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arXiv:1303.5182 · Laser Physics

Autler–Townes multiplet spectroscopy

Fazal Ghafoor

Published Feb 14, 2014• 11 citations
arXivHTMLPDF

Abstract

The Autler–Townes doublet and triplet spectroscopy are well known in the literature. Here, atomic systems for quartuplet, quintuplet emission spectroscopy and their linkages with the sodium atom are investigated for display of the corresponding spectra. We explore the involved fundamental processes of quantum interference in these systems by examining the Laplace transform of the corresponding state-vector subjected to steady coherent illumination in the rotating wave approximation and Weisskopf–Wigner treatment of spontaneous emission as a simplest probability loss. In the quartuplet (quintuplet), four (five) fields interact appropriately and resonantly with the five-level (six-level) atom. The spectral profile of the single decaying level, upon interaction with three (four) other levels, splits into four (five) destructively interfering dressed states generating three (four) dark lines in the spectrum. These dark lines divide the spectrum into four (five) spectral components (bright lines) whose widths are effectively controlled by the relative strength of the laser fields and the relative width of a single decaying level. The idea is also extended to higher-ordered spectroscopy. The apparent disadvantage of these schemes is the successive increase in the number of laser fields required for the strongly interactive atomic states. However, these complexities are naturally inherited and are the beauty of these atomic systems. They provide the foundations for the basic mechanisms of the quantum interference involved in the higher-ordered multiplet spectroscopy.

DOI
10.1088/1054-660x/24/3/035702

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Autler–Townes quadruplet spectroscopy

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We suggest an atomic scheme of Autler–Townes quadruplet spectroscopy by extending the concepts of Autler–Townes doublet and triplet spectroscopy. The present scheme is analyzed in detail with the help of a state vector approach to calculate its emission spectrum. By applying rotating wave and Weisskopf–Wigner approximations to our proposed scheme, we have successfully attained a simple analytical expression of the spectrum interpreting the basic mechanism involved in the process of quantum interference. All the spectroscopic parameters, like the locations of dark lines and the locations and widths of all the peaks, are presented in analytical form. These analyses provide a better understanding of the phenomenon of the Autler–Townes quadruplet spectrum.

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Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.

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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.

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SPECTROSCOPIC TECHNIQUES FOR SINGLE ATOM LOCALIZATION

Sajid, Qamar

Entanglement of the atom and field leads towards the measurement of the state of the atom or field depending on the kind of measurement made. Taking advantage of this fact, we propose spectroscopic methods for the single atom localization within the subwavelength domain of the optical standing wave field. \n \nWhen a two-level atom interacts with some intense radiation field the spectrum of the scattered light signal exhibits a three-peak Mollow spectrum. We propose a scheme of atom localization based on the resonance fluorescence from a two-level atom interacting with a standing wave field. The Rabi frequency is considered to be position dependent and therefore, the spontaneously emitted photon carries the information about the center-of-mass motion of the atom. This leads to the localization of the single atom by measuring the frequency of the spontaneously emitted photon even during the passage of the atom through the standing wave field. We predict a spatial resolution in position information of up to λ/60 where λ is the optical wavelength. \n \nDetuning of the coherent field with the atomic transition plays an important role in the characterization of the peaks present in the Autler- Townes spectrum of a three-level atom. Strong line narrowing is observed in one of the peaks of the Autler- Townes doublet depending on the choice of the detuning. We investigate how this detuning effects the position information of the atom inside the standing wave field in upper-level and lower-level coupling schemes of Autler- Townes microscopy. We show an enhancement in precision position measurement by factor of at least 4 in upper-level coupling scheme due to the quantum interference phenomenon. This enhancement is not observed in lower-level coupling scheme where the quantum interference is not taking place. \n \nWe also consider a system where a three-level atom is interacting with a monochromatic radiation field in such a way that the decay takes place from upper level to the intermediate level with a rate T and from intermediate level to lower level at a rate γ. This type of system exhibits a non stationary scattered light signal. We report the results of the spontaneous emission spectrum for non stationary scattered light signal by using the definition of time-dependent physical spectrum. This is a rare example of problems where time-dependent physical spectrum can be calculated exactly. We study the characteristics of the spontaneous spectrum for a resonant and off-resonant case and show that this physical spectrum recovers the results of earlier work quite successfully. We also show that the decay rate r disturbs the atomic coherence and finally eliminates the dark line from the center of the spontaneous spectrum. Here we only consider upper-level coupling case for the time-dependent spontaneous spectrum because in lower-level coupling case the system automatically evolved a pumping mechanism due to the coupling of ground level to the upper level via radiation field. Thus a steady-state limit exists in lower-level coupling scheme. \n \nWe investigate the phenomenon of atom localization by using the non stationary Autler-Townes microscopy. The decay rate T reduces the precision in position measurement which is consistent with the results of the non stationary spontaneous emission spectrum. This is due to the fact that for the upper-level coupling case, the standing wave field is coupled to atomic transition and it induces a coherence in the upper-level atomic transition but the spontaneous decay from the upper level to the intermediate level disturbs this coherence. When the effect of the spontaneous decay dominates the coherence effect the quantum interference phenomenon vanishes and thus the precision in localization reduces.

•Jan 1, 2000•0 citations
The Autler–Townes doublet and triplet spectroscopy are well known in the literature. Here, atomic systems for quartuplet, quintuplet emission spectroscopy and their linkages with the sodium atom are investigated for display of the corresponding spectra. We explore the involved fundamental processes of quantum interference in these systems by examining the Laplace transform of the corresponding state-vector subjected to steady coherent illumination in the rotating wave approximation and Weisskopf–Wigner treatment of spontaneous emission as a simplest probability loss. In the quartuplet (quintuplet), four (five) fields interact appropriately and resonantly with the five-level (six-level) atom. The spectral profile of the single decaying level, upon interaction with three (four) other levels, splits into four (five) destructively interfering dressed states generating three (four) dark lines in the spectrum. These dark lines divide the spectrum into four (five) spectral components (bright lines) whose widths are effectively controlled by the relative strength of the laser fields and the relative width of a single decaying level. The idea is also extended to higher-ordered spectroscopy. The apparent disadvantage of these schemes is the successive increase in the number of laser fields required for the strongly interactive atomic states. However, these complexities are naturally inherited and are the beauty of these atomic systems. They provide the foundations for the basic mechanisms of the quantum interference involved in the higher-ordered multiplet spectroscopy.
We suggest an atomic scheme of Autler–Townes quadruplet spectroscopy by extending the concepts of Autler–Townes doublet and triplet spectroscopy. The present scheme is analyzed in detail with the help of a state vector approach to calculate its emission spectrum. By applying rotating wave and Weisskopf–Wigner approximations to our proposed scheme, we have successfully attained a simple analytical expression of the spectrum interpreting the basic mechanism involved in the process of quantum interference. All the spectroscopic parameters, like the locations of dark lines and the locations and widths of all the peaks, are presented in analytical form. These analyses provide a better understanding of the phenomenon of the Autler–Townes quadruplet spectrum.
Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.
Understanding the behavior of quantum systems under external perturbations is fundamental in quantum mechanics and has numerous applications in fields such as spectroscopy and quantum computing. In this thesis, we investigate the phenomenon of Autler-Townes doublets in hydrogen atoms numerically, focusing on a three-level model. Autler-Townes doublets arise when a two-level quantum system, such as a hydrogen atom, is subjected to an external electromagnetic field, leading to the splitting of spectral lines due to the Autler-Townes effect. The study involves formulating and solving the population amplitude equations describing the time evolution of the hydrogen atom’s probability amplitudes under the influence of external fields. We employ the Range-Kutta method in MATLAB to numerically solve these equations and analyze the shape and characteristics of Autler-Townes doublets. Our simulations explore the influence of various parameters such as field strength and frequency on the doublet structure. Additionally, our research compares the numerical results obtained from the simulation with the three-level model solutions, providing insights into the dynamic interference and understanding the physical reasons for the modulations in the spectrum. Our findings not only contribute to the understanding of Autler-Townes doublets in hydrogen atoms but also shed light on potential applications in quantum technologies and spectroscopic techniques.
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.
The damped and coherently-driven JaynesndashndashndashCummings 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.
Entanglement of the atom and field leads towards the measurement of the state of the atom or field depending on the kind of measurement made. Taking advantage of this fact, we propose spectroscopic methods for the single atom localization within the subwavelength domain of the optical standing wave field. \n \nWhen a two-level atom interacts with some intense radiation field the spectrum of the scattered light signal exhibits a three-peak Mollow spectrum. We propose a scheme of atom localization based on the resonance fluorescence from a two-level atom interacting with a standing wave field. The Rabi frequency is considered to be position dependent and therefore, the spontaneously emitted photon carries the information about the center-of-mass motion of the atom. This leads to the localization of the single atom by measuring the frequency of the spontaneously emitted photon even during the passage of the atom through the standing wave field. We predict a spatial resolution in position information of up to λ/60 where λ is the optical wavelength. \n \nDetuning of the coherent field with the atomic transition plays an important role in the characterization of the peaks present in the Autler- Townes spectrum of a three-level atom. Strong line narrowing is observed in one of the peaks of the Autler- Townes doublet depending on the choice of the detuning. We investigate how this detuning effects the position information of the atom inside the standing wave field in upper-level and lower-level coupling schemes of Autler- Townes microscopy. We show an enhancement in precision position measurement by factor of at least 4 in upper-level coupling scheme due to the quantum interference phenomenon. This enhancement is not observed in lower-level coupling scheme where the quantum interference is not taking place. \n \nWe also consider a system where a three-level atom is interacting with a monochromatic radiation field in such a way that the decay takes place from upper level to the intermediate level with a rate T and from intermediate level to lower level at a rate γ. This type of system exhibits a non stationary scattered light signal. We report the results of the spontaneous emission spectrum for non stationary scattered light signal by using the definition of time-dependent physical spectrum. This is a rare example of problems where time-dependent physical spectrum can be calculated exactly. We study the characteristics of the spontaneous spectrum for a resonant and off-resonant case and show that this physical spectrum recovers the results of earlier work quite successfully. We also show that the decay rate r disturbs the atomic coherence and finally eliminates the dark line from the center of the spontaneous spectrum. Here we only consider upper-level coupling case for the time-dependent spontaneous spectrum because in lower-level coupling case the system automatically evolved a pumping mechanism due to the coupling of ground level to the upper level via radiation field. Thus a steady-state limit exists in lower-level coupling scheme. \n \nWe investigate the phenomenon of atom localization by using the non stationary Autler-Townes microscopy. The decay rate T reduces the precision in position measurement which is consistent with the results of the non stationary spontaneous emission spectrum. This is due to the fact that for the upper-level coupling case, the standing wave field is coupled to atomic transition and it induces a coherence in the upper-level atomic transition but the spontaneous decay from the upper level to the intermediate level disturbs this coherence. When the effect of the spontaneous decay dominates the coherence effect the quantum interference phenomenon vanishes and thus the precision in localization reduces.