We investigate the fluorescence spectrum of a two-level system driven by a monochromatic classical field by the Born-Markovian master equation based on a unitary transformation. The main purpose is to understand the effects of counter-rotating-wave terms of the driving on spectral features of the fluorescence. We have derived an analytical expression for the fluorescence spectrum, which is different from Mollow's theory, while Mollow's result on resonance is the limiting case of ours in moderately weak driving regimes. Our results demonstrate precisely that the counter-rotating-wave terms of the driving play an important role in the fluorescence spectrum for intense driving: (i) the counter-rotating coupling suppresses the red sideband in the Mollow triplet and it enhances the blue one in explicitly contrast to the well-known equal intensity of the sideband in Mollow's theory, (ii) the higher-order Mollow triplets appear as a characteristic spectral feature arising from counter-rotating-wave terms of the driving, and (iii) a significant frequency shift of the sidebands is observed, which depends on both the detuning and driving strength.
We investigate the fluorescence spectrum of a two-level system driven by a monochromatic classical field by the Born-Markovian master equation based on a unitary transformation. The main purpose is to understand the effects of counter-rotating-wave terms of the driving on spectral features of the fluorescence. We have derived an analytical expression for the fluorescence spectrum, which is different from Mollow's theory, while Mollow's result on resonance is the limiting case of ours in moderately weak driving regimes. Our results demonstrate precisely that the counter-rotating-wave terms of the driving play an important role in the fluorescence spectrum for intense driving: (i) the counter-rotating coupling suppresses the red sideband in the Mollow triplet and it enhances the blue one in explicitly contrast to the well-known equal intensity of the sideband in Mollow's theory, (ii) the higher-order Mollow triplets appear as a characteristic spectral feature arising from counter-rotating-wave terms of the driving, and (iii) a significant frequency shift of the sidebands is observed, which depends on both the detuning and driving strength.
We study the fluorescence spectrum of a strongly driven two-level system (TLS) with modulated transition frequency, which is a bichromatically driven TLS and has multiple resonance frequencies. We are aiming to provide a reliable description of the fluorescence in a regime that is difficult to tackle with perturbation theory and the rotating-wave approximation (RWA), and illustrate the spectral features of the fluorescence under off- and multiphoton-resonance conditions. To go beyond the RWA, we use a semianalytical counter-rotating-hybridized rotating-wave method that combines a unitary transformation and Floquet theory to calculate the two-mode Floquet states and quasienergies for the bichromatically driven TLS. We then solve the master equation accounting for the spontaneous decay in the bases of the two-mode Floquet states, and derive a physically transparent fluorescence spectrum. In comparison with the numerically exact spectrum from the generalized Floquet-Liouville approach, the present spectrum is found to be applicable in a wide range of the parameters where the RWA and the secular approximation may break down. We find that the counter-rotating (CR) terms of the transverse field omitted in the RWA have non-negligible contributions to the spectrum under certain conditions. Particularly, at the multiphoton resonance the width of which is comparable with the Bloch-Siegert shift, the RWA and non-RWA spectra markedly differ from each other because of the CR-induced shift. We also analyze the symmetry of the spectrum in terms of the transition matrix elements between the two-mode Floquet states. We show that the strict symmetry of the spectrum cannot be expected without the RWA but the almost symmetric spectrum can be obtained at the single-photon resonance that takes the Bloch-Siegert shift into account if the driving is moderately strong and at the multiphoton resonance with a sufficiently weak transverse field.
We consider the resonance fluorescence of a two-level atom in a vacuum with a high intensity driving field, such that the Rabi frequency of the field is non-negligible up to frequencies comparable to the transition frequency of the atom. At these high intensities, the conventional rotating wave approximation cannot be applied to the atom-laser Hamiltonian and the modal densities of the vacuum at the dressed transition frequencies differ significantly from each other. On treating the counter-rotating part of the Hamiltonian as a perturbation and carrying out the Weisskopf-Wigner approximation in the dressed states basis, we find that the high driving intensity leads to significant deviations from the traditional Mollow resonance fluorescence spectrum. In particular we find unequally intense Mollow side-bands and that the generation of higher order triplets and harmonics is substantially enhanced by the high vacuum modal density at the corresponding high resonance frequencies.
We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.
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 use an analytical method to study the dissipative dynamics of a two-level system (TLS) under a harmonic driving. The method is based on a combination of the unitary transformation and Born--Markov master-equation approach. Our main aim is to clarify the effects of counter-rotating (CR) terms of both the driving and TLS-bath (dissipative) coupling on the dynamics, in comparison with the rotating-wave results of different schemes, i.e., the well-known traditional rotating-wave approximation method, and two particular methods: one just takes into account the effects of the driving CR terms and the other the effects of the dissipative CR terms, which are derived from our general treatment. Our main results are as follows: (i) by calculating the time-dependent population difference and coherence, in the case of resonant strong driving, we demonstrate that the CR terms of both the driving and dissipative coupling play an important role in the relaxation and dephasing processes, and also the properties of the steady state; (ii) in the case of largely detuned driving, we find that the CR terms of the dissipative coupling become negligible while those of the driving contribute dominant modifications to the time evolution and steady state. Moreover, we examine the influence of the dissipation on coherent destruction of tunneling under a largely detuned strong driving. We show that an almost complete suppression of the tunneling can be achieved for a relatively long time; (iii) under certain conditions, we find numerical equivalence between one of two particular methods and the Floquet--Born--Markov approach based on exact numerical treatment of the Floquet Hamiltonian. It turns out that our method is more simple and efficient than the Floquet--Born--Markov approach for both analytical and numerical calculations. By the general comparison of different treatments we demonstrate the dynamical effects of CR terms of both the driving and the dissipative coupling on the coherence and population difference.
Abstract Strong polychromatic driving reshapes characteristics of the resonance fluorescence spectrum of a two-level system. Employing bichromatic driving feild with a low beat-frequency smaller than the emission rate of the system we demonstrate the exotic features of the fluorescence spectrum calculated by the numerical Floquet-Liouville approach and analytical method. It is found that fluorescence spectrum possesses two broadened sidebands in the place of the Rabi sidebands under certain conditions. Moreover, the heights and widths of the sidebands can be controlled by tuning the driving parameters. The properties of the spectrum is determined by the transitions between the Floquet states in a rotating frame. The broadened sidebands result from the quasi-continuous quasienergy spectrum which happens with steering the beat frequency lower. The present study provides insights into the Floquet engineering of the fluorescence spectral features with polychromatic excitation fields.