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Journal of the Optical Society of America B

Properties of a three-level Λ-type atom driven by coherent and stochastic fields

Sajad Ahmadi, Mohsen Akbari, Shahpoor Saeidian, Ali Motazedifard

Published May 6, 2026• 0 citations
Publisher

Abstract

We present a theoretical investigation of a three-level Λ-type atom driven by a strong coherent laser and a weak stochastic field exhibiting amplitude and phase fluctuations. The stochastic field is modeled as a complex Gaussian–Markovian random process with finite bandwidth to describe realistic laser noise. Using the Born–Markov and rotating-wave approximations, we derive a Lindblad-form master equation that incorporates spontaneous emission and noise-induced terms, and we solve for the steady-state regime. We examine level populations in both the bare and dressed bases and compute the incoherent resonance-fluorescence spectrum. Our analysis shows that the stochastic drive is not merely a source of decoherence but a versatile control parameter. By detuning the stochastic-field central frequency relative to the coherent drive (especially for narrow bandwidths), we observe pronounced changes in emission characteristics, including selective enhancement or suppression, and reshaping of the multi-peaked fluorescence spectrum when the detuning matches the generalized Rabi frequency. Numerical results reveal nontrivial steady-state modifications distinct from purely coherent driving, enabling precise control of populations and suggesting applications in quantum control, quantum technologies, spectroscopy, and noise-assisted manipulation of atomic systems.

DOI
10.1364/josab.592274

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We present a theoretical investigation of a three-level Λ-type atom driven by a strong coherent laser and a weak stochastic field exhibiting amplitude and phase fluctuations. The stochastic field is modeled as a complex Gaussian–Markovian random process with finite bandwidth to describe realistic laser noise. Using the Born–Markov and rotating-wave approximations, we derive a Lindblad-form master equation that incorporates spontaneous emission and noise-induced terms, and we solve for the steady-state regime. We examine level populations in both the bare and dressed bases and compute the incoherent resonance-fluorescence spectrum. Our analysis shows that the stochastic drive is not merely a source of decoherence but a versatile control parameter. By detuning the stochastic-field central frequency relative to the coherent drive (especially for narrow bandwidths), we observe pronounced changes in emission characteristics, including selective enhancement or suppression, and reshaping of the multi-peaked fluorescence spectrum when the detuning matches the generalized Rabi frequency. Numerical results reveal nontrivial steady-state modifications distinct from purely coherent driving, enabling precise control of populations and suggesting applications in quantum control, quantum technologies, spectroscopy, and noise-assisted manipulation of atomic systems.
Properties of a Three-Level ΛΛΛ-Type Atom Driven by Coherent and Stochastic Fields
We present a theoretical investigation of a three-level ΛΛΛ-type atom driven by a strong coherent laser and a weak stochastic field exhibiting amplitude and phase fluctuations. The stochastic field is modeled as a complex Gaussian-Markovian random process with finite bandwidth to describe realistic laser noise. Using the Born-Markov and rotating-wave approximations, we derive a Lindblad-form master equation that incorporates spontaneous emission and noise-induced terms, and we solve for the steady-state regime. We examine level populations in both the bare and dressed bases and compute the incoherent resonance-fluorescence spectrum. Our analysis shows that the stochastic drive is not merely a source of decoherence but a versatile control parameter. By detuning the stochastic-field central frequency relative to the coherent drive (especially for narrow bandwidths), we observe pronounced changes in emission characteristics, including selective enhancement or suppression, and reshaping of the multi-peaked fluorescence spectrum when the detuning matches the generalized Rabi frequency. Numerical results reveal nontrivial steady-state modifications distinct from purely coherent driving, enabling precise control of populations and suggesting applications in quantum control, quantum technologies, spectroscopy, and noise-assisted manipulation of atomic systems.
The steady-state populations and the absorption spectrum of a V-type three-level atom driven by a strong coherent field and a weak stochastic one simultaneously are investigated. The population inversion in bare-state and dressed-state bases can happen significantly due to the effect of the stochastic field. A relation between the level gap of both atomic excited states and the Rabi frequency is found to decide in which excited state the population is larger than in another one for the same frequency detuning δ between the coherent and the stochastic fields. The line profiles of the absorption spectrum are strongly dependent on the frequency detuning δ. Different lineshapes such as a sharp emission peak (gain), an absorption peak or a dispersion-like peak can be exhibited at the line centre for different δ. Asymmetrical spectral features and line narrowing can be reached by adjusting δ and the Rabi frequency. Probe gain in sidebands can occur due to the unbalanced population distribution in dressed states.
The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.
The squeezing spectrum of the fluorescent light is investigated for a laser-driven three-level atom of the $\ensuremath{\Lambda}$ configuration when quantum interference of the decay channels is accounted for. We show that when the two atomic transitions contribute to the detected fluorescence field, squeezing at certain frequency intervals is obtained in both the weak- and the high-Rabi-frequency regimes even for equally decay rates of the transitions. Unlike in two-level atoms in free space, squeezing can be obtained in both the in-phase and out-of-phase quadrature spectra although in different spectral regions. We also show that the squeezing spectrum can be controlled by an adequate selection of the Rabi frequencies and atomic detunings. Another remarkable effect is that squeezing can be achieved with proper relative phases of the driving fields. We provide an analytical description in the dressed basis which accounts for the main features of the squeezing spectra obtained from the numerical work.
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.
We generalize our earlier formalism to treat the effects of both the finite-bandwidth excitations and finite arbitrary detunings, on the fluorescent spectra and second-order intensity correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom in cascade configuration. Under the conditions that one or both of these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity correlation functions which explicitly display the effects due to detunings and fluctuations.