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We have theoretically and experimentally investigated the laser-detected magnetic resonance induced by radio-frequency two-photon processes in ${F}_{g}=4$ of ${D}_{1}$ line of cesium atoms. The effective Hamiltonian for the interaction between the two radio-frequency magnetic fields and sublevels at the ground state of ${F}_{g}=4$ is derived. By appropriately selecting the frequencies of the two radio-frequency fields, the Raman two-photon process and the cascade two-photon process can occur, which induce the magnetic resonance detected through laser transmission spectra. The theoretical calculation results fit well with the experimental data. Our results maybe apply for measuring the high bandwidth radio-frequency magnetic fields in space and studying the magnetic-induction tomography.

By constructing a quantum filtering system to synthesize the spectral and spatial properties of stimulated radiation, the directionality of spectrally correlated nonclassical properties of resonance fluorescence from a three-body quantum antenna is investigated. The quantum antenna consists of three two-level quantum emitters, two of which are identical and strongly driven by an external laser field to radiate the collective resonance fluorescence with three distinct spectral components. The collective stimulated radiation is shaped by the remaining auxiliary emitter via its spontaneous emission, which is assumed to be resonant with the higher-frequency spectral component of the two identical emitters. Due to the presence of the auxiliary emitter, highly directional nonclassicality of the spectral correlations can be generated, which is the consequence of the internal interference of the source and the spatial interference of the radiation field. The electric dipole-dipole interaction between the undriven emitter and the dressed two-body radiating source plays a crucial role in breaking the rotational symmetry of nonclassical signals, which is embodied by various photon correlation functions with a frequency-resolved version for different spectral combinations. By correlating the two opposite sidebands, the frequency-resolved intensity-intensity correlation functions can signal highly directional nonclassicality, and the frequency-resolved two-mode entanglement along a specific emission direction can be tested by the frequency-resolved anomalous correlation function. While the directional nonclassical correlations between the central-frequency and the three-body collective higher-frequency components can be identified through the frequency-resolved intensity-field correlation function. These various frequency-resolved correlation functions characterize the spatial asymmetry of nonclassical properties of the collective stimulated radiation from different perspectives, including the particle properties and the quantum coherences of the filtered photons. When the three-body collective higher-frequency sidebands are correlated with the central band and the lower-frequency sideband, respectively, the schemes of using the auxiliary undriven emitter to generate optimal nonclassical correlations with well-defined directions are discussed analytically. In addition, the results obtained from the three-body quantum antenna and a dressed two-body quantum antenna are compared.

We investigate the absorption spectra for the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=0$ transition of the ${D}_{2}$ line of $^{87}\mathrm{Rb}$ excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.

Two different schemes are proposed for deterministically generating a pure motion-entangled state for two well-separated ions trapped in a cavity. The first one is that through adjusting the amplitudes and the frequencies of transverse lasers, the two ions trapped in a bimodal cavity can unconditionally evolve into a two-mode squeezed vacuum state with the aid of the cavity dissipation. The second one is based on the interactions of two appropriate series of the driving laser pulses with the two ions trapped in a single-mode cavity, it allows us to produce a two-mode squeezed vacuum state for the trapped ions' center-of-mass motion.

The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength ${r}_{1}$ of the coupling between the first ion and the cavity field is stronger than the strength ${r}_{2}$ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When ${r}_{1}l{r}_{2}$, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.