Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
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.
We examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.
The damped and coherently-driven JaynesndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.
Abstract When a two-level system is driven on resonance by a strong incident field, its emission spectrum is characterized by the well-known Mollow triplet. If the absorption from the excited state, in this continuously driven two-level system, to a third, higher energy level, is probed by a weak field, the resulting absorption spectrum features the Autler-Townes doublet with two peaks separated by the Rabi frequency of the strong driving field. It has been shown that when the two-level system is instead driven by a periodic pulse sequence, the emission spectrum obtained has similarities with the Mollow triplet even though the system is only driven during the short application time of the pulses and is allowed to evolve freely between pulses. Here, we evaluate the absorption spectrum of the three-level system in the ladder/cascade configuration when the bottom two levels are driven by a periodic pulse sequence while the transition between the middle and the highest level is probed by a weak field. The absorption spectrum displays similarities with the Autler-Townes doublet with frequency separation between the main peaks defined by the inter-pulse delay. In addition, this spectrum shows little dependence on the pulse carrier frequency. These results demonstrate the capacity to modulate the absorption spectrum of a three-level system with experimentally achievable pulse protocols.
We study the Autler-Townes absorption spectrum of the upper and intermediate levels of a three-level cascade atom in which the intermediate and ground levels are strongly driven by a laser field as well as weakly coupled by a cavity mode [Phys. Rev. 100, 703 (1955)]. Surprisingly, one of the Autler-Townes peaks may be greatly suppressed or enhanced by tuning the cavity resonant frequency. The larger the Rabi frequency, the more pronounced the cavity-induced suppression or enhancement. The Autler-Townes spectrum carries full information on the cavity-induced modification of the strongly driven levels. A physical interpretation is presented in the dressed-state basis.
We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.