the input polarization is π/4, then the total phase retardance Γ introduced by the LCVR and QWP is Γ=δ+π/2. When δ=π/2, the total phase retardance Γ is π and the output laser from the QWP is still in linear polarization. When the δ is changed to π, Γ is equal to 3π/2 and the output laser is shifted to circular polarization. We measure the extinction ratio of the output laser by a polarization analyzer (SK010PA). The polarization extinction ratio of linearly polarized laser is about 38 dB and the polarization extinction ratio of circularly polarized laser is almost 0 dB. The switching time of the polarization is in the order of millisecond, which is fast enough for the AI experiments. Thus the requirement of the polarization in different stages can be satisfied.
2.4. Laser intensity stabilization
Due to the mechanical deformation of the laser system, the imperfect extinction ratio of the fiber components, the alignment error of the PM fiber connecters, the vibration and temperature fluctuation of the environment, the intensity of the output laser varies with time. This degrades the performance of the AI. We design a simple scheme to stabilize the intensity of the laser beam without adding any additional components. The photodiode in the detection zone is used to measure not only the fluorescence of atom cloud, but also the background fluorescence, which is mainly contributed by the scattering of the vertical counter-propagated beams, and is proportional to the beam intensity. The background fluorescence is recorded by the photodiode and compared with a preset reference. The differential value is processed by a program written by LabVIEW language to produce a feedback signal. Then this signal is fed back to control the power of the radio frequency generator, which is used to drive the FAOM. We record the laser intensity for each experiment loop, and then feed the error signal back at the beginning of the next experiment loop, therefore the feedback bandwidth is limited by the time of the loop. For our experiment, the circle time is about 0.5 s, hence the feedback bandwidth is about 2 Hz.
By using this scheme, we can stabilize the laser intensity at any stage of the AI experiments. Figure 4 shows the Allan deviation of the relative laser intensity of the π Raman pulse before and after the intensity locking. The short-term Allan deviations are similar due to the limited feedback bandwidth. The long-term Allan deviation is improved for about 2 orders of magnitudes and it is better than 0.001 after intensity locking. According to our experimental perameters, this laser intensity noise will contribute to a noise level of less than 1 μGal in gravity measurement.
Fig. 4 Allan deviation of the relative laser intensity of the Raman pulse before (black dashed line) and after locking (red solid line). The dots are Allan deviations of experimental data, the lines are connecting lines of the dots.
3. Application of the one-seed laser system in an atom gravimeter
By using this one-seed laser system, we realize a Mach-Zehder-type 85Rb atom gravimeter. The operation process of the atom gravimeter includes 5 stages: 3D-MOT, polarization gradient cooling (PGC), state preparation, the Raman interference and detection. A typical time sequences of these stages are shown in Fig. 5. In the following part of the article, without special instructions, the transition means 85Rb D2 line transition.
Fig. 5 Experimental time sequences of the atom gravimeter at different stages. (a) The carrier frequency (detuning with respect to F=3 → F′ = 4 transition of 85Rb D2 line). (b) Switch of the laser intensity. (c) The modulation of FEOM (b). (d) The polarization of output laser.
At the 3D-MOT stage, the microwave frequency of FEOM (a) is 1.1654 GHz, the frequency of the carrier is detuned by −14.4 MHz from the F=3 → F′ = 4 transition and the carrier acts as the cooling laser. The microwave frequency of FEOM (b) is 2.9295 GHz, the generated +1-order sideband is in resonance with the F=2 → F′ = 3 transition. This laser sideband acts as the repumping laser. The output laser is kept in circular polarization. A pair of anti-Helmholtz coils is used to create a gradient magnetic field. The three pairs of counter-propagated beams together with the magnetic field constitute the 3D-MOT. About 108 atoms are cooled and trapped in the MOT within 301 ms.
The PGC stage is added to reduce the temperature of the atom cloud further. First, the current of anti-Helmholtz coils is turned off, and wait for 5 ms to let the magnetic field ramp to zero. Then the microwave frequency of FEOM (a) is swept to 1.1192 GHz in 1 ms, the frequency of the carrier is then detuned by −60.6 MHz from the F=3 → F′ = 4 transition. The microwave frequency of FEOM (b) is swept to 2.9757 GHz synchronously to make sure that the +1-order sideband is always in resonance with the F=2 → F′ = 3 transition. Then the laser intensity is decreased to 50% of its maximum in 1 ms and continues to fall to zero in 2 ms. The atom cloud with temperature of 12 μK is obtained at the end of this stage.
Then a state preparation stage is carried out to pump the atoms to the F=2 state. The microwave supply for the FEOM (b) is turned off and the microwave frequency of FEOM (a) is swept to 1.0592 GHz in 2 ms. Then the carrier is in resonance with F=3 → F′ = 3 transition and no sideband is created. A 40-μs laser pulse is applied to the atom cloud for the pumping process. Almost all atoms are prepared in the F=2 state after this stage.
Following the state preparation stage, the π/2-π-π/2 Raman interference stage is performed. The microwave frequency of FEOM (a) is swept to 0.602 GHz in 10 ms and the frequency of the carrier is then 578 MHz red detuned from the F=3 → F′ = 4 transition. The carrier acts as one of the Raman beams. The microwave supply for the FEOM (b) is turned on and switched to the 3.035 GHz DDS. The generated +1-order sideband acts as another Raman beam. The ratio of the sideband to the carrier can be adjusted by controlling the microwave power of the DDS. In this stage, the polarization of laser is turned to linear polarization by the LCVR to drive the Doppler sensitive Raman transition. The polarization shifting costs about 10 ms. Then the π/2-π-π/2 Raman pulses are applied to realize the Raman interference process. The time interval between pulses is T=50 ms.
After the interference stage, a fluorescence detection scheme is designed and realized. The microwave frequency of FEOM (a) is swept to 1.1798 GHz and the carrier is in resonance with F=3 → F′ = 4 transition and acts as the detection beam. When the atom cloud reaches the detection zone, a detection pulse of several ms is applied to the atom cloud. The laser-induced fluorescence of atoms in the F=3 state will be detected by the detection module. The detection signal represents the number of the F=3 atoms in the atom cloud.
A standard frequency-shift keying (FSK) process is implemented during the interference process to compensate the Doppler shift induced by the gravity [1]. An additional FSK process is inserted into the interference process to change the phase of the AI. After several interference loops, we obtain an interference fringe from which the value of gravity is obtained. Figure 6 shows a best interference fringe for 100 measurement points in about t=53.9 s. The uncertainty of the phase is δϕ=12.3 mrad, corresponding to a gravity measurement sensitivity of 230 μGal/Hz1/2, calculated by the formula δg/g=t1/2δϕ/(keffT2g). The gravity measurement sensitivity is mainly limited by the vibration noise and the detection noise.
Fig. 6 The Doppler sensitive interference fringe for T=50 ms. The red dots are experimental data, the blue solid line is Sine fitting. There are 100 measurement points in the fringe and the time for a single point is 539 ms. The uncertainty of the phase is 12.3 mrad, corresponding to a gravity measurement sensitivity of 230 μGal/Hz1/2.
From Fig. 6, we can see that the contrast of the AI fringe is only about 10%. This low contrast is caused by several reasons. First, in this version of laser system, the maximum single photo detuning of the Raman pulses is about −578 MHz from the F=3 → F′ = 4. This is mainly limited by the frequency range of the VCO for FEOM (a). When the Raman lasers interact with the cold atoms prepared in the F=2 state, beside the stimulated Raman transition produce, atoms will be pumped to the F=3 state by the optical pumping and spontaneous radiation. This will contribute a nearly constant background to the interference signal, which describes the population of atoms in the F=3, mF=0 state for our experiment. By adjusting the double photons detuning of the Raman beams to a non-resonant position, we measure that this background is about 0.035 for the scale used in Fig. 6. Second, in order to realize a compact vacuum system, the diameter of the Raman beams (1/e2 diameter of its maximum intensity) is about 9.5 mm. At the same time, the stray magnetic field in the MOT region cannot be ignored. This stray magnetic field results two problems: (1) a perfect PGC process cannot be performed, so the temperature of the atom cloud is limited to about 12 μK; (2) about 70 ms of free fall time is wasted to avoid this stray magnetic field region before the Raman operation. By calculating the AI’s signal similar to the produce of [39], and involving the effect of the size of the Raman beams and the temperature of the atom cloud, we find that the resulting contrast of the AI is about 20%, by adding the 0.035 spontaneous radiation background, the final contrast should be about 15%, which is consistent with the experiment result in Fig. 6.
Several parameters such as the ac-Stark shift and Zeeman shift induce systematic errors of the gravity measurement. By applying the effective wave vector keff reversing method, the keff unrelated systematic errors are suppressed greatly [40]. We carry out a continuous gravity measurement for more than one day. The effective wave vector reversing method is utilized for the measurement. Figure 7 shows the data of the gravity measurement and Allan deviation of the gravity data after deducing the theoretical tide value. The measured temporal variation of gravity (Δg) agrees well with the tide model and the long-term stability of the atom gravimeter is 5.5 μGal, which is mainly limited by the short-term stability and the finite integration time.
Fig. 7 (a) The Allan deviation of the gravity data after deducing theoretical tide value. 100 measurement points are averaged to give a gravity value, and the time for the total measurement points is about 1.4 days. (b) The long-term gravity measurement compared with the theoretical tide value. Same measurement points are used as in (a), and 3328 measurement points are averaged to give a gravity value.
4. Conclusion
We present a simple and compact one-seed laser system based on the 780-nm fiber components for 85Rb AIs. Several advanced techniques such as the offset sideband locking, phase modulation, polarization control and laser intensity stabilization are adopted in this laser system. As a result, the frequency, polarization and intensity of the laser are turned flexibly, and the output laser is alternately used for laser cooling, state preparation, the Raman transition and detection. An AI-based gravimeter is realized by using this laser system, and a continuous gravity measurement for more than one day is performed.
There is still room to improve our laser system. First, the fiber coupling efficiency of some fiber components is not stable enough. A careful simulation of the temperature and vibration stability and a more compact design will be carried out in the next version of the laser system. Second, the contrast of the interference fringe is low. By enlarging the single photon detuning and the diameter of Raman beams, and adding microwave selection in the state preparation stage, it is possible to reduce the constant background caused by spontaneous radiation and improve the contrast. The simple and compact design of our laser system is helpful for the field and space applications in the future.
Funding
National Key Research and Development Program of China (2016YFA0302002); National Natural Science Foundation of China (NSFC) (91536221, 91736311,11504411); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB21010100).
Acknowledgments
We acknowledge the helpful discussion with Peng Xu and Zhanwei Yao.
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