We obtain time-resolved spectra of spontaneous emission and resonance fluorescence of a single multilevel emitter where two antiparallel transitions interfere and cause quantum beats. After rising as a single broad peak, the spontaneous emission spectrum turns into a doublet of subnatural peaks and then fades for long times. For strong field resonance fluorescence, the beat signature is the formation of doublet sidebands, which initially grow asymmetrically but end up symmetrical. We stress the filter bandwidth's crucial role in the spectral resolution and causal evolution.
We obtain time-resolved spectra of spontaneous emission and resonance fluorescence of a single multilevel emitter where two antiparallel transitions interfere and cause quantum beats. After rising as a single broad peak, the spontaneous emission spectrum turns into a doublet of subnatural peaks and then fades for long times. For strong field resonance fluorescence, the beat signature is the formation of doublet sidebands, which initially grow asymmetrically but end up symmetrical. We stress the filter bandwidth's crucial role in the spectral resolution and causal evolution.
Working with a beam of two-level--atom--like 174Yb, we have measured the temporal evolution of strong-field resonance fluorescence spectra during square-pulse excitation. In the case of resonant excitation, it is found that driving-field phase shifts transform the normal three-peaked Mollow spectrum into a transient doublet spectrum asymmetric with respect to the atomic transition frequency. This qualitatively new type of spectrum provides fundamental insight into the connection between atomic dynamics and spectra, and results from a nearly perfect polarization of the dressed atom-field states.
The time-resolved fluorescence spectrum of a driven two-level system is investigated using a time-dependent variational method. We first establish the transient build-up of the Mollow triplet via the Lindblad master equation under the rotating-wave approximation, providing a complete visualization of the spectral evolution from initial turn-on to steady state. To go beyond the perturbative regime, we employ the multiple Davydov D2 ansatz (multi-D2), which uses the σz eigenstates as the basis and naturally accommodates arbitrary system–bath coupling types and spectral densities. The multi-D2 method converges with M = 4 multiplicities in studied cases, outperforming the multi-D1 ansatz (M = 8) for the σx coupling benchmark. For pure σz (dephasing) coupling under resonant driving, we find that the time-resolved spectrum reveals a distinct fluorescence peak at the Rabi frequency—a signature of dressed-state transitions induced by the dephasing channel that remains hidden in population dynamics. Under mixed σx–σz coupling, the spectrum exhibits combined features of both Mollow triplet and σz-mediated emission. The effects of sub-Ohmic, Ohmic, and super-Ohmic spectral densities are systematically compared. While the resonant spectral weight J(ω0) governs the overall dissipation rate, a controlled comparison at fixed J(ω0) reveals that the super-Ohmic regime exhibits an intrinsic shape-dependent suppression of sideband emission under resonant driving, highlighting an asymmetric role of the spectral density exponent in engineering transient fluorescence. Our work establishes the multi-D2 ansatz as a versatile tool for simulating time-resolved fluorescence in complex bosonic environments.
We study theoretically quantum statistical and spectral properties of the resonance fluorescence of a single atom or system with angular momentum $J=1/2\ensuremath{-}{J}^{\ensuremath{'}}=1/2$ driven by a monochromatic linearly polarized laser field, due to quantum interference among its two antiparallel $\ensuremath{\pi}$ transitions. A magnetic field parallel to the laser polarization is applied to break the degeneracy (Zeeman effect). In the nondegenerate case, the $\ensuremath{\pi}$ transitions evolve at different generalized Rabi frequencies, producing quantum beats in the intensity and the dipole-dipole, intensity-intensity, and quadrature-intensity correlations. For a strong laser and large Zeeman splitting the beats have mean and modulation frequencies given by the average and difference, respectively, of the Rabi frequencies, unlike the beats studied in many spectroscopic systems, characterized by a modulated exponential-like decay. Further, the Rabi frequencies are those of the pairs of sidebands of the Mollow-like spectrum of the system. In the two-time correlations, the cross contributions, i.e., those with products of probability amplitudes of the two $\ensuremath{\pi}$ transitions, have a lesser role than those from the interference of the probability densities. In contrast, there are no cross terms in the total intensity. We also consider nonclassical and non-Gaussian properties of the phase-dependent fluorescence for the cases of weak to moderate excitation and in the regime of beats. The fluorescence in the beats regime is nonclassical, mainly from third-order dipole fluctuations, which reveal them to be also strongly non-Gaussian, and their quadrature spectra show complex features around the Rabi frequencies. For small laser and Zeeman detunings, a weak to moderate laser field pumps the system partially to one of the ground states, showing slow decay in the two-time correlations and a narrow peak in the quadrature spectra.
A study is presented for the time-dependent resonance-fluorescence spectrum of two-level atoms irradiated by hyperbolic-secant pulsed lasers, allowing for an arbitrary spontaneous-emission rate from the excited level to the ground level. Novel features of the temporally transient spectrum have been observed. The spectrum is dominated by a central peak which oscillates in time and is accompanied by multiple side peaks. Asymptotically (i.e., after the pulse has passed) the side peaks disappear, leaving a tail at the line center which displays a Lorentzian shape of width equal to the sum of the spontaneous-emission rate and the width of the spectrometer considered and of magnitude proportional to the instantaneous intensity of the pulse. The exact behavior of the spectrum is dictated by the area of the engaged pulse and by how the atom is prepared initially. In particular, it is found that the spectrum can be asymmetric even when the laser is tuned to exact resonance if the atoms are initially prepared in a certain class of proper coherent states, irrespective of how the field amplitude may vary in time. An analysis of the spectral symmetry without resorting to any explicit evaluation of the spectrum itself is also presented. Furthermore, the associated optical Bloch equations are solved analytically in terms of hypergeometric functions in a similar manner to that done previously for the undamped two-level Schr\"odinger equation. Specific numerical results are presented for pulses of area equal to \ensuremath{\pi}, 2\ensuremath{\pi}, 3\ensuremath{\pi}, 4\ensuremath{\pi}, and 5\ensuremath{\pi} for both symmetric and asymmetric cases.
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.
This study concerns the shape of the resonance fluorescence spectrum emitted by a V-type three-level atom driven by two coherent fields which are resonant with the transitions connecting the ground state and the second and third level, respectively. We are especially interested in monitoring the spontaneous emission from the top level to the ground state. If the field connecting levels 1 and 2 is absent or small, the spontaneous emission from level 3 is characterized by the standard Mollow spectrum. If instead the 1-2 transition is saturated, the spectrum of resonance fluorescence from the top level is characterized by the following signatures: (i) the appearance of sidebands due to Rabi splitting effects, (ii) a reduction of its integrated area because of coherent population trapping1, and (iii) a significant reduction of its linewidth if the natural lifetime of level 2 is longer than level 3. The latter effect is especially interesting and rather unexpected, as the decay properties of an optical transition are being transferred to another by controlling the relative magnitudes of the driving fields. We have carried out our calculations with the help of the regression theorem and also developed a simple physical interpretation in terms of appropriate dressed states2.