We describe in this Letter how inhomogeneous line broadening affects the Autler-Townes (AT) splitting in a three level open molecular cascade system. For moderate Rabi frequencies in the range of 300 to 500 MHz the fluorescence line shape from the uppermost level |3> in this system depends strongly on the frequency ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level |2> appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the probe laser/coupling field frequency ratio and laser propagation geometry based on our theoretical analysis of the Doppler integral. This is important for applications such as molecular angular momentum alignment as well as for the measurement of the transition dipole moment matrix element.
We consider the Autler-Townes effect when a strong coupling field is applied in the hyperfine manifold of an alkali atom. Explicit solution is obtained in the case of the D1-line. We show how the hyperfine interaction modifies the dressing effects associated with the strong field as well as the sample susceptibility with respect to the probe mode. Particularly, if the strong field is far detuned from the atomic resonance line the Autler-Townes structure differs significantly from the prediction of the Lambda-type approximation. We also find that tuning the strong field in between the upper sta…
We study the Autler-Townes spectrum of a V-type atom coupled to a single-mode, frequency-tunable cavity field at finite termperature, with a pre-selected polarization in the bad cavity limit, and show that, when the mean number of thermal photons $N\gg 1$ and the excited sublevel splitting is very large (the same order as the cavity linewidth), the probe gain may occur at either sideband of the doublet, depending on the cavity frequency, due to the cavity-induced interference.
We study nonlinear optical effects in the laser excitation of Rydberg states. $5S_{1/2}$ and $5P_{3/2}$ levels of $^{85}$Rb are strongly coupled by a strong laser field and probed by a weak laser tuned to the $5P_{3/2} - 44D$ Rydberg resonance. We observe high contrast Autler-Townes spectra which are dependent on the pump polarization, intensity and detuning. The observed behavior agrees with calculations, which include the effect of optical pumping.
We have experimentally studied the reflection of a weak probe beam from a dense atomic potassium vapor in the presence of a strong laser field tuned to the atomic resonance transition. We have observed an Autler-Townes doublet under hitherto unexplored conditions, namely that the Rabi frequency induced by the strong laser field is much smaller than the self-broadened width of the resonance transition of the unexcited vapor. We attribute our observation to a reduction of the atomic decoherence by the strong drive field. We present a theoretical model of nonlinear processes in a dense atomic gas…
The atom-light interaction in a three-level system has shown significant physical phenomena, such as electromagnetically induced transparency and Autler{Townes splitting (ATS), for broad applications in classical and quantum information techniques. Here, we optimally demonstrated the ATS with a quantum state manipulation method. The ATS in the dephasing-dominated diamond NV center system was successfully recovered by coherent microwave control, which cannot be observed with traditional method. The dynamical process of ATS was investigated in detail, revealing a nontrivial quantum interference …
Autler-Townes splitting (ATS) and electromagnetically-induced transparency (EIT) both yield transparency in an absorption profile, but only EIT yields strong transparency for a weak pump field due to Fano interference. Empirically discriminating EIT from ATS is important but so far has been subjective. We introduce an objective method, based on Akaike's information criterion, to test ATS vs. EIT from experimental data and determine which pertains. We apply our method to a recently reported induced-transparency experiment in superconducting circuit quantum electrodynamics.
We consider non-degenerate pump-probe spectroscopy of V-systems under conditions such that interference among decay channels is important. We demonstrate how this interference can result in new gain features instead of the usual absorption features. We relate this gain to the existence of a new vacuum induced quasi-trapped-state. We further show how this also results in large refractive index with low absorption.
We investigate electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral fea…
Photon number splitting is observed in a transmon coupled to a superconducting quasi-lumped-element resonator in the strong dispersive limit. A thermal population of 5.474 GHz photons at an effective resonator temperature of T = 120mK results in a weak n = 1 photon peak along with the n = 0 photon peak in the qubit spectrum in the absence of a coherent drive on the resonator. Two-tone spectroscopy using independent coupler and probe tones reveals an Autler-Townes splitting in the thermal n = 1 photon peak. The observed effect is explained accurately using the four lowest levels of the dispersi…
We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler- Townes splitting (ATS). We also find that the parameter change from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum …
We investigated the Autler-Townes splitting produced by microwave transitions between atomic Rydberg states explored by optical spectroscopy from the ground electronic state. The laser-atom Hamiltonian describing the double irradiation of such a multilevel system is analysed on the basis of the Morris-Shore transformation. The application of this transformation to the microwave-dressed atomic system allows the identification of bright, dark, and spectator states associated with different configurations of atomic states and microwave polarisation. We derived synthetic spectra that show the main…
We experimentally study a vacuum-induced Autler-Townes doublet in a superconducting three-level artificial atom strongly coupled to a coplanar waveguide resonator and simultaneously to a transmission line. The Autler-Townes splitting is observed in the reflection spectrum from the three-level atom in a transition between the ground state and the second excited state when the transition between the two excited states is resonant with a resonator. By applying a driving field to the resonator, we observe a change in the regime of the Autler-Townes splitting from quantum (vacuum-induced) to classi…
The nonlocal emitter-waveguide coupling, which gives birth to the so called giant atom, represents a new paradigm in the field of quantum optics and waveguide QED. In this paper, we investigate the single-photon scattering in a one-dimensional waveguide on a two-level or three-level giant atom. Thanks to the natural interference induced by the back and forth photon transmitted/reflected between the atom-waveguide coupling points, the photon transmission can be dynamically controlled by the periodic phase modulation via adjusting the size of the giant atom. For the two-level giant-atom setup, w…
We present a proof-of-principle of how electronic transport measurements permits the observation of the Autler-Townes doublet, an optical property of nanodevices. The quantum physical system consists of one optically pumped quantum dot, a second auxiliary quantum dot, and a superconductor lead which provides an effective coupling between the dots via crossed Andreev reflection. Electrodes, working as source and drain, acts as nonequilibrium electronic reservoirs. Our calculations of the photocurrent at both, transient and stationary regimes, obtained using a density matrix formalism for open q…
We propose quantum control protocols for the high-fidelity preparation of target states in systems with Autler-Townes splitting. We investigate an approximated three-level system obtained from a four-level one by adiabatically eliminating a state that does not participate in the evolution. In our work we use linear, arctan, and Roland-Cerf functions for transferring population between two eigenstates of the system obtaining a high fidelity for long evolution times. Additionally, in order to overcome the restriction given by the lifetimes of the experimental setup, we propose an accelerated adi…
Routers, switches, and repeaters are essential components of modern information-processing systems. Similar devices will be needed in future superconducting quantum computers. In this work we investigate experimentally the time evolution of Autler-Townes splitting in a superconducting phase qubit under the application of a control tone resonantly coupled to the second transition. A three-level model that includes independently determined parameters for relaxation and dephasing gives excellent agreement with the experiment. The results demonstrate that the qubit can be used as a ON/OFF switch w…
When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, …
We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the qubit coupled off-resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher …
We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field an…
We propose a method to achieve significant optical signal delays exploiting the effect of Autler-Townes splitting in an inhomogeneously broadened quantum dot medium. The absorption and slow-down effects are compared for three schemes i.e. $Ξ$, V and $Λ$, corresponding to different excitation configurations. Qualitative differences of the V-scheme compared to the $Ξ$- and $Λ$-scheme are found, which show that features of Autler-Townes splitting are only revealed in the V-scheme. The underlying physical mechanisms causing this discrepancy are analyzed and discussed. Finally we compare field prop…
We have observed the Autler-Townes doublet in a superconducting Al/AlOx/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time (~40 us) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameter…
We present the direct measurements of electric-dipole moments for $5P_{3/2}\to nD_{5/2}$ transitions with $20<n<48$ for Rubidium atoms. The measurements were performed in an ultracold sample via observation of the Autler-Townes splitting in a three-level ladder scheme, commonly used for 2-photon excitation of Rydberg states. To the best of our knowledge, this is the first systematic measurement of the electric dipole moments for transitions from low excited states of rubidium to Rydberg states. Due to its simplicity and versatility, this method can be easily extended to other transitions and o…
We present a detailed theoretical analysis of a multi-level quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as the Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanpaa et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by ex…
Two phenomena can affect the transmission of a weak signal field through an absorbing medium in the presence of a strong additional field: electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS). Being able to discriminate between the two is important for various applications. Here we present an experimental investigation into a method that allows for such a disambiguation as proposed in [Phys. Rev. Lett. 107, 163604 (2011)]. We apply the proposed test based on Akaike's information criterion to a coherently driven ensemble of cold cesium atoms and find a good agreement…
We theoretically investigate the tunneling-induced transparency (TIT) and the Autler-Townes (AT) doublet and triplet in a triple-quantum-dot system. For the resonant tunneling case, we show that the TIT induces a transparency dip in a weak-tunneling regime and no anticrossing occurs in the eigenenergies of the system Hamiltonian. However, in a strong-tunneling regime, we show that the TIT evolves to the AT splitting, which results in a well-resolved doublet and double anticrossings. For the off-resonance case, we demonstrate that, in the weak-tunneling regime, the double TIT is realized with a…
A theoretical spectroscopic analysis of a microwave driven superconducting charge qubit (Cooper-pair box coupled) to an RLC oscillator model is performed. By treating the oscillator as a probe through the backreaction effect of the qubit on the oscillator circuit, we extract frequency splitting features analogous to the Autler-Townes effect from quantum optics, thereby extending the analogies between superconducting and quantum optical phenomenology. These features are found in a frequency band that avoids the need for high frequency measurement systems and therefore may be of use in qubit cha…
We present a combined experimental and theoretical study of the effects of Rydberg interactions on Autler-Townes spectra of ultracold gases of atomic strontium. Realizing two-photon Rydberg excitation via a long-lived triplet state allows us to probe the thus far unexplored regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atom-loss spectra. The experiment is analyzed within a one-body density matrix approach, accounting for interaction-induced level shifts and de…
In this work we present a theoretical frame work to identify the role and the nature of interference between Autler-Townes (AT) peaks (or dressed states) in generic multi-level system. The destructive interference between the AT peaks, gives rise to sharp transparency window known as electromagnetically induced transparency (EIT). In the three-level system, the two AT peaks interferes pair-wise with each other, almost similar to the two-slit interference. In the four-level system, the interference between the three AT peaks is also pair-wise analogous to three-slit interference but has a bit m…
We study the Autler Townes (AT) effect derived from a strong electric dipole transition stimulated by a resonant laser beam and probing it by means of a weak electric quadrupole transition with a controlled frequency detuning in a ladder configuration. The experiment was carried out for a $^{87}$Rb atomic gas at room temperature in a velocity-selective scheme. The AT effect was monitored via the splitting of the fluorescence spectra associated with the spontaneous decay to the ground state. The theoretical description incorporates the modification of standard few-level schemes introduced by fo…
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are similar,but different quantum optical phenomena: EIT results from a Fano interference, whereas ATS is described by the AC-Stark effect. Likewise, despite their close resemblance, light-storage techniques based on the EIT memory protocol and the recently-proposed ATS memory protocol (E. Saglamyurek et al. Nature Photonics 12, 2018) are distinct: the EIT protocol relies on adiabatic elimination of absorption, whereas the ATS protocol is based on absorption. In this article, we elaborate on the distinction betwee…
The coherent control of light with matter, enabling storage and manipulation of optical signals, was revolutionized by electromagnetically induced transparency (EIT), which is a quantum interference effect. For strong electromagnetic fields that induce a wide transparency band, this quantum interference vanishes, giving rise to the well-known phenomenon of Autler-Townes splitting (ATS). To date, it is an open question whether ATS can be directly leveraged for coherent control as more than just a case of "bad" EIT. Here, we establish a protocol showing that dynamically controlled absorption of …
We extend the concepts of the Autler-Townes doublet and triplet spectroscopy to quartuplet, quintuplet and suggest linkages in sodium atom in which to display these spectra. We explore the involved fundamental processes of quantum interference of the corresponding spectroscopy 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, four fields interact appropriately and resonantly with the five-level …
Broadband spin-photon interfaces for long-lived storage of photonic quantum states are key elements for quantum information technologies. Yet, reliable operation of such memories in the quantum regime is challenging due to photonic noise arising from technical and/or fundamental limitations in the storage-and-recall processes controlled by strong electromagnetic fields. Here, we experimentally implement a single-photon-level spin-wave memory in a laser-cooled Rubidium gas, based on the recently proposed Autler-Townes splitting (ATS) protocol. We demonstrate storage of 20-ns-long laser pulses, …
We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new SI traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT …
The absorption and dispersion of probe light is studied in an unified framework of three-level system, with coherent laser driving and incoherent pumping and relaxation. The electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are studied in details. In the phase diagram of the unified three-level system, there are distinct parameter regimes corresponding to different lineshapes and mechanisms, and the incoherent transition could control the cross-over between EIT and ATS. The incoherent control of the three-level system enables the investigation of various phenomen…
We describe how a coherent optical drive that is near-resonant with the upper rungs of a three-level ladder system, in conjunction with a short pulse excitation, can be used to provide a frequency-tunable source of on-demand single photons. Using an intuitive master equation model, we identify two distinct regimes of device operation: (i) for a resonant drive, the source operates using the Autler-Townes effect, and (ii) for an off-resonant drive, the source exploits the ac Stark effect. The former regime allows for a large frequency tuning range but coherence suffers from timing jitter effects…
Enhanced Sensitivity in Rydberg Atom Electric Field Sensors through Autler-Townes Effect and Two-Photon Absorption: A Theoretical Analysis Using Many-Mode Floquet Theory
Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler-Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a ?-type three-level system. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more…
In this paper we explore the physical origin of the transparency induced in absorbing three-level cascade atoms by the simultaneous interplay of two coherent beams of light. By utilizing the scattering technique we offer what we believe is a very convincing physical evidence for the existence, or for the absence, of quantum interference effects in the Autler-Townes (AT) and Electromagnetically Induced Transparency (EIT) phenomena.
Electromagnetically induced transparency (EIT) has been realized in atomic systems, but fulfilling the EIT conditions for artificial atoms made from superconducting circuits is a more difficult task. Here we report an experimental observation of the EIT in a tunable three-dimensional transmon by probing the cavity transmission. To fulfill the EIT conditions, we tune the transmon to adjust its damping rates by utilizing the effect of the cavity on the transmon states. From the experimental observations, we clearly identify the EIT and Autler-Townes splitting (ATS) regimes as well as the transit…
We offer a general treatment of electromagnetically induced transparency (EIT) in a five level system consisting of four metastable ground states. Two additional RF/microwave fields coherently couple the two ground states of the standard EIT $Λ$ atom to a pair of additional hyperfine states in the ground state manifold, generating two sets of dressed states that interact via the probe and control lasers, which couple to the electronic excited state. These new hyperfine dressed states manifest themselves in the linear optical susceptibility of the probe as new resonances in addition to the Autl…
We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solid-state materials. We observe EIT lineshapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous values. We obtain quantitative agreement between experiment and theory for the width of the transpa…
Frequency conversion process is studied in a medium of atoms with a $Λ$ configuration of levels, where transition between two lower states is driven by a microwave field. In this system, conversion efficiency can be very high by virtue of the effect of electromagnetically induced transparency (EIT). Depending on intensity of the microwave field, two regimes of EIT are realized: ''dark-state'' EIT for the weak field, and Autler-Townes-type EIT for the strong one. We study both cases via analytical and numerical solution and find optimum conditions for the conversion.
The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)-traceable and self-calibrated method for measuring a microwave electric field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between microwave Rabi frequency and Autler-Townes splitting is more valid a…
Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, …
We study spontaneous emission from an atom under the action of laser fields. We consider two different energy level diagrams. The first one consists of two levels resonantly driven by laser radiation where either of levels may decay to a separate level. For such a system we show that the presence of the second decay channel may deteriorate the destructive interference occurring in case of one decay channel because of Autler-Townes effect. The second diagram represents two two-level resonantly driven systems with the upper levels decaying to a common level. For this diagram we show that there i…
