We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits.
We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits.
We study a classically driven two-level system in a harmonic trap and a lossy two-mode cavity, with the first mode being resonant to the driving field and an electronic transition, and the second mode being off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we compute the steady state as well as the time evolution of the photon statistics. We further investigate the photon correlations of both the cavity modes and identify the laser parameters and coupling strength that give the nonclassical sub-Poissonian property. The work is useful for coherent control of photon statistics and photon correlations in the trapped two-level system.
We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\ensuremath{\Lambda}$ shaped and driven at two-photon resonance by a pair of lasers, which cool the center-of-mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb-Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second-order perturbation theory. We find that the spectrum of resonance fluorescence is composed of two narrow sidebands---the Stokes and anti-Stokes components of the scattered light---while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow-type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behavior of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two levels.
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.
The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement, and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not been observed yet. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra with up to five pairs of side peaks, excitation detuning induced spectral asymmetry, and cavity filtering effect are observed and quantitatively modeled by a full quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.
Abstract The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement, and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not been observed yet. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra with up to five pairs of side peaks, excitation detuning induced spectral asymmetry, and cavity filtering effect are observed and quantitatively modeled by a full quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.
We study the time-resolved fluorescence spectrum in two-level systems interacting with an incident coherent field, both in the weak and intermediate coupling regimes. For a single two-level system in the intermediate-coupling case, as time flows, the spectrum develops distinct features that are not captured by a semiclassical treatment of the incident field. Specifically, for a field on resonance with the atomic transition energy, the usual Mollow spectrum is replaced by a four-peak structure, and for a frequency that is half of the atomic transition energy, the time-dependent spectrum develops a second-harmonic peak with a superimposed Mollow triplet. In the long-time limit, our description recovers results previously found in the literature. After analyzing why a different behavior is observed in the quantum and classical dynamics, the reason for the occurrence of a second-harmonic signal in a two-level system is explained via a symmetry analysis of the total (electron and photon) system and in terms of a three-level system operating in limiting regimes. We find an increased second-harmonic signal in an array of two-level systems, suggesting a superradiance-like enhancement for multiple two-level systems in cavity setups. Finally, initial explorative results are presented for two-level model atoms entering and exiting a cavity, which hint at an interesting interplay between cavity-photon screening and atomic dynamics effects.