1 Introduction

Quantum Atom Interferometry (QAI) has become a promising tool for high-precision sensing and metrology applications [1,2,3,4]. It is analogous to optical interferometry, where the optical state splits and recombines, giving an interference pattern that provides information about the phase introduced to the two split states. Atom interferometry replaces the optical states of an optical interferometer with the matter-wave states [5, 6]. Hence, it is highly sensitive to inertial forces [7, 8], making it one of the most suitable candidates for testing fundamental physics and the theory of quantum electrodynamics [9,10,11,12,13,14,15,16,17,18,19]. The availability of compact inertial sensors based on AI could potentially lead to a breakthrough in future generation of ultra-high sensitive gyroscopes and accelerometers based on quantum technology [18,19,20]. AIs also have applications in geophysical research [23], interplanetary observations [21,22,23,24], underground prospecting [25,26,27], micro-gravity experiments [28], and civil engineering [29]. Thus, the demand for highly efficient AI sensors is continuously increasing. The development of novel technologies for robust sub-systems would enable miniaturization of ultra-cold atom interferometers and make it suitable for field applications, implying the development of efficient laser sources which can provide the frequency requirements of QAI with high stability and reduced noise. A typical laser system for QAI should provide optical pulses of a well-defined duration and different frequencies at different stages of operation, namely cooling and re-pumping beams for magneto-optic trap (MOT), two counter-propagating Raman beams with frequency separation equal to the hyperfine splitting of the ground state of the atomic species used in AI, and the beams for reference transition and detection [5, 6].

Generally, 87Rb is used in AI because of its convenient room-temperature vapor pressure, chemical compatibility, magnetically insensitive transitions, and convenient transition wavelength (780 nm) and line strengths. Its excellent scattering properties allow efficient evaporative cooling [30, 31] and smaller collision shifts [32]. The use of a 780 nm laser source for this operation typically requires the employment of either several acousto-optic modulators (AOMs) or multiple laser sources [33,34,35,36]. Therefore, utilizing the coincidence of telecom wavelength 1560 nm being twice the operation wavelength 780 nm for 87Rb AI, fiberized laser systems based on frequency-doubled architecture are developed with fiberized off-the-shelf components available due to advancements in the telecom industry [35,36,37]. With a telecom laser, the frequency requirements can be achieved using an electro-optic modulator (EOM) with a single laser source and switching electronics [37]. The advanced integrated modulators (made possible due to the coherent telecommunications industry) and compact nonlinear waveguides lead to miniaturized components with less power consumption and increased flexibility in operation. Also, an all-fibered optical amplifier allows high power outputs with a compact and integrable design. Being an all-fiber system, the components can be arranged multi-dimensionally, allowing a small form factor and providing the ease of replacement and rearrangement of components in case of any component malfunction during the operation. All these advantages are not available with either free-space or fibered optics systems having a 780 nm laser source. Hence, the laser system with a 1560 nm source is a strong alternate contender for source development for AIs for field applications [38,39,40,41,42,43,44,45,46,47,48,49,50].

Most of the previous works are based on development of the fiberized laser system with an IQ modulator (dual-parallel Mach–Zehnder modulator) to generate the full-carrier single-sideband modulation (FC-SSB) providing the frequency requirements of QAI [37,38,39,40,41,42]. Considering the importance of an EOM in frequency-doubled architecture based laser system for 87Rb QAI, this paper investigates the performance of different EOMs in this laser system. Here, an intensity modulator (IM), a phase modulator (PM), a dual-drive Mach–Zehnder modulator (DDMZM), and a dual-parallel Mach–Zehnder modulator (DPMZM) are experimentally explored. The PM with a tunable optical filter turns out to be a suitable choice of EOM for this laser system.

2 Principle of operation

For metrology and sensing applications, QAI is performed to extract information from the change in the atomic state. Any phase introduced to the atomic species during the operation of QAI, will result into error in the measurement. Therefore, if the optical beams required at different stages of QAI are generated from the same laser source, due to experiencing the same optical path perturbations, it will minimize the phase noise contribution from the laser source [40] in the overall measurement.

In practice, multiple frequencies can simultaneously be achieved from a single laser source using modulation techniques [51,52,53]. One such modulation technique is the use of EOM. We primarily have four EOMs: IM, PM, DDMZM, and DPMZM.

Consider Fig. 1 to understand the working of all four modulators for QAI. The electric field of the input CW laser at an angular frequency \(\omega\) is given by \({E}_{in}={E}_{0}{e}^{i\omega t}\), with \({E}_{0}\) the amplitude of the field. The following equations give the modulator transfer functions:

$${E}_{M,\mathrm{trans}}\left(t\right)\propto \left\{\begin{array}{c}\frac{1}{2}\left[{e}^{i\phi \left(t\right)}-1 \right] ;\; {for}\, {IM}\, (1a)\\ {e}^{i{\phi }_{0}(t)} ; \;{for}\, {PM}\, (1b)\\ \frac{ 1}{2}\left[{e}^{i\phi \left(t\right)}-{e}^{i{\phi }^{^{\prime}}\left(t\right)}\right] ;\; {for}\, {DDMZM}\, (1c)\\ \\ \frac{1}{2}\left\{\left[{e}^{i\phi \left(t\right)}-1 \right]+{e}^{i{\phi }_{0}\left(t\right)}\left[{e}^{i{\phi }^{^{\prime}}\left(t\right)}-1 \right]\right\} ; \; {for}\, {DPMZM} \,(1d) \end{array}\right.$$

where \(\phi \left(t\right)={\phi }_{dc1}+{\phi }_{rf}sin\left({\omega }_{rf}t\right)\) and \({\phi }^{^{\prime}}\left(t\right)={\phi }_{dc2}+{\phi }_{rf}cos\left({\omega }_{rf}t\right)\) are the phases introduced to an MZM by the applied electrical signal, with RF frequency \({\omega }_{rf}\), and DC and RF voltage-dependent phases, \({\phi }_{dc}=\frac{\pi {V}_{dc}}{{V}_{\pi ,dc}}\) and \({\phi }_{rf}=\frac{\pi {V}_{rf}}{{V}_{\pi ,rf}}\), respectively. \({V}_{\pi ,x}\) denotes the voltage required to achieve \(\pi\) phase difference at 'x' frequency. \({\phi }_{0}\left(t\right)\) is the phase due to modulating RF signal in the case of PM, whereas it is a DC voltage-dependent phase contributing to phase modulation in the parent MZI of the DPMZM. Depending upon the biasing condition of the modulators, unwanted frequency components can be removed, and the power in the carrier and sideband is controlled via the applied RF signal [54]. We should bear in mind that, because of the non-linear optical properties of the modulator, its total output power also depends on the polarization of the input field, which should be continuously maintained using a polarization controller unit to obtain maximum power after the modulator.

Fig. 1
figure 1

Schematic diagram of different modulators with the specification about applied electrical inputs and the phase introduced by them. a Intensity modulator, b phase modulator, c dual-drive Mach–Zehnder modulator, and d DPMZM (IQ) modulator

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The frequency requirements of different stages of QAI are achieved by FC-SSB modulation, where, the carrier of frequency \(\omega\) is modulated by the RF signal of frequency \({\omega }_{rf}\) that either corresponds to the hyperfine splitting of the ground state of 87Rb, 6.834 GHz [29, 34] to provide Raman beams or to the frequency offset required in the MOT beams, 6–7 GHz [29, 34].

FC-SSB is achieved using DC bias for DDMZM and DPMZM by adjusting the modulation index \({\phi }_{rf}\) to obtain only 1st-order sideband, while IM requires an optical filter along with DC bias, whereas FC-SSB is achieved only using an optical filter for PM [55, 56]. Expanding the set of Eqs. (1) using Jacobi–Anger expansion for FC-SSB format showing only 1st-order sideband (with upper sideband) will result in the following form:

$${E}_{\mathrm{IM},\mathrm{out}}=\frac{\gamma }{2} \mathrm{cos}\left(\omega t\right){-\frac{\gamma }{2}{J}_{0}\left({\phi }_{rf}\right) \mathrm{sin}\left(\omega t\right)- \frac{\gamma }{2} J}_{1}\left({\phi }_{rf}\right) \mathrm{sin}\left(\omega t+{\omega }_{rf}t\right),$$
(2a)
$${E}_{\mathrm{PM},\mathrm{out}}= \gamma {J}_{0}\left({\phi }_{rf}\right) \mathrm{cos}\left(\omega t\right)+ \gamma {J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(\omega t+{\omega }_{rf}t\right)-\gamma \mathrm{cos}\left(\omega t\right),$$
(2b)
$${E}_{\mathrm{DDMZM},\mathrm{out}}=\gamma \frac{{J}_{0}\left({\phi }_{rf}\right)}{2}\left[\mathrm{sin}\left(\omega t\right)+\mathrm{cos}\left(\omega t\right)\right]-\gamma {J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(\omega t+{\omega }_{rf}t\right),$$
(2c)
$${E}_{\mathrm{DPMZM},\mathrm{out}}= 2 \gamma \mathrm{sin}\left(\omega t\right)-\gamma {J}_{0}\left({\phi }_{rf}\right)\left[\mathrm{sin}\left(\omega t\right)+ \mathrm{cos}\left(\omega t\right)\right]-\gamma {J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(\omega t+{\omega }_{rf}t\right)+ \gamma {J}_{1}\left({\phi }_{rf}\right) \mathrm{sin}\left(\omega t+{\omega }_{rf}t\right),$$
(2d)

where \(\gamma\) is the overall optical power loss factor and \({J}_{n}\) are the Bessel’s functions, representing the variation of the modulation index with an applied RF electric field.

After achieving these beams in the telecom wavelength range, to use them in QAI with 87Rb atoms, they are frequency-doubled by passing through a second harmonic generation (SHG) element-PPLN (periodically poled Lithium Niobate). Here also, the input polarization to PPLN should be properly set to achieve maximum possible efficiency. The output electric field after PPLN is given as:

$${E}_{\mathrm{IM},\mathrm{PPLN}}=\frac{{\gamma }^{2}}{8}\left[1+{J}_{o}^{2}\left({\phi }_{rf}\right)+{J}_{1}^{2}\left({\phi }_{rf}\right)+\mathrm{cos}\left(2\omega t\right)-2 {J}_{0}\left({\phi }_{rf}\right) \mathrm{sin}\left(2\omega t\right)-{J}_{o}^{2}\left({\phi }_{rf}\right)\mathrm{cos}\left(2\omega t\right)-2 {J}_{1}\left({\phi }_{rf}\right) \mathrm{sin}\left(\omega t+{\omega }_{rf}t\right)+2 {J}_{1}\left({\phi }_{rf}\right) \mathrm{sin}\left({\omega }_{rf}t\right)-2 {J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(2\omega t+{\omega }_{rf}t\right)+2 {J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left({\omega }_{rf}t\right)-{J}_{1}^{2}\left({\phi }_{rf}\right) \mathrm{cos}\left(2\omega t+{2\omega }_{rf}t\right)\right],$$
(3a)
$${E}_{\mathrm{PM},\mathrm{PPLN}}= \frac{{\gamma }^{2}}{2}\left[{1+J}_{o}^{2}\left({\phi }_{rf}\right)+{J}_{1}^{2}\left({\phi }_{rf}\right)-2{ J}_{0}\left({\phi }_{rf}\right) +\mathrm{cos}\left(2\omega t\right)+{J}_{o}^{2}\left({\phi }_{rf}\right)\mathrm{ cos}\left(2\omega t\right)+2 {J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(2\omega t+{\omega }_{rf}t\right)+2{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left({\omega }_{rf}t\right)-2{ J}_{0}\left({\phi }_{rf}\right)\mathrm{cos}\left(2\omega t\right)-2 {J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left(2\omega t+{\omega }_{rf}t\right)+{J}_{1}^{2}\left({\phi }_{rf}\right) \mathrm{cos}\left(2\omega t+{2\omega }_{rf}t\right)-2{ J}_{1}\left({\phi }_{rf}\right)\mathrm{ cos}\left({\omega }_{rf}t\right)\right],$$
(3b)
$${E}_{\mathrm{DDMZM},\mathrm{PPLN}}= \frac{{\gamma }^{2}}{4}\left[{J}_{o}^{2}\left({\phi }_{rf}\right)+2 {J}_{1}^{2}\left({\phi }_{rf}\right)+{J}_{o}^{2}\left({\phi }_{rf}\right) \mathrm{sin}\left(2\omega t\right)-2{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{sin}\left({2\omega t+\omega }_{rf}t\right)+2{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right)\mathrm{sin}\left({\omega }_{rf}t\right)-2{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left({2\omega t+\omega }_{rf}t\right)-2{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right)\mathrm{cos}\left({\omega }_{rf}t\right)+2 {J}_{1}^{2}\left({\phi }_{rf}\right)\mathrm{cos}\left({2\omega t+2\omega }_{rf}t\right)\right],$$
(3c)
$${E}_{\mathrm{DPMZM},\mathrm{PPLN}}={\gamma }^{2}\left[2{-2{ J}_{0}\left({\phi }_{rf}\right)+ J}_{o}^{2}\left({\phi }_{rf}\right)+ {J}_{1}^{2}\left({\phi }_{rf}\right)\right]-{2 \gamma }^{2}\left[1-{ J}_{0}\left({\phi }_{rf}\right)\right]\mathrm{cos}\left(2\omega t\right)+{\gamma }^{2}\left[2{ J}_{0}\left({\phi }_{rf}\right)+{ J}_{o}^{2}\left({\phi }_{rf}\right)\right] \mathrm{sin}\left(2\omega t\right)-{\gamma }^{2}{ J}_{1}\left({\phi }_{rf}\right) \mathrm{cos}\left({2\omega t+\omega }_{rf}t\right)+{\gamma }^{2}{ J}_{1}\left({\phi }_{rf}\right)\left[1-{ J}_{0}\left({\phi }_{rf}\right)\right] \mathrm{cos}\left({\omega }_{rf}t\right)-2 {\gamma }^{2} \mathrm{sin}\left({2\omega t+\omega }_{rf}t\right)+{\gamma }^{2}\left[2-{ J}_{0}\left({\phi }_{rf}\right){J}_{1}\left({\phi }_{rf}\right)\right]\mathrm{sin}\left({\omega }_{rf}t\right)-{\gamma }^{2}{J}_{1}^{2}\left({\phi }_{rf}\right) \mathrm{sin}\left({2\omega t+2\omega }_{rf}t\right),$$
(3d)

As it can be noticed from the set of Eqs. (3), the output contains a central frequency \(2\omega\) with sidebands of frequencies \({2\omega +\omega }_{rf}, {\omega }_{rf}\) and \({2\omega +2\omega }_{rf}\), which can be observed on the optical spectrum analyzer (OSA). The \({\omega }_{rf}\) (order of GHz) being far away from the required frequencies (order of THz), the term with \({\omega }_{rf}t\) will not contribute to any of the operations. For QAI, \(2\omega\) and \({2\omega +\omega }_{rf}\) frequencies are of importance. With \({\omega }_{rf}\) ranging from 6 to 7 GHz, it fulfills the requirement for MOT. And, \({\omega }_{rf}\) equal to 6.834 GHz gives Raman beams. For the remainder of the text, the sideband of frequency \({2\omega +\omega }_{rf}\) is called the first-order sideband, and that of frequency \({2\omega +2\omega }_{rf}\) is referred to as the second-order sideband.

For any laser source to be suitable for QAI, it should not provide unnecessary frequency components which will contribute to the phase noise in the measurement and hence limiting the sensitivity of the instrument. Here, by providing proper biasing condition to the EOM or/and using tunable filter, all other sidebands, except the 1st-order sideband are suppressed by more than 20 dB (@1560 nm). However, it is highly required to study the effect of varying RF power on the second-order sideband obtained after SHG.

3 Experimental setup

Figure 2 shows the general schematic of the experimental setup to investigate different modulation formats for QAI. It consists of an external cavity diode laser (ECDL) operating at 1560 nm (Pure Photonics, PPCL700), an isolator, polarization controllers (PCs), electro-optic modulator (EOM) with an optical filter (if required for IM and PM only), RF source, DC power supply, Erbium–Ytterbium-doped fiber amplifier (EYDFA), variable optical attenuator (VOA), polarization beam splitter (PBS), periodically poled Lithium Niobate (PPLN) with a temperature controller (Covesion, WGP-M-1560-40), optical power meter (OPM) and an optical spectrum analyzer (OSA).

Fig. 2
figure 2

Experimental setup to compare different modulation formats for QAI. LD laser diode; OI optical isolator; PC polarization controller; EOM electro-optic modulator; EDFA Erbium–Ytterbium-doped fiber amplifier; VOA variable optical attenuator; OPM optical power; PPLN periodically poled Lithium Niobate; OSA optical spectrum analyzer. SSB single sideband, SHG second harmonic generation. * indicates the use of optical filter if necessary, such as in the case of IM and PM

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The output of a 1560 nm laser is fed to an optical isolator to avoid any damage to the laser from back reflections. EOM being a nonlinear optical element, effect of input polarization is vital. Therefore, isolator’s output is then given to a PC, where the polarization state is optimized before it is fed into an EOM. This experiment is performed for four EOMs: IM (Covega-Mach-40™ 085), PM (Thor Labs-LN65S-FC), DDMZM (Fujitsu-FTM7921ER/051), and DPMZM or IQ modulator (Fujitsu-FTM7962EP/301), to obtain the best suitable modulation format for QAI. Considering the requirement of output with two frequencies separated by a fixed difference, equal to the hyperfine splitting of the ground state of 87Rb atoms or that corresponding to the cooling and re-pumping beams, we have used the full-carrier single-sideband (FC-SSB) modulation technique. The variation in power ratio of these two sidebands with the carrier is experimentally investigated and EOM with the best performance is identified at 18 GHz RF frequency due to the limited resolution of the optical spectrum analyzer. The same analysis applies to the 6–7 GHz RF frequency range for QAI.

The RF modulating signal is applied to the modulator using an RF source to generate a modulated optical signal. The power distribution in the carrier and sidebands can be controlled by applying a DC bias to the modulator in the case of IM, DDMZM, and DPMZM (Eq. 2). The applied DC allows to achieve FC-SSB in the case of DDMZM and DPMZM. However, a tunable optical filter is required to obtain FC-SSB in the case of IM and PM.

After achieving FC-SSB using an EOM, the optical signal is fed to the optical amplifier, Erbium–Ytterbium-doped fiber amplifier (EYDFA), followed by a variable optical attenuator, which gives an optical signal at 23 dBm for each modulation scheme.

The amplified optical signal is then sent to PPLN for the second harmonic generation. Being a nonlinear optical element, the input polarization at PPLN is critical to ensure it works with the highest possible conversion efficiency. Therefore, a combination of PBS with PC is used before feeding the 1560 optical signal to the PPLN. The output spectrum of PPLN is observed on an OSA, and powers in carrier and sidebands are recorded for various RF power values.

4 Results and discussion

The carrier at 1560 nm wavelength is modulated using an electrical signal. Depending on the power in the carrier and the first-order sideband at 1560 nm, there will be a change in power distribution in the carrier and sidebands after frequency doubling, as can be noticed from the sets of Eqs. (2) and (3).

The effect of RF modulation power at 1560 nm wavelength on the sideband-to-carrier ratio after frequency doubling is shown below for different modulators. To compare different modulation schemes, we focused on the RF power requirement for 0 dB sideband-to-carrier ratio (SBCR) for the 1st-order sideband. However, depending upon the considerations of detuning and the AC Stark shift compensation in QAI, the actual operation requires slightly different value of 1st-order SBCR. But, as it can be noticed from the results, the comparison will remain unaffected. Also, it is important to know the effect of 2nd-order sideband at this power level which may lead to noise in the detection if not suppressed well. Therefore, the variation in 2nd-order SBCR is also shown in the graphs.

4.1 Intensity modulator

Figure 3 shows the experimental and corresponding simulation results obtained from mathematical analysis of the system for sideband-to-carrier ratio variation with increasing RF power from 3 to 120 mW in IM with a tunable filter. Here, the simulations are performed by taking \({V}_{\pi ,rf}=5.5 V\) and \({V}_{\pi ,dc}=5.0 V\). Figure 3 shows the experimental results match well with the simulations at higher RF power for both the sidebands. The 0 dB 1st-order sideband-to-carrier ratio (SBCR) is achieved at 40 mW of RF power and the 2nd-order sideband is suppressed by almost 8 dB with respect to 1st-order sideband at this RF power.

Fig. 3
figure 3

Variation in sideband-to-carrier ratio (SBCR) after SHG (in dB) with increasing RF power for IM with tunable optical filter. Continuous lines show the simulated results, and * denotes experimental results

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4.2 Phase modulator

Figure 4 shows the experimental and corresponding simulation results for sideband-to-carrier ratio variation with increasing RF power from 3 to 120 mW in PM with a tunable filter. Here, the simulations are performed by taking \({V}_{\pi ,rf}=4.3 V\). As it can be noticed from Fig. 4 that for PM also, the experimental results match well with the simulations and the 0 dB 1st-order SBCR is achieved at 25 mW of RF power with more than 10 dB less 2nd-order SBCR.

Fig. 4
figure 4

Variation in sideband-to-carrier ratio (SBCR) after SHG (in dB) with increasing RF power for PM with tunable optical filter. Continuous lines show the simulated results, and * denotes experimental results

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4.3 Dual drive Mach–Zehnder modulator

Figure 5 shows the experimental and corresponding simulation results for sideband-to-carrier ratio variation with increasing RF power from 3 to 120 mW in DDMZM. Here, the simulations are performed by taking \({V}_{\pi ,rf}=5.5 V\) and \({V}_{\pi ,dc}=3.05 V\) with DC biasing of 9.25 V. As can be noticed from Fig. 5 for DDMZM, the experimental results for the first-order sideband match well with the simulations, while there is a slight deviation for the second-order sideband, possibly due to the slight variation in the experimental parameters. The 0 dB SBCR is achieved at the RF power slightly higher than 95 mW with almost 8 dB less 2nd-order SBCR.

Fig. 5
figure 5

Variation in sideband-to-carrier ratio (SBCR) after SHG (in dB) with increasing RF power for DDMZM. Continuous lines show the simulated results, and * denotes experimental results

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4.4 Dual parallel Mach–Zehnder modulator

Figure 6 shows the experimental and corresponding simulation results for sideband-to-carrier ratio variation with increasing RF power from 3 to 120 mW in DPMZM. Here, the simulations are performed by taking \({V}_{\pi ,rf}=4.1 V\) and \({V}_{\pi ,dc}=14 V\) with the three DC biasing of 3.18 V, 4.20 V, and 0.30 V. As can be noticed from Fig. 6, for the DPMZM, the experimental results show a slight deviation from the simulations, which could be due to the uncertainty in the values of \({V}_{\pi }\).

Fig. 6
figure 6

Variation in sideband-to-carrier ratio (SBCR) after SHG (in dB) with increasing RF power for DPMZM. Continuous lines show the simulated results, and * denotes experimental results

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The 0 dB 1st-order SBCR is achieved at the RF power slightly higher than 25 mW with more than 10 dB less 2nd-order SBCR.

From Figs. 3, 4, 5 and 6, it can be observed that the PM and DPMZM show better performance with a lower RF power requirement as compared to IM and DDMZM. Considering DPMZM for QAI application, it requires a minimum of three DC biases (six for a differential input configuration), which leads to a complex architecture with a higher form factor and difficult handling, whereas PM does not require any DC bias. Architecture-wise, it is the simplest EOM among the four modulators. A PM is also more stable in its operation and has a more linear response. Moreover, because of its straightforward architecture, PM is cheaper than other EOMs. Also, using PM, the output power can be stabilized using a voltage-tunable optical filter, which is easy to operate. Furthermore, using a voltage-tunable filter also leads to compactness and ease of operation. Table 1 provides a performance summary of various modulators for better comprehension, which indicates a PM with an adjustable filter is a potential option for this laser system.

Table 1 Comparison of all four EOMs in terms of RF power, DC bias and filter requirement
Full size table

5 Conclusion and future work

Simultaneous generation of two frequencies with specific power values is essential for the laser system used in quantum atom interferometry (QAI). One of the methods to achieve this requirement for 87Rb QAI is a full-carrier single-sideband (FC-SSB) modulation technique with an electro-optic modulator (EOM) in a laser system having a telecom laser source and frequency-doubled architecture. Considering the importance of the use of an EOM in a laser system for QAI, this paper particularly focuses on the experimental investigation of comparative performance of the four common EOMs, namely intensity modulator (IM), phase modulator (PM), dual-drive Mach–Zehnder Modulator (DDMZM), and dual-parallel Mach–Zehnder modulator (DPMZM). Simulation results produced from the mathematical analysis of the system supporting the experimental data are also presented.

The comparison of experimental data and corresponding simulation results for different modulators shows that for any required power levels of the two frequencies (1st-order SBCR), a PM with a tunable optical filter is the most suitable choice in this laser system. The use of PM leads to a cost-effective and stabilized laser system with simple architecture, small form factor, and low power consumption. Also, using a tunable filter can allow power stabilization and control, leading to a more compact system. However, development of the complete laser system for QAI needs every component of it to be optimized for the best performance, contributing least noise in the measurement performed using QAI. As in future work, the packaging of this laser system can be considered, which provides a very compact and robust solution for QAI sources with the least power consumption and high stability.