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arXiv:2312.15841 · Physical Review A

Strong frequency correlation and anticorrelation between a Raman laser and its pump laser for positive and negative dispersions

Zifan Zhou, Ruoxi Zhu, M. S. Shahriar

Published Jun 14, 2024• 0 citations
arXivHTMLPDF

Abstract

We show that the frequency of a Raman laser is highly correlated or anticorrelated with the frequency of the Raman pump laser, depending on whether the dispersion experienced by the Raman laser is positive or negative. For a subluminal laser, corresponding to a positive dispersion with a group index that is much larger than unity, the shift in its frequency is approximately the same as that in the Raman pump laser. In contrast, for a superluminal laser, corresponding to a negative dispersion with a group index that is close to zero, its frequency shifts in the direction opposite to that of the Raman pump lasers and has an amplitude that is larger by a factor approximately equaling the inverse of the group index. These findings would play a critical role in determining the maximum achievable sensitivity of sensors employing such lasers, especially under conditions where the pump laser linewidth is broadened significantly beyond the Schawlow-Townes linewidth due to classical fluctuations.

DOI
10.1103/physreva.109.063513

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We show that the frequency of a Raman laser is highly correlated or anticorrelated with the frequency of the Raman pump laser, depending on whether the dispersion experienced by the Raman laser is positive or negative. For a subluminal laser, corresponding to a positive dispersion with a group index that is much larger than unity, the shift in its frequency is approximately the same as that in the Raman pump laser. In contrast, for a superluminal laser, corresponding to a negative dispersion with a group index that is close to zero, its frequency shifts in the direction opposite to that of the Raman pump lasers and has an amplitude that is larger by a factor approximately equaling the inverse of the group index. These findings would play a critical role in determining the maximum achievable sensitivity of sensors employing such lasers, especially under conditions where the pump laser linewidth is broadened significantly beyond the Schawlow-Townes linewidth due to classical fluctuations.
We study theoretically the lasing properties and the cavity lifetime of super and sub-luminal lasers. We find that obtaining the necessary conditions for superluminal lasing requires care and that a laser operating under these conditions can under some conditions tend towards bi-frequency lasing. In contrast, conditions for a subluminal laser are less stringent, and in most situations its steady-state properties are well predicted by the self-consistent single-frequency laser equations. We also study the relaxation time of power perturbation in super and sub-luminal lasers using a finite-difference-time-domain tool and present the impact of the lasing power, the group velocity and the dispersion properties of the cavity on the relaxation dynamic of such perturbations. For the subluminal laser, we find that the time constant changes by a factor that is close to the group index. In contrast, for the superluminal laser, we find that the time constant does not change by the factor given by the group index, and remains close to or above the value for an empty cavity. These finding may be interpreted to imply that the quantum noise limited linewidth of the subluminal laser decreases with increasing group index, while the same for the superluminal laser does not increase with decreasing group index. The implications of these findings on the sensitivity of sensors based on these lasers are discussed in details.
Use of a double-Raman pump applied to a three-level system is a convenient method for generating negative dispersion. When the gain at the center is high enough, such a system can be used to realize a superluminal laser, which in turn can be used to enhance the sensitivity of rotation sensors. For this condition, it is often necessary to apply strong pumps that are closely spaced in frequency. Accurate modeling of this system thus requires taking into account interference between the two pumps. We present such an analysis where we allow for an arbitrary number of harmonics that result from this interference, and investigate the behavior of the gain profile under a wide range of conditions. We also describe an experimental study of double-Raman gain in a Rb vapor cell, and find close agreement between the experimental result and the theoretical model. The technique reported here can be used in developing a quantitative model of a superluminal laser under wide-ranging conditions.
In this paper, we report a Raman laser which is extremely sensitive to a variation of the cavity length, using a scheme employing two stable isotopes of Rb. One isotope is used for producing a broad gain spectrum via the optically pumped Raman gain process, while the other is used for producing a narrow dip via the optically pumped Raman depletion process. By tuning the frequencies of the two Raman pumps, the center frequencies of the gain and dip can be aligned to the same frequency. This approach allows tuning of the gain and dip parameters independently over a broad range of operating conditions. With such a configuration, we can produce a negative dispersion around the two-photon resonance frequency in the vapor cell, which leads to a group index that is close to zero. By theoretically matching the experimental observations, we can infer that the sensitivity of such laser is enhanced by a factor of more than 2800, which is nearly a factor of three larger than the highest value reported previously using a different approach.
Superluminal lasers operate under the condition in which the average group velocity in the cavity exceeds the vacuum speed of light, or alternatively, the group index is between 0 and 1 [1]. It has been shown in previous works that the sensitivity of the lasing frequency of such a laser with respect to a change in its optical roundtrip due to an external perturbation is expected to be substantially larger than that of a conventional laser, with an enhancement factor which is inversely proportional the group index [2]. This property makes superluminal lasers highly attractive for various sensing applications, primarily for challenging tasks such as gravitational wave detection and navigation grade rotation sensing. The realization of superluminal lasers requires the presence of a narrow dip in the center of a broad gain profile. The depth and width of the dip must be tailored carefully to produce the required dispersion profile yielding the enhanced sensitivity.
We investigate the feasibility of realizing a superluminal ring laser with enhanced sensitivity by using the gain produced via double-Raman pumping in an inverted three-level system. If the laser cavity is tuned to the center between the two gain peaks produced in such a system, it is expected to experience an effective negative dispersion, which can be tuned to the condition necessary for enhancing the sensitivity of the laser frequency to a change in the cavity length. Using a model of two idealized, independent Lorentzian gains, we solve the laser equations to show the enhancement of sensitivity. We then extend our analysis to calculate the gain profile in a real lambda system. Unlike the idealized system mentioned above, where the dual gain peaks are modeled as two adjacent Lorentzians in a manner that ignores the relative coherence between the Raman pumps, we present a more accurate model where this coherence is not neglected. As such, the Hamiltonian remains time dependent after making the rotating wave transformation. Using an approximation --- valid for practical systems --- where higher order terms in the density matrix are neglected, we determine the gain experienced by a weak probe beam. Numerical techniques are needed to incorporate the resulting gain and dispersion profiles into the laser equation to determine accurately the behavior of the superluminal laser. This work will be carried out in the near future. Experimental realization of a superluminal laser based on this approach may prove to be easier than other approaches proposed previously.
Generation of frequency correlated laser beams is of importance in various applications, in particular, for extending the frequency of the laser Raman microwave clock1 into the millimeter region where acoustooptic methods are not available. We propose and demonstrate an all-optical technique for such a purpose. The technique is based on the recently observed Raman-shifted oscillation2 that occurs when a three-level atomic system of Λ type is optically pumped and placed in a ring cavity. Our initial experiments are performed in sodium vapor pumped by a cw ring dye laser. Raman-shifted oscillation, detuned from the pump laser by 1.772 GHz which is the ground state hyperfine splitting of sodium, occurs in the wings of the Doppler broadened D1 line. This Raman-shifted oscillation is demonstrated to be highly frequency correlated with the pumping laser when the two are heterodyned on a fast photodetector. In our experiments the heterodyne beat signal at 1.772 GHz had a linewidth as low as 17 kHz, whereas the pumping laser has a rms frequency fluctuation of 300 kHz. The beat signal stays narrowband when the pumping laser is unlocked from the reference cavity increasing its rms frequency fluctation to ~10MHz.