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Physical Review A

Synchronization with harmonics in an injected nuclear-magnetic-resonance laser

Yu. V. Pavlov, А.Н. Пивкин, R. M. Umarkhodzhaev, E G Lariontsev

Published Sep 8, 2010• 2 citations
Publisher

Abstract

In injected lasers, only synchronization of the order $1/1$ (when a frequency of laser oscillations becomes equal to the master laser frequency) is usually observed. Such locking appears due to single-photon transitions in a laser. We show that with the use of multiple-photon transitions a higher-order synchronization can arise. We present the results of numerical simulations and the preliminary experimental observations, which demonstrate that in the mercury NMR laser, with the use of triple-photon transitions, a frequency of locked laser oscillations becomes three times higher than the frequency of an external rf magnetic field. Such synchronization appears only in the case of a linearly polarized (oscillating) external magnetic field. For the circularly polarized (rotating) external field, only synchronization of the order $1/1$ is possible.

DOI
10.1103/physreva.82.033802

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In injected lasers, only synchronization of the order 1/11/11/1 (when a frequency of laser oscillations becomes equal to the master laser frequency) is usually observed. Such locking appears due to single-photon transitions in a laser. We show that with the use of multiple-photon transitions a higher-order synchronization can arise. We present the results of numerical simulations and the preliminary experimental observations, which demonstrate that in the mercury NMR laser, with the use of triple-photon transitions, a frequency of locked laser oscillations becomes three times higher than the frequency of an external rf magnetic field. Such synchronization appears only in the case of a linearly polarized (oscillating) external magnetic field. For the circularly polarized (rotating) external field, only synchronization of the order 1/11/11/1 is possible.
In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency or the amplitude of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency-, or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic mmm of the Larmor frequency ${\ensuremath{\omega}}_{L}$ (either by DC or phase sensitive detection at harmonics qqq of the modulation frequency ${\ensuremath{\omega}}_{\mathrm{mod}}$) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum FFF in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated light.
We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n \pm 1)th harmonic. For an irradiating field2H_{1} \cos \omegat of pulsation ω such thatn\omega= \gamma H_{0}=\omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesS\min{n}\max{n}andS\min{n}\max{n+1}of these components are given byS\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n},S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) \omega, n\omega, or(n + 1) \omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.
We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided appropriate phase matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We suppose the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold and even in the absence of an inversion. In these cases the steady state laser frequency is locked to the atomic line center. As the excitation increases, the ability of the injected atomic coherence to lock the laser frequency decreases. Slightly above the usual laser threshold, the system unlocks and produces an output weakly modulated in time.
The all-optical control of the polarization in a vectorial bistable monomode laser by injection with a second laser is analyzed theoretically and performed experimentally. The polarization is shown to switch following either an externally induced rotation or an externally induced inhibition mechanism. The usual theory of scalar-locking phenomena is extended to vectorial systems. We show that there is a single locking range in the induced rotation process occurring for low phase anisotropy values, whereas there are two distinct locking ranges in the induced inhibition process for higher anisotropy values. The theoretical results are in good agreement with experiments realized with 3He–20Ne lasers. By scanning the injected signal frequency, optical gates with high signal-to-noise ratios are experimentally obtained.
Superradiant lasers based on atomic ensembles exhibiting ultranarrow optical transitions can emit light of unprecedented spectral purity and may serve as active atomic clocks. We consider two frequency-detuned active atomic clocks, which are coupled in a cascaded setup, i.e., as master and slave lasers, and study the synchronization of the slave to the master clock. In a setup where both atomic ensembles are coupled to a common cavity mode, such synchronization phenomena have been predicted by Xu et al. [M. Xu, D. A. Tieri, E. C. Fine, J. K. Thompson, and M. J. Holland, Phys. Rev. Lett. 113, 154101 (2014).] and experimentally observed by Weiner et al. (J. M. Weiner et al., arXiv:1503.06464). Here we demonstrate that synchronization still occurs in cascaded setups but exhibits distinctly different phase diagrams. We study the characteristics of synchronization in comparison to the case of coupling through a common cavity. We also consider synchronization through a classical channel where light of the master laser is measured phase sensitively and the slave laser is injection locked by feedback and compare to the results achievable by coupling through quantum channels.
Abstract We have observed the Autler–Townes (AT) effect in single- and suspected double-photon magnetic-dipole transitions in the Cesium ground-state magnetic-sublevel manifold. Experiments were performed in a Cesium vapor cell at room temperature. The D1 line was excited by laser radiation to create ground-state optical polarization, and transitions between the ground-state magnetic sublevels were excited by radio-frequency (RF) radiation. Two different excitation geometries were studied: in one case the electric field vector of the linearly polarized laser radiation was parallel to the static magnetic field, whereas in the other case these vectors were perpendicular. The oscillating magnetic field produced by the RF coils was in the plane perpendicular to the electric field vector of the laser radiation. The AT effect was confirmed by its linear dependence on the RF magnetic field amplitude, which is proportional to the Rabi frequency, in the case of single-photon transitions. With increasing RF power we also observed peaks that by their position appeared to correspond to double and even triple photon transitions, which were more pronounced when the DC magnetic field and optical electric field vectors were perpendicular. In the peak at an energy that corresponds to two photons, splitting with a quadratic dependence on the RF magnetic field amplitude could be observed. The experimental measurements are supplemented by theoretical calculations of a model J = 1 ⟶ J = 0 system.