Ac Stark Effect Research Articles

Phase-controlled dual-wavelength resonance in a self-coupling whispering-gallery-mode microcavity

We report a novel, to the best of our knowledge, way to achieve phase-controlled dual-wavelength resonance based on whispering-gallery-mode (WGM) microcavities experimentally. With the help of a feedback waveguide, not only two optical pathways but also a unidirectional coupling between counter-propagating waves are formed, which is the requirement of all-optical analogues of electromagnetically induced transparency and Autler-Townes splitting. By adjusting the accumulating phase introduced from the fiber waveguide, we observe the signal lineshape changes from symmetric to asymmetric, i.e., the resonant transmission and extinction ratio of two splitting modes can be controlled, which brings a new degree of freedom to the WGM resonator system. These results may boost the development of quantum state control and pave the way for reconfiguring devices such as narrow-band filters.

The analysis of coherent phenomena for both linear and non-linear interactions in a four-level ladder (Ξ)-type configuration using density matrix formalism in dressed state representation

In this paper, we present a theoretical study of Autler-Townes (AT) splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a four-level ladder (Ξ)-type configuration formed by two coupling and one probe laser fields using density matrix formalism in dressed state representation (DSR). The DSR is followed by the analytical solution of the optical Bloch equations (OBEs) under density matrix formalism in bare state representation (BSR). The density matrix elements are presented in both linear and non-linear interaction regimes under DSR. The concept of transfer of population (TOP) mechanism has been shown by calculating the different transition probabilities in DSR. It has been found that the population in a particular dressed state is greatly enhanced by increasing the strength of coupling field and played a key role to manipulate the induced coherence between different energy levels. The present theoretical model of DSR offers an excellent interpretation of the formation of EIT, EIA and conversion from EIT to EIA in both linear and third order non-linear probe absorption profiles. Besides, the dispersion profiles in both linear and non-linear interaction regimes have also been studied and the conversion of normal to anomalous dispersion profile which drastically modifies the optical responses of the medium has been discussed. We have found that the amplitudes of the coherent signals are more sensitive to the third order non-linear interaction compared to first order linear interaction.

Using Circular Dichroism to Control Energy Transfer in Multiphoton Ionization.

Chirality causes symmetry breaks in a large variety of natural phenomena ranging from particle physics to biochemistry. We investigate one of the simplest conceivable chiral systems, a laser-excited, oriented, effective one-electron Li target. Prepared in a polarized p state with |m|=1 in an optical trap, the atoms are exposed to co- and counterrotating circularly polarized femtosecond laser pulses. For a field frequency near the excitation energy of the oriented initial state, a strong circular dichroism is observed and the photoelectron energies are significantly affected by the helicity-dependent Autler-Townes splitting. Besides its fundamental relevance, this system is suited to create spin-polarized electron pulses with a reversible switch on a femtosecond timescale at an energy resolution of a few meV.

Microwave quantum optics as a direct probe of the Overhauser field in a quantum dot circuit quantum electrodynamics device

We show theoretically that a quantum-dot circuit quantum electrodynamics (CQED) device can be used as a probe of the Overhauser field in quantum dots. By coupling a transmission line to the interdot tunneling gate, an electromagnetically-induced-transparency (EIT) scheme can be established, whose Fano-type interference leads to a sharp curvature in the reflection spectrum around resonance. This sharp feature persists even in the presence of the fluctuating spin bath, rendering a high-resolution method to extract the bath's statistical information. For strong nuclear spin fields, the reflection spectrum exhibits an Autler-Townes splitting, where the peak locations indicate the strengths of the Overhauser field gradient (OFG).

Rabi Oscillations and Coherence Dynamics in Terahertz Streaking-Assisted Photoelectron SpectrumSupported by the National Natural Science Foundation of China (Grant Nos. 11827806, 11874368 and 61675213).

We present an approach, a Terahertz streaking-assisted photoelectron spectrum (THz SAPS), to achieve direct observations of ultrafast coherence dynamics with timescales beyond the pulse duration. Using a 24 fs probe pulse, the THz SAPS enables us to well visualize Rabi oscillations of 11.76 fs and quantum beats of 2.62 fs between the 5S 1/2 and 5P 3/2 in rubidium atoms. The numerical results show that the THz SAPS can simultaneously achieve high resolution in both frequency and time domains without the limitation of Heisenberg uncertainty of the probe pulse. The long probe pulse promises sufficiently high frequency resolution in photoelectron spectroscopy allowing to observe Autler–Townes splittings, whereas the streaking THz field enhances temporal resolution for not only Rabi oscillations but also quantum beats between the ground and excited states. The THz SAPS demonstrates a potential applicability for observation and manipulation of ultrafast coherence processes in frequency and time domains.

Controlling the ac Stark effect of RbCs with dc electric and magnetic fields

We investigate the effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic $^{87}$Rb$^{133}$Cs molecules, for light of wavelength $\lambda = 1064~\mathrm{nm}$. Near this wavelength we observe unexpected two-photon transitions that may cause trap loss. We measure the ac Stark effect in external magnetic and electric fields, using microwave spectroscopy of the first rotational transition. We quantify the isotropic and anisotropic parts of the molecular polarizability at this wavelength. We demonstrate that a modest electric field can decouple the nuclear spins from the rotational angular momentum, greatly simplifying the ac Stark effect. We use this simplification to control the ac Stark shift using the polarization angle of the trapping laser.

Improvement of Microwave Electric Field Measurement Sensitivity via Multi-Carrier Modulation in Rydberg Atoms

The microwave electric field intensity is precisely measured by the Autler–Townes splitting of electromagnetically induced transparency spectrum in a 5S1/2−5P3/2−57D5/2−58P3/2 four-level ladder-type 85Rb atomic system. A robust multi-carrier modulation scheme is employed to improve the spectral signal-to-noise ratio, which determines the optical readout of Rydberg atom-based microwave electrometry. As a result, a factor of 2 measurement sensitivity improvement is clearly achieved compared with the on resonant Autler–Townes splitting case credit to the advantage of matched filtering. This research paves the way for building a high sensitivity, portable sensor and offers a platform for achieving compact and sensitive receiver.

RF E-field Sensing Using Rydberg Atom-Based Microwave Electrometry

In this work, a microwave field is sensed by rubidium atoms instead of a conventional antenna like dipole or horn antenna. Microwave field is projected onto a glass cell containing Rb vapors which act as an antenna in this case. A four-level ladder atomic system is considered for analytical solution, and E-field measurement is reported by utilizing quantum phenomena like electromagnetically induced transparency and Autler–Townes splitting. It has been shown that atoms can also sense weak microwave field with this approach. The amplitude measurement of microwave E-field is changed to frequency measurement, and E-field is evaluated by monitoring the frequency difference between two EIT peaks. Measurement results are reported for variable input microwave power at frequency 15.09 GHz varying from 12.5 μW to 4 mW generated from synthesized signal generator. Moreover, the effect on the EIT resonance due to the distance variation of the source antenna is also discussed. The microwave frequency is detuned from the resonant frequency, and results are reported in this work.

A new method for high-bandwidth servo control of the power ratio between two Raman beams for cold atom interferometer.

Light shift produced by the AC Stark effect is one of the major factors limiting the accuracy and long-term stability of a cold atom interferometer. The first order light shift can be canceled by fixing the power ratio of the Raman beams at a specified value. We report here a new method to stabilize the power ratio of the two Raman lasers with ∼100 kHz locking bandwidth, suppressing the effect of the first order light shift. We first mixed the two Raman lasers (at different optical frequencies) with a reference beam and then used two Schottky diode detectors to extract the corresponding beat note signals for each beam, which are much easier to be manipulated and processed as they are in the microwave band. The stability of the power ratio is improved by three orders of magnitude from 5.84 × 10-3 to 3.51 × 10-6 at 1 s averaging time and reaches 1.59 × 10-7 at 10 000 s integrating time when the servo loop is engaged. This method can be used in other precise quantum measurement based on the stimulated Raman transition and can be applied to compact inertial sensors.

Dispersive microwave electrometry using Zeeman frequency modulation spectroscopy of electromagnetically induced transparency in Rydberg atoms

We herein developed and demonstrated a Zeeman frequency modulation scheme for improving the signal-to-noise ratio of microwave electric field measurement using Rydberg atoms. The spectra of the electromagnetically induced transparency (EIT) and Autler-Townes splitting of Rydberg atoms is frequency modulated by an alternating current magnetic field. The signal-to-noise ratio of the corresponding dispersive error signal is enhanced more than 10 times than that of the original spectrum. Furthermore, we show that the slope of the dispersive error signal near the resonance of the Rydberg EIT can be used to characterize the weak microwave electric field amplitudes. The more intuitive and simpler structure compared with other existing frequency modulation technologies greatly reduces the difficulties of experiments and experimental data analysis.

Effect of coating few-layer WS2 on the Raman spectra and whispering gallery modes of a microbottle resonator

Multi-layered tungsten disulfide (WS2) coated silicon/silica (Si/SiO2) substrate and SiO2 micro-bottle resonators (MBRs) have been prepared by van der Waals epitaxy method. Raman spectra of WS2-coated MBR show that the out-of-plane Raman mode is sensitive to the polarization of the excitation laser. The quality factor (Q) values of the whispering gallery modes (WGMs) in the transmission spectrum of an MBR decrease by 2 orders of magnitude on coating with WS2. On coating, a cleaner spectrum is obtained along with a concomitant effect of decrease in the number of lossy modes. Fano resonances as well as Autler-Townes splitting (ATS) was observed for the WGMs in the cleaned transmission spectrum. From the simulations it has been verified that the scattered electric field of the WS2 flakes contributes to the observation of the Fano resonances and ATS in the coated MBR spectra.

Tunable Autler-Townes-Like Resonance Splitting in a Bent Fiber-Optic Fabry-Perot Resonator: 3D Modeling and Experimental Verification

We present a numerical and experimental study of resonance splitting in the transmission and reflection spectra of the Fabry-Perot resonator made of a bent section of a conventional single-mode optical fiber with metallized end faces. We show the splitting to be similar in nature to the well-known Autler-Townes effect and to arise from the strong coupling between the core mode and cladding whispering gallery mode of the bent fiber. The effect of all major parameters of the bent resonator on the splitting of its resonances is demonstrated. Potential applications of the observed effects in the field of precision optical refractometry as well as further research directions are discussed.

Polarization-insensitive complementary metamaterial structure based on graphene for independently tuning multiple transparency windows**Project supported by the National Natural Science Foundation of China (Grant No. 61275174).

Polarization-insensitive multiple transparency windows are obtained with a graphene-based complementary metamaterial structure in terahertz regions, which is composed of two kinds of monolayer graphene perforated in shapes of a cross and four identical split rings that construct a resonator. The geometric parameters of resonators are different from each other. Numerical and theoretical results show that the quantum effect of Autler–Townes splitting is the key factor for appearance of transparency windows within the resonant dips. Further investigation demonstrates that by employing the fourfold-symmetry graphene complementary structure, polarization-independent transparency windows can be achieved. Moreover, multiple transparency windows can be separately manipulated over a broad frequency range via adjusting the chemical potential of the corresponding graphene resonators, and the bandwidth as well as resonance strength can also be tuned by changing the relative displacement between resonators each consisting of a cross and four split rings. The proposed metamaterial structure may be utilized in some practical applications with requirements of no polarization-varied loss and slowing the light speed.

All-THz pump-probe spectroscopy of the intersubband AC-Stark effect in a wide GaAs quantum well.

We report the observation of the intersubband AC-Stark effect in a single wide GaAs/AlGaAs quantum well. In a three-level configuration, the n = 2 to n = 3 intersubband transition is resonantly pumped at 3.5 THz using a free-electron laser. The induced spectral changes are probed using THz time-domain spectroscopy with a broadband pulse extending up to 4 THz. We observe an Autler-Townes splitting at the 1 - 2 intersubband transition as well as an indication of a Mollow triplet at the 2 - 3 transition, both evidencing the dressed states. For longer delay times, a relaxation of the hot-electron system with a time constant of around 420 ps is measured.

Experimental Observation of the Autler-Townes Splitting in Polyatomic Molecules.

Autler-Townes (AT) splitting has been experimentally observed in the optical transition between the zero-point levels of S1 and S0 for supersonically cooled 2-methoxythiophenol, 2-fluorothiophenol, and 2-chlorothiophenol. This is the first experimental observation of the light-dressed quantum states of polyatomic molecules (N > 3) in the electronic transition. In the resonance-enhanced ionization process involving the optically coupled states, if Rabi cycling is ensured within the nanosecond laser pulse, AT splitting is clearly observed for the open system for which the excited-state lifetime is shorter than hundreds of picoseconds. Semiclassical optical Bloch equations and a dressed-atom approach based on the three-level atomic model describe the experiment quite well, giving deep insights into the light-matter interaction in polyatomic molecular systems.

Self-induced splitting of x-ray emission lines

We present a theoretical approach for describing collective x-ray emission processes in extended multilevel targets, based on a combination of propagation equations for the quantum correlation functions and the semiclassical Maxwell-Bloch equations. Such a description overcomes the key deficiencies of the two constituent sets of equations, which have until now been independently used to describe these phenomena. The model developed is employed to study the spectral properties of superfluorescence of $K\ensuremath{\alpha}$ emission in zinc at $\ensuremath{\sim}8630\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ after inner-shell photoionization with intense attosecond free-electron laser pulses. At high pump intensities, the numerical simulations predict a splitting of the $K{\ensuremath{\alpha}}_{1}$ emission line due to a self-induced Autler-Townes effect, which could readily be observed with standard high-resolution x-ray spectrometers. As short duration of the pump pulse is one of the crucial parameters for the manifestation of this phenomenon in the hard-x-ray regime, experimental verification could be possible due to the most recent developments of free-electron laser sources.

Microwave Electric Field Measurement Based on Electromagnetically-Induced Transparency and Absorption in Atomic Vapor Cell at Room Temperature

The traceability of microwave electric field is measured based on the Rydberg atomic quantum interference effect. The rubidium atomic vapor cell at room temperature is used as the probe, and the Autler-Townes splitting of two-photon electromagnetically-induced transparency, three-photon electromagnetically-induced transparency and three-photon electromagnetically-induced absorption effect are analyzed theoretically. The measurement limit of atomic shot noise is also discussed. This method is not only suitable for the traceability and self-calibration measurement of the microwave electric field but also for the sub-wavelength imaging and vector measurement of the microwave electric field and will provide a reference for further miniaturization and integration of the atomic microwave probe.

Photoelectron imaging on vibrational excitation and Rydberg intermediate states in multi-photon ionization process of NH3 molecule**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574116, 11534004, and 10704028).

The ionization processes of NH3 molecule are studied by photoelectron velocity map imaging technique in a linearly polarized 400-nm femtosecond laser field. The two-dimensional photoelectron images from ammonia molecules under different laser intensities are obtained. In the slow electron region, the values of kinetic energy of photoelectrons corresponding to peaks 1, 2, 3, and 4 are 0.27, 0.86, 1.16, and 1.6 eV, respectively. With both the kinetic energy and angular distribution of photoelectrons from NH3 molecules, we can confirm that the two-photon excited intermediate Rydberg state is A∼1 () state for photoelectron peaks 2, 3, 4, and the three peaks are marked as 1223 (2 + 2), 1123 (2 + 2), and 1023 (2 + 2) multi-photon processes, respectively. Then, peak 1 is found by adding a hexapole between the source chamber and the detection chamber to realize the rotational state selection and beam focusing. Peak 1 is labeled as the 1323 (3 + 1) multi-photon process through the intermediate Rydberg state . The phenomena of channel switching are found in the slow electron kinetic energy distributions. Our calculations and experimental results indicate that the stretching vibrational mode of ammonia molecules varies with channels, while the umbrella vibration does not. In addition, we consider and discuss the ac-Stark effect in a strong laser field. Peaks 5 and 6 are marked as (2 + 2 + 1) and (2 + 2 + 2) above threshold ionization processes in the fast electron region.

THz white light cavity with nonlinear dispersion in graphene.

A white light cavity (WLC) scheme is proposed to achieve broadband response in the terahertz (THz) region by enhanced nonlinear dispersion in a magnetized graphene system. In the weak probe field limit, the cavity linewidth is narrowed due to electromagnetically induced transparency, and then it becomes nearly as broad as the empty-cavity linewidth under the condition of Autler-Towns splitting. It is interesting to find that the cavity linewidth can be further broadened by enhanced nonlinear dispersion. The simulation result shows that the response range of the cavity is from 6.273 THz to 6.308 THz under the given condition, which is nearly 11 times larger than the empty-cavity linewidth. Furthermore, the improvement in cavity transmission and the response of WLC at different frequencies are investigated.

The discerning of optomechanically induced transparency and Autler-Townes splitting in an optomechanical system

Optomechanically induced transparency (OMIT) which exhibits a transparent window in the absorption spectrum of the optical field has been observed in the optomechanical systems. Autler-Townes splitting (ATS) which describes the coherent superposition of the fields presents also a similar transmission spectrum. Here in this study, we analyze these two effects and find that the performance of OMIT and ATS could be effectively manipulated through the tuning of the coupling rate and the loss rate. We numerically compare the quantity of the two phenomena using the Akaike Information Criterion, the Bayesian Information Criterion and the Hannan-Quinn Criterion, respectively.