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arXiv:1802.08874 · Physical Review A

Phase-locked bifrequency Raman lasing in a double- Λ system

Hadiseh Alaeian, M. S. Shahriar

Published May 21, 2018• 3 citations
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Abstract

We show that it is possible to realize simultaneous Raman lasing at two different frequencies using a double-$\mathrm{\ensuremath{\Lambda}}$ system pumped by a bifrequency field. The bifrequency Raman lasers are phase-locked to one another and the beat-frequency matches the energy difference between the two metastable ground states. Akin to a conventional Raman laser, the bifrequency Raman lasers are expected to be subluminal. As such, these are expected to be highly stable against perturbations in cavity length and have quantum noise limited linewidths that are far below that of a conventional laser. Because of these properties, the bifrequency Raman lasers may find important applications in precision metrology, including atomic interferometry and magnetometry. The phase-locked Raman laser pair also represent a manifestation of lasing without inversion, albeit in a configuration that produces a pair of nondegenerate lasers simultaneously. This feature may enable lasing without inversion in frequency regimes not accessible using previous techniques of lasing without inversion. To elucidate the behavior of this laser pair, we develop an analytical model that describes the stimulated Raman interaction in a double-$\mathrm{\ensuremath{\Lambda}}$ system using an effective two-level transition. The approximation is valid as long as the excited states adiabatically follow the ground states, as verified by numerical simulations. The effective model is used to identify the optimal operating conditions for the bifrequency Raman lasing process. This model may also prove useful in other potential applications of the double-$\mathrm{\ensuremath{\Lambda}}$ system, including generation of squeezed light and spatial solitons.

DOI
10.1103/physreva.97.053829

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We show that it is possible to realize simultaneous Raman lasing at two different frequencies using a double-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system pumped by a bifrequency field. The bifrequency Raman lasers are phase-locked to one another and the beat-frequency matches the energy difference between the two metastable ground states. Akin to a conventional Raman laser, the bifrequency Raman lasers are expected to be subluminal. As such, these are expected to be highly stable against perturbations in cavity length and have quantum noise limited linewidths that are far below that of a conventional laser. Because of these properties, the bifrequency Raman lasers may find important applications in precision metrology, including atomic interferometry and magnetometry. The phase-locked Raman laser pair also represent a manifestation of lasing without inversion, albeit in a configuration that produces a pair of nondegenerate lasers simultaneously. This feature may enable lasing without inversion in frequency regimes not accessible using previous techniques of lasing without inversion. To elucidate the behavior of this laser pair, we develop an analytical model that describes the stimulated Raman interaction in a double-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system using an effective two-level transition. The approximation is valid as long as the excited states adiabatically follow the ground states, as verified by numerical simulations. The effective model is used to identify the optimal operating conditions for the bifrequency Raman lasing process. This model may also prove useful in other potential applications of the double-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system, including generation of squeezed light and spatial solitons.
The technology of generating Raman laser is not only an important research content in the field of quantum precision measurement, but also a core technology of quantum inertial sensors such as cold atom gravimeter, gyroscope. For 87Rb atoms, two 780-nm lasers with a frequency difference of 6.834 GHz and a stable phase are needed to generate Raman light. Raman lasers can be generated by optical phase-locked loops of two 780-nm narrow linewidth external cavity tunable semiconductor lasers (ECDL). But the system thus developed is complicated in structure and very poor in environmental adaptability. The other method to generate Raman laser is based on intracavity 1560-nm laser with frequency doubling and electro-optic modulation technology. This system is simple in structure and strong in environmental adaptability, but it will introduce sideband effects and cannot achieve phase lock due to the limit by the linewidth and feedback bandwidth performance of the laser. In view of this, based on two new 1560-nm external cavity lasers and a home-made phase-locked circuit, in this paper the phase lock of the laser is achieved, and a Raman laser with low phase noise is obtained. The phase noise of beat note signal is as low as –95 dBc/Hz at the Fourier frequency in a range from 1 kHz to 10 kHz. A comparison of this system with the phase-locked performance of the 780-nm dual laser and the hybrid dual laser shows that this scheme has a slight advantage. In addition, the effect of the phase-locking performance on the phase noise of the cold atom interferometer through the method of piecewise integration is analyzed in this work. The experimental results given in this work provide a scheme for developing a miniaturized Raman optical system suitable for external fields.
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.
The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.
We consider a four-level atomic system with a degenerate or quasidegenerate ground-state doublet and two excited states. One of the upper levels is coupled to the ground doublet by a coherent field of variable strength, which we refer to as the Raman field, whose role is to create atomic coherence between the driven atomic states. The other higher lying state is coupled to the ground states when laser action develops. This model includes an incoherent pump mechanism to create some population in the top lasing state. In appropriate conditions, for the incoherent pump rate and the Raman field strength, the absorption profile of the laser transition develops gain features. We discuss the physical origin of this gain which we find to be the consequence of a population inversion between dressed atomic states. It is interesting to compare the results of this analysis with a similar study of a three-level lambda system which was previously recognized to yield lasing without inversion.1 In this case the appearance of gain can be attributed to the induced atomic coherence.