1. Introduction

A superluminal ring laser (SRL) is a type of laser in which the group velocity of light exceeds the vacuum speed of light, without violating causality or special relativity [1]. In recent years, it has been shown that an SRL exhibits enhanced spectral sensitivity compared to conventional ring lasers [2–12]. In general, the SRL requires a gain profile which has a narrow dip superimposed on a broader background [13–17]. Many possible techniques can be used to realize such a profile. The anomalous dispersion associated with such a gain profile has been studied under several different contexts [18–23]. Previously, we have proposed and studied various approaches for obtaining superluminal lasing, including Diode-Pumped Alkali Laser (DPAL) type gain combined with Raman depletion [24], double Raman gain [25], optically pumped Raman gain combined with self-pumped Raman depletion [26], and optically pumped Raman gain combined with optically pumped Raman depletion [27]. The approach employing the DPAL type gain has the disadvantage that the gain is bidirectional, thus making it difficult to realize two independent SRLs in the same cavity without gain competition or cross-talk, as needed for rotation sensing using the Sagnac effect. The other approaches do not suffer from this constraint, because of strong unidirectionality of Raman gain in a warm vapor [28,29]. However, these approaches require several different laser pump beams, thus making the systems highly complex. As such, there is a need for pursuing simpler techniques employing smaller numbers of lasers.

To this end, we recently showed [30] that it is possible to create the requisite gain profile using a scheme that employs only two lasers and a single isotope of Rb. In this scheme, an optical pumping beam produces a population inversion among two ground states, thus generating Raman gain in the presence of a Raman pump laser. Furthermore, for a sufficiently large power in the optical pumping beam, a dip in the gain profile is generated due to the Autler-Townes splitting, which is a manifestation of Electromagnetically Induced Transparency (EIT) in the strong-pump regime. In Ref. [30], the gain at the bottom of the dip was insufficient to exceed the lasing threshold. In this paper, we demonstrate the realization of superluminal lasing in such a system, employing EIT in Raman gain, by optimizing the operating parameters. The use of only two diode lasers and a single isotope of Rb make this approach potentially superior to more complex techniques demonstrated earlier. It should also be noted that because of the strong unidirectionality of the Raman gain process, it should be possible to realize a pair of counter-propagating SRLs in the same cavity using this approach, as needed for rotation sensing. Furthermore, the same two lasers can be used for generating the gain for both SRLs.

Each of the alternative approaches for realizing a rotation sensor with a superluminal laser previously investigated by us [25–27] requires the use of multiple Raman pumps. Because of the relatively large difference in frequencies for these Raman pumps, it is difficult to generate all of the Raman pumps using modulators. As such, we had used the technique of off-set phase locking to stabilize the relative phase between the Raman pumps. When the off-set phase lock system is operating optimally, the beat between them would be essentially a delta-function, with a width determined by the stability of the frequency source used for off-set phase locking. In practice, however, we and others [31] have found that the beat signal displays a broad pedestal, indicating imperfect phase-locking. The technique demonstrated here, in addition to simplifying the system, eliminates the need for off-set phase locking, since only one Raman pump laser is used, thus by-passing this problem altogether.

The rest of the paper is organized as follows. The experimental configuration is described in Section 2. The experimental results and analysis are presented in Section 3. We conclude the paper in Section 4.

2. Experimental configuration

For the EIT in Raman gain scheme, the relevant energy levels and the optical fields are shown in Fig. 1. The optical pump is applied on resonance with the 5S_1/2, F = 2 to 5P_1/2. The Raman pump is applied to couple the 5S_1/2, F = 3 to 5P_3/2 transition with a detuning of δ_p. Under these conditions, if a probe beam is sent through this medium, it will experience Raman gain in the vicinity of the two-photon resonance condition. The optical pump has two functionalities in this scheme. First, it produces population inversion between the two ground states, i.e. the hyper fine states F = 2 and F = 3 in the 5S_1/2 manifold. This is due to the fact that it excites the atoms from the 5S_1/2, F = 2 state to the 5P_1/2 manifold, from which the atoms decay to both ground states. After several iterations of this sequence of excitations and decay, the population in the 5S_1/2, F = 3 state becomes greater than that in the 5S_1/2, F = 2 state. Second, when the Rabi frequency of the optical pump is large enough, the 5S_1/2, F = 2 state splits into two effective states, without affecting the optical pumping mechanism. Under this condition, the gain spectrum experienced by the probe beam is split into two peaks and manifests a dip in the gain profile. The magnitude of the gain is maximum for δ_s=δ_p with δ_s being the frequency detuning of the probe field. To produce a negative dispersion, which is essential to create a superluminal laser, we increase the intensity of the optical pump. For a sufficiently large optical pump power, the spectrum of the gain experienced by the probe splits into two gain peaks that are separated by ∼Ω_op, which is the Rabi frequency of the optical pump. To estimate the actual degree of splitting, it is necessary to take into account the spread of velocities in the vapor cell. For zero velocity atoms, the splitting would be given by the Rabi frequency. For a non-zero velocity atom, there will be a detuning. If the detuning is comparable to the Rabi frequency, the splitting would be given by the generalized Rabi frequency, defined as the rms value of the detuning and the Rabi frequency. When the detuning is much larger than the Rabi frequency, the effect is a light shift, rather than splitting. As described later, in our experiment the Rabi frequency is estimated to be ${\sim} 9\Gamma $. On the other hand, the spread of velocities in the vapor cell produces mean detunings of ${\sim}{\pm} 50\Gamma $. Thus, most of the atoms contribute only light shifts symmetrically, which broadens the Raman gain spectrum. Only the atoms with detunings of the order of the Rabi frequency contribute significantly to the splitting. For atoms with a detuning of ${\sim}{\pm} 9\Gamma $, the generalized Rabi frequency is ${\sim} 13\Gamma $. The Raman gain profile is therefore expected to have a splitting close to this value, and some broadening due to the light shifts.

 

Fig. 1. Relevant energy levels and the optical fields in the EIT in the Raman gain scheme.

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The optical pump power is tuned to ensure that the separation between the peaks is somewhat smaller than the width of the envelope of the Raman gain spectrum. Consequently, the gain spectral profile exhibits a narrow dip on top of a broader background. If this gain medium is placed inside a cavity with the gain at the center of the dip being larger than the cavity loss, lasing action will occur. By tuning the experimental parameters, including Ω_op, Ω_p, δ_p, the cell temperature, and the cavity length, we are able to produce superluminal Raman lasing inside the cavity. In principle, the optical pump frequency can also be varied in order to optimize the superluminal laser. However, due to experimental constraints, as described later, we chose not to vary this parameter.

The experimental configuration is illustrated schematically in Fig. 2. The ring cavity is mounted on an invar plate, and enclosed in a vacuum chamber, with all the components being vacuum compatible. Two concave mirrors with a radius of curvature of 30 cm and a planar output coupler are used to construct the cavity. The concave mirrors are coated for high reflectivity and the output coupler has an intensity reflectance of 90%. One of the concave mirrors is attached to a piezoelectric transducer (PZT), enabling accurate control over the cavity roundtrip length. The total cavity length is 24.5 cm. By making use of the fact that the Raman gain is maximized when the Raman pump and the Raman laser are cross-polarized, the Raman pump is coupled into the cavity and dumped out through two polarizing beam splitters (PBSs). The same approach is used for inserting and extracting the optical pump beam. The two pump beams are combined outside the vacuum chamber and directed into the cavity through an observation port in the vacuum chamber. To match the spatial cavity mode size, which has a beam waist diameter of ∼268 µm, the combined pump beam is focused by a convex lens with a focal length of 15 cm. A Rb vapor cell with a length of 5 cm is placed inside the cavity, serving as the gain medium. During the experiment, the vacuum chamber is pumped down to ∼10 mTorr using a rotary vane pump. Evacuating the chamber substantially suppresses fluctuations in the cavity mode frequencies.

 

Fig. 2. Schematic of the experimental configuration of the vacuum chamber enclosed unidirectional superluminal ring laser.

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To determine the frequency of the Raman laser and monitor its power, we employ a multi-step process. First, the output of the cavity is combined with a portion of the Raman pump. The combined beam is then split into two parts. One part is directed into a low-speed photodetector (PD, Thorlabs PDA36A) for monitoring the power level. The other part is sent to a high-speed PD (Thorlabs RXM10CF) through a fiber. The high-speed PD, with a bandwidth of ∼10 GHz, is used for measuring the beat-signal between the Raman laser and the Raman pump. The beat signal is then mixed with a reference signal at 3.036 GHz, which is the separation between the F = 2 and F = 3 hyperfine states in the 5S_1/2 manifold. A frequency to voltage converter, made by Digital Optics Technologies, is then used to produce a voltage that is proportional to the difference between the frequency of the beat signal and the frequency of the reference signal.

The frequency of each pump laser is stabilized with the reference of an atomic transition using different techniques. Consider first the process for stabilizing the frequency of the optical pump laser. We use a commercial laser locking servo (Moku:Lab Laser Lock Box) to lock the frequency of the optical pump to the 5S_1/2, F = 2 to 5P_1/2, F′ = 2 transition, employing saturated absorption spectroscopy. This peak appears at essentially the center of the unsaturated absorption profile for the transition from the 5S_1/2, F = 2 to the 5P_1/2 manifold. As such, in our model, we treat the optical pump as being resonant with the 5S_1/2, F = 2 to 5P_1/2 transition, and the 5P_1/2 manifold is treated as a single level for simplicity. Consider next the process for stabilizing the frequency of the Raman pump laser. Since the Raman pump is tuned off resonance, its frequency cannot be directly locked to an atomic transition. Therefore, we send a portion of the Raman pump beam to an acoustic optical modulator (AOM), which produces a beam at a frequency downshifted by 1012 MHz. This frequency shifted beam is then sent through another saturated absorption spectroscopy setup and locked to the cross-over resonance occurring between the 5S_1/2, F = 3 to 5P_3/2, F′=3 and 5S_1/2, F = 3 to 5P_3/2, F′=4 transitions. Again, for the sake of simplicity, we treat the 5P_3/2 manifold as a single level in our theoretical model. The locking configuration described above thus corresponds to a pump detuning (δ_p) of approximately 1 GHz.

It is not a priori obvious that the frequency we have chosen here for the optical pump is necessarily optimal for the superluminal Raman laser. As such, one might want to implement the option of varying the frequency of the optical pump around this value. However, this would require the use of the off-set frequency locking technique, similar to the one described above for the Raman pump. The frequency off-set needed in this case would have to be continuously tunable, down to a null value. Since the lowest frequency shift that can be produced with an AOM is of the order of 35 MHz, this process would require the use of two different AOMs, one of which would shift the frequency up and the other would shift the frequency down. We plan to implement such a scheme in order to investigate the effect of detuning the frequency of the optical pump. However, for the initial demonstration reported here, we have chosen to use a resonant optical pump.

3. Results and analysis

As mentioned above, to realize the superluminal condition for the Raman laser, it is necessary to produce a negative dispersion in the gain medium. Clearly, the gain and dispersion experienced by a weak probe beam in the absence of a cavity are somewhat different from the effective gain and dispersion experienced by the Raman laser due to saturation effects. Therefore, the effect of the dispersion experienced by the Raman laser is determined indirectly by measuring the output power as a function of the lasing frequency, by tuning the cavity length. The output powers of the Raman laser as functions of the cavity length are presented in Fig. 3, for three different levels of optical pump power. In all cases the cell is at a temperature of ∼90°C, and the power of the Raman pump is 4.2 mW. As can be seen, Raman lasing with different power variation profiles were produced for different values of optical pump power. As the optical pump power increases, the profile first splits from a single peak to two peaks, where the separation between the peaks increases with increasing optical pump power.

 

Fig. 3. The cavity output as functions of the cavity length scan for (a) a conventional Raman laser with optical power of 31.8 mW, (b) and (c) the EIT in Raman gain configuration with optical pump powers of 48.0 mW and 60.2 mW, respectively. The cell temperature is ∼90°C for these data.

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The conventional Raman laser output power as a function of the cavity length is shown in Fig. 3(a). As can be seen, under the conventional Raman lasing condition with a relatively low optical pump power, a single gain peak is observed. In Fig. 3(b), we show the cavity output when scanning the cavity length under the EIT in Raman gain condition. The output of the laser splits into two peaks, where the separation between the peaks is determined by the Rabi frequency of the optical pumping transition and the velocity spread of the atoms, as discussed earlier. It should also be noted that the maximum output power is lower than that for the conventional Raman laser case shown in Fig. 3(a). When the optical pump power is increased further, the splitting between the peaks increases and the peak output power is reduced further, as shown in Fig. 3(c).

To estimate the dispersion experienced by the Raman laser field, we utilized the density matrix approach [30,32] to determine the susceptibility of the 4-level system shown in Fig. 1, and solve the single mode laser equations [33] to find the steady state solutions for the lasing power and the lasing frequency. This calculation is repeated while varying the length of the laser cavity. Since the dip in the gain profile in Fig. 3(b) is significantly smaller than the same in Fig. 3(c), we focus only on the data shown in Fig. 3(c) for comparison with theoretical simulation. In Fig. 4(a), we show comparison between the results of this theoretical model and the experimental results shown in Fig. 3(c). Because of some practical constraints [34], it is difficult to determine accurately the effective diameters of the Raman pump and the optical pump. The pump beams also diverge when propagating through the Rb vapor cell. Therefore, we use the beam diameters of the pumps as fitting parameters to match the simulation results to the experimental data. The beam diameters of the Raman pump and the optical pump used for generating Fig. 4 are 349.7 µm and 2.03 mm, respectively. The other parameters (powers of the pump beams, cell temperature, and cavity dimensions) are identical to those used in the experiment. For these parameters, the Rabi frequency for the optical pump is ${\sim} 9\Gamma $. As discussed earlier, this value of the Rabi frequency is expected to produce a splitting roughly of the order of ${\sim} 13\Gamma $, which corresponds to 78 MHz. The observed separation between the peaks in Fig. 4(a) is ∼80 MHz, which is close to this rough estimate.

 

Fig. 4. (a) The experimental results and the corresponding simulation results and (b) the inferred SEF as functions of the cavity length scan for the optical power of 60.2 mW.

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It should be noted that the scale of the output power for the simulation is significantly larger than that for the experimental result. This is most likely attributable to a combination of factors. First, it is difficult to take into account sources of loss inside the cavity from elements such as the cell windows and the polarizing beam splitters. Second, it is hard to determine the actual temperature, and therefore the density, of the atoms. Third, when the cavity is tuned via linear displacement of one of the cavity mirrors, the propagation loss likely increases significantly; however, it is not easy to determine the nature of this variation in the propagation loss.

It should also be noted that the model used for generating Fig. 4 is an approximation employing only four energy levels, thus ignoring details such as the presence of additional hyperfine levels in the excited state manifold, and the Zeeman sublevels within each hyperfine state. Thus, the match between the experiment and the simulation is not perfect. To obtain more rigorous simulation results that should agree better with the experiments, a more complete model that includes all the hyperfine levels and the Zeeman levels is necessary. While we have developed such codes previously in a different context, carrying out the simulation for this experiment with such a code is extremely time consuming for two reasons. First, we need to carry out velocity averaging over the Doppler width. Second, an iterative method has to be used to find the solution to the laser equations. Work is in progress to carry out such a simulation, along with detailed characterization of various loss mechanisms, in order to achieve better convergence between the simulation and the experiment, and findings of this study will be reported in the near future.

Figure 4(b) shows the inferred sensitivity enhancement factor (SEF) according to parameters used for generating Fig. 4(a). This plot is generated as follows: We start with a cavity length that corresponds to the minimum of the output power in the vicinity of the dip. We then perturb the cavity length and determine the change in the frequency of the Raman laser. This change is then compared with the corresponding change in the resonant frequency of an empty cavity for similar perturbation of the cavity length. The ratio of the change in the frequency of the Raman laser to the change in the frequency of the empty cavity is defined as the SEF. As can be seen in Fig. 4(a), the value of the SEF is not constant, and depends on the amplitude of the change in the cavity length. The peak value of the SEF is found to be ∼360.4 for a very small change (∼6 pm) in the cavity length.

To determine experimentally the spectral sensitivity of the Raman laser, we measure the lasing frequency shift caused by a small perturbation in the cavity length. To carry out this measurement, we extract the frequency information from the beat-signal (between the Raman laser and the Raman pump) when the Raman laser is operating at the center of the dip employing the following procedure. We first tune the offset voltage applied to the PZT to move the lasing frequency to the center of the dip. Then a sinusoid modulation signal (with a frequency of 9 Hz), whose amplitude corresponds to a variation of ∼±0.75 nm in the cavity length, is applied to the PZT. Consequently, the output frequency of the Raman laser is modulated at the same frequency (9 Hz). A frequency demodulator is used to measure the corresponding frequency shifts in the beat-signal. The output of the demodulator is a voltage level which is proportional to the frequency shift in the beat-signal, as shown in Fig. 5.

 

Fig. 5. Lasing frequency shift of the Raman laser and the expected empty cavity resonance frequency shift with the same cavity length for (a) operating in the vicinity of the center of the dip in Fig. 3(c), and (b) operating on the side of the gain spectrum. (c) A comparison between (a) and (b). In (a), both curves use the same vertical scale, while in (b) and (c), the left y-axes are for the black curves and the right y-axes are for the red curves.

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Figure 5(a) includes two curves. The red curve shows the theoretically expected change in the frequency of the empty cavity for the applied voltage to PZT, which was determined via the following procedure. Before producing lasing, a probe beam was sent through the cavity at a frequency that is away from any atomic resonance. A ramp voltage was applied on the PZT to produce a change in the cavity length that corresponds to more than one free spectral range. The coefficient that converts the PZT voltage to the empty cavity resonance frequency was then measured from this process. It should be noted that the optical components inside the cavity, including the Rb vapor cell and the polarizing beam splitters, were not removed during this calibration process, since removal of these components would modify the cavity mode. As such, what we mean by the “empty cavity” actually contains the walls of the glass cell and the polarizing beam splitters. The residual noise in the red curve is due to the corresponding noise in the voltage applied to the PZT. The black curve shows the measured change in the frequency of the Raman laser when operating at the bottom of the dip in the output power shown in Fig. 3(c). The measured maximum frequency shift is ∼0.89 times that of the empty cavity resonance frequency shift.

In Fig. 5(b), the red curve again shows the theoretically expected change in the frequency of an empty cavity, while the black curve shows the measured change in the frequency of the Raman laser when operating on the side of the lasing peak shown in Fig. 3(c) and far away from the dip. To explain the meaning of the result shown here, we recall first that the dip that produces superluminal condition is achieved by increase the power in the optical pump. As such, it is difficult to turn off the superluminal condition without modifying other parameters. Moreover, due to the relatively broad gain profile of the Raman laser, when operating on the side of the same lasing peak but far away from the dip, the dispersion of the dip is insignificant. As such, the behavior of the superluminal Raman laser when operating on the side of the lasing peak can be considered to the be similar to that of a conventional Raman laser with the same experimental parameters. It should be noted that a conventional Raman laser is a subluminal laser, whose SEF is usually much smaller than unity. Therefore, we applied a larger voltage to the PZT to acquire a clearer output signal. The measured maximum frequency shift is ∼0.07 times the empty cavity resonance frequency shift. It should also be noted that for a conventional (i.e., subluminal) Raman laser, the value of the SEF is highly insensitive to the value of the change in the cavity length, as well as any shift in the operating frequency away from center of the dispersion profile. A comparison between the two cases discussed above is shown in Fig. 5(c). The black and red curves correspond to the measurements when the Raman laser operates at the center of the dip and far away from the dip but in the same mode, respectively. If we consider the conventional Raman laser as the reference, the EIT in the Raman gain scheme improves the spectral sensitivity of the Raman laser by a factor of ∼12.7.

In order to determine the frequency shift in a superluminal laser when a sinusoid modulation signal is applied to the cavity length, it is important to account for the fact that the SEF in this case is highly non-linear. The SEF presented in Fig. 4(b) was obtained using the numerical model that considers a 4-level system, including velocity averaging, and solves iteratively the Liouville equation and the laser equations simultaneously. This plot was generated using a step size of 6 pm for cavity length variation, dL. When a sinusoidal voltage is applied to the PZT, the value of dL gets scanned continuously, including the null value and very small values. Thus, in order to determine accurately the corresponding frequency shifts in the superluminal laser, it is necessary to make use of a step size of dL that is much smaller than what was used in generating Fig. 4(b). However, carrying out the numerical analysis using the iterative algorithm becomes extremely time consuming when a very small step size is used for dL. Furthermore, this model determines the final operating frequency and the laser power by stopping the iteration once a threshold value is reached for convergence. This thresholding mechanism introduces an artificial source of noise (as can be seen in Fig. 4(b)) in this model, which becomes more prominent when a very small step size is used for dL. Lowering the convergence threshold yields smoother plots, but at the cost of increasing the calculation time dramatically.

To circumvent this constraint, we resort to using an analytical model where the pre-lasing gain profile is approximated by two Lorentzians: one for the broad background and the other for the narrow dip [2]. Then the gain and the dispersion, as well as the operating frequency, are found analytically under the steady state lasing condition. Given the analytic expression for the lasing frequency found this way, it is then possible to determine the frequency shift for an arbitrarily small step size of dL. To use this model, it is necessary to estimate the parameters for the two Lorentzian profiles that approximate the 4-level model and the iterative solution of the laser equations. To this end, we first vary the parameters in the analytical model to generate a plot of the SEF as a function of the cavity length variation that matches closely the result of the numerical model. Specifically, we vary the parameters for the two Lorentzians until the SEF plots match in two different limits of dL: 6 pm and -4 nm. The first limit, 6 pm, is dictated by the fact that this is the smallest step size used in the numerical model. The second limit, -4 nm, is dictated by the fact that the SEF becomes nearly constant for values beyond this. The SEFs as functions of the cavity length change generated using the analytical model and the numerical model are illustrated in Fig. 6(a). It should be noted that the result for the numerical model shown as the blue trace in Fig. 6(a) is the same as the result shown earlier in Fig. 4(b), reproduced here for convenient comparison with the analytical model result.

 

Fig. 6. (a) The SEF as functions of the cavity length variation for the numerical (blue) and the analytical (red) models. The former is the same as the plot shown in Fig. 4(b)Fig. 4(b), reproduced here for convenient comparison. (b) The red plot is the calculated laser frequency shift of the superluminal Raman laser with the analytical SEF profile shown, and the black plot is the empty cavity resonance frequency shift when the cavity length is modulated with an amplitude of ∼±0.75 nm. (c) The measured (black) and the expected (red) frequency shift of the superluminal Raman laser for a PZT modulation of ∼±0.75 nm.

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We then calculate the expected frequency shift of the superluminal Raman laser using this effectively equivalent analytical model when a sinusoid modulation signal is applied to the cavity length with an amplitude of ∼±0.75 nm. The frequency shift in the superluminal Raman laser as a function of time in the presence of the cavity length modulation is shown as the red plot in Fig. 6(b). As a reference, we also generate the plot for the empty cavity resonance frequency shift for the same parameters (black plot in in Fig. 6(b)). It should be noted that the expected frequency shift is highly non-sinusoidal over the range where the cavity length is changed by a small amount (that is, in the vicinity of zero line of the y-axis), due to the strong non-linearity of the SEF.

In Fig. 6(c), we show a comparison between the measured and the expected frequency shifts of the superluminal Raman laser when a ∼±0.75 nm cavity length modulation is applied sinusoidally. Here, the black trace shows the measured frequency shifts, with the PZT modulated at 9 Hz. It should be noted that the original data was somewhat noisy, and we have applied a first order band-pass filter (with 3 dB cutoff edges at 7 Hz and 19 Hz) to produce the results shown here. The solid red trace shows the theoretically expected shift based on the analytical model. For a proper comparison between the experimental and theoretical results, we show in the dotted red trace the theoretically expected shift when the same band-pass filter is applied. Note that we have used a different vertical scale for the theoretical plots, as indicated on the right-hand side. As can be seen from these traces, the non-linearity evident in the unfiltered theoretical results are not observed in the experimental result. We believe this is due to the application of the band-pass filtering to the experimental result. When the experimental data is viewed without the band-pass filter, the non-linearity does not become evident due to the presence of the noise. In the future, attempts will be made to suppress the noise via stabilization of jitters in the Raman pump frequency, as described later in this section, in order to reveal the non-linearity.

Taking into account the two different scales used in Fig. 6(c), we see that the measured value is somewhat larger than the expected value. This difference is attributable to some extent to the fact that both the numerical and the analytical models are approximate. The limitation of the numerical model results from two factors: it does not consider the Zeeman sublevels within the hyperfine states, and it does not take into account all the hyperfine states. The resulting inaccuracy of the numerical model carries over to the analytical model, which is guided by the results of the numerical model. Carrying out a more detailed analysis that takes into account all the hyperfine levels and the Zeeman sublevels would be extremely time consuming, even with a supercomputer. Efforts are currently underway to develop such a comprehensive model, employing the N-level algorithm developed earlier by us [32], and findings from such a model and comparison thereof with the experimental results would be reported in the near future.

Due to the constraints in the experiment, it is difficult to modulate the PZT to produce peak-to-peak length variation small enough to correspond to a very large value of the SEF, with a reasonable signal to noise ratio. In the current design of the experiment, the dominant source of noise is the frequency fluctuation in the Raman pump. As demonstrated in Ref. [35], the frequency of the Raman laser has about the same amount of fluctuation as the Raman pump frequency. As such, we are unable to measure the peak when the cavity length is modulated with a small amplitude (∼6 pm) that yields maximum SEF predicted by the theory. To stabilize the frequency of the Raman pump, we are in the process of implementing a locking system which uses the Pound–Drever–Hall technique and an ultra-low expansion glass cavity with a finesse of ∼250,000. With such a system, the frequency of the Raman pump can be stabilized to less than 1 kHz. With this locking system, it should be feasible to measure the small frequency shift in the Raman laser produced by a few picometers of perturbation in the cavity length.

As discussed in Ref. [30], the gain mechanism employed here is a manifestation of electromagnetically induced transparency (EIT), as a limiting case of the Autler-Townes Splitting (ATS) effect. The transitions between these two regimes have been studied previously by others in different contexts [36–40]. In our case, the primary objective is to produce a gain profile that yields the degree of anomalous dispersion necessary for superluminal operation of the laser. As such, a detailed exploration of different regimes of operation in the context of ATS versus EIT is beyond the scope of this work.

4. Conclusions

In this paper, we present experimental demonstration of a superluminal laser in which the optical pumping laser plays dual roles. It creates the ground state population inversion necessary for generating Raman gain. In addition, it produces a dip in the gain profile necessary for anomalous dispersion via electromagnetically induced transparency, thus obviating the need for a different isotope for generating such a dip, and simplifying the operation of the superluminal laser. Compared to an empty cavity, the peak value of the sensitivity enhancement factor under optimal operation parameters is inferred to be ∼360, based on comparison with a theoretical model. We also measure the sensitivity enhancement factor (SEF) of such a laser under different conditions. Compared to a conventional Raman laser with similar operating parameters but without the dip in the gain profile, the SEF for the superluminal Raman laser is demonstrated to be enhanced by a factor of ∼12.7.