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arXiv:2601.20296

Electromagnetically Induced Transparency Spectra of Ladder Four-Level System with Quantum Frequency Mixing

Sheng-Xian Xiao, Tao Wang

quant-phSubmitted Jan 28, 2026• Announced Jan 29, 2026• 0 citations
arXivHTMLPDF

Abstract

In this paper, we generalized the quantum frequency mixing technology to a ladder-type four-level system and studied its effect on electromagnetically induced transparency spectra. We found a secondary splitting of Autler-Townes splitting in the probing field transmission spectra, which could be understood by the effective Hamiltonian derived with multi-mode Floquet theory. The Frequency mixing scheme developed here enables continuous tunablity of the resonant frequency between upper levels, which facilitates the broad band sensing of AC field. Furthermore, by introducing an additional periodic driving, we realize an effective model that two distinct quantum interference effects coexist: interference among Floquet channels and loop interference arising from closed coherent pathways. Both interference effects could be read out from the transmission spectra independently. The changing of the distance between double splitting peaks represents the interference of Floquet channels, while their asymmetric linewidth broadening is linked with the total effective phase of the loop. This not only provides complementary readout for extracting the phase of AC field, but also establishes a new paradigm for coherent control in multi-level quantum systems.

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Quantum interference effects in the unmodulated quantum systems with light-matter interaction have been widely studied, such as electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS). However, the similar quantum interference effects in the Floquet systems (i.e., periodically modulated systems), which might cover rich new physics, were rarely studied. In this article, we investigate the quantum interference effects in the Floquet two- and three-level systems analytically and numerically. We show a coherent destruction tunneling effect in a lotuslike multipeak spectrum with a Floquet two-level system, where the intensity of the probe field is periodically modulated with a square-wave sequence. We demonstrate that the multipeak split into multiple transparency windows with tunable quantum interference if the Floquet system is asynchronously controlled via a third level. Based on phenomenological analysis with Akaike information criterion, we show that the symmetric central transparency window has a similar mechanism to the traditional ATS or EIT depending on the choice of parameters, additional with an extra degree of freedom to control the quantum interference provided by the modulation period. The other transparent windows are shown to be asymmetric, different from the traditional ATS and EIT windows. These nontrivial quantum interference effects open up a scope to explore the applications of the Floquet systems.

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Crossover from electromagnetically induced transparency to Autler–Townes splitting in open ladder systems with Doppler broadening

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We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.

arXiv:1311.2149•Journal of the Optical Society of America B•Mar 4, 2014•34 citations
In this paper, we generalized the quantum frequency mixing technology to a ladder-type four-level system and studied its effect on electromagnetically induced transparency spectra. We found a secondary splitting of Autler-Townes splitting in the probing field transmission spectra, which could be understood by the effective Hamiltonian derived with multi-mode Floquet theory. The Frequency mixing scheme developed here enables continuous tunablity of the resonant frequency between upper levels, which facilitates the broad band sensing of AC field. Furthermore, by introducing an additional periodic driving, we realize an effective model that two distinct quantum interference effects coexist: interference among Floquet channels and loop interference arising from closed coherent pathways. Both interference effects could be read out from the transmission spectra independently. The changing of the distance between double splitting peaks represents the interference of Floquet channels, while their asymmetric linewidth broadening is linked with the total effective phase of the loop. This not only provides complementary readout for extracting the phase of AC field, but also establishes a new paradigm for coherent control in multi-level quantum systems.
Quantum interference effects in the unmodulated quantum systems with light-matter interaction have been widely studied, such as electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS). However, the similar quantum interference effects in the Floquet systems (i.e., periodically modulated systems), which might cover rich new physics, were rarely studied. In this article, we investigate the quantum interference effects in the Floquet two- and three-level systems analytically and numerically. We show a coherent destruction tunneling effect in a lotuslike multipeak spectrum with a Floquet two-level system, where the intensity of the probe field is periodically modulated with a square-wave sequence. We demonstrate that the multipeak split into multiple transparency windows with tunable quantum interference if the Floquet system is asynchronously controlled via a third level. Based on phenomenological analysis with Akaike information criterion, we show that the symmetric central transparency window has a similar mechanism to the traditional ATS or EIT depending on the choice of parameters, additional with an extra degree of freedom to control the quantum interference provided by the modulation period. The other transparent windows are shown to be asymmetric, different from the traditional ATS and EIT windows. These nontrivial quantum interference effects open up a scope to explore the applications of the Floquet systems.
Abstract In this paper, the physical origin of interferences has been explored in a four-level cascade rubidium atom by simultaneous interaction with three energies; two optical fields and one radio frequency (RF) field. The atomic system is investigated by a combination of the analytical method introduced by Zhu et al (2010 Phys. Rev. A 81 053836) and resonant pole method introduced by Anisimov (2008 J. Mod. Opt. 55 ). A substantial amount of variation in the probe absorption has been observed in various regimes. The transition from electromagnetically induced transparency (EIT) to Autler–Townes spitting (ATS) is observed. It is found that a definite threshold value exists governing the crossover from EIT to ATS. The applied analytical method gives a clear insight into the nature of interferences; one may observe EIT as a consequence of destructive interference, whereas ATS is a consequence of constructive interference. Furthermore, a transition from single EIT to double electromagnetically induced transparency has been detected when the system is illuminated by RF-driving field in weak control regime. Further, transition from ATS to double Autler–Townes splitting has been observed in the strong control regime.
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.
The A-type three-level system coupled by two coherent fields is a basic model to study the electromagnetically induced transparency(EIT).Based on that,the cascade quasi- A-four-level configuration is formed when a radio-frequency(RF)field drives the transition between the excited state and an additional excited state level.The absorption property is studied along with the parameters of the coupling field and the RF driving field by numerically solving the relevant equations of motion of the density matrix.It is shown that under the applying of the coupling field and the RF driving field,both the Autler-Townes doublet and the EIT are observed in the absorptive spectra and it can be explained properly by the theory of dressed state.An important conclusion is that the Autler-Townes doublet originates from the atom system interaction with the strong RF field,while the EIT originates from atom system quantum interference interaction with the coupling field.
To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.
We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.