We present a theoretical analysis of the cavity lifetime of a superluminal laser. In contrast to the naive intuition, the lifetime is only slightly shorter than that of conventional lasers, facilitating ultra-sensitive sensors.
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.
Abstract : We demonstrated that an optical laser can operate with less than 1 photons on average inside the cavity while also obtaining significant spectral narrowing of the emitted light relative to the single atom transition linewidth. We further explored the power output properties and threshold conditions of this laser. We made direct measurements that showed that the lasing frequency can be made greater than 10000 times less sensitive to the resonance frequency of the optical cavity than is the case for normal lasers or for passive optical reference cavities. Such a large reduction in sensitivity would essentially remove both thermal and technical mirror vibrations as a limitation on laser linewidth. Other studies included how phase information can be stored and manipulated inside of our laser, such that it may be possible to have both an active laser and a passive Ramsey-like sensor in the same setup. We considered the fundamental limits on the atomic quantum information that can be extracted from the laser light and found that it corresponded closely to the fundamental atomic standard quantum limit on phase estimation.
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.