Ac Stark Effect Research Articles

Electromagnetically induced transparency in indirectly coupled high‐temperature superconducting resonators

AbstractIn this letter, electromagnetically induced transparency (EIT) is implemented in the microwave region with an experimental system composed of two indirectly coupled high‐temperature superconducting resonators. The transition condition between EIT and Autler–Townes splitting is analyzed, giving a physical explanation of this transition based on the superposition of dressed modes in a three‐level system. Benefit from the ultra‐low loss of superconducting circuit, it is experimentally shown that either EIT or Autler–Townes splitting can be explicitly achieved through control of the detuning between the two resonators and a group delay as high as 5 μs is obtained for the EIT case. This work suggests that high temperature superconducting circuit is a concise and explicit platform for investigating indirectly coupled resonators with standing‐wave modes and the physical mechanism underneath coherence phenomena in the microwave region.

Two-Photon Laser Excitation of Rb Rydberg Atoms in the Magneto-Optical Trap and Vapor Cell

We present our experimental results of two-photon laser excitation 5S1/2→5P3/2→nS1/2 of Rb atoms to Rydberg nS1/2 states with a homemade 480 nm laser in the second excitation step. In an experiment with cold Rb atoms, we excited the 42S1/2 state and detected Rydberg atoms with a selective-field-ionization (SFI) detector that provides single-atom resolution. The resonance line shapes well agreed with numerical simulations in a three-level theoretical model. We also studied the multiatom spectra of Rydberg excitation of mesoscopic atom ensembles which are of interest to quantum information processing. In the experiment with hot Rb atoms, we first excited the 30S1/2 state and observed a narrow Rydberg EIT resonance. Its line shape also agreed well with theory. Then, we performed a similar experiment with the higher 41S1/2 state and observed the Autler–Townes splitting of the EIT resonance in the presence of a microwave field, which was in resonance with the microwave transition 41S→41P3/2. This allowed us to measure the average strength of the microwave field and, thus, demonstrate the operation of a Rydberg microwave sensor. We may conclude that the developed homemade laser at 480 nm substantially extends our capabilities for further experiments on quantum information and quantum sensing with Rydberg atoms.

Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency and Autler-Townes spectra in 87Rb vapor cell.

We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each mF state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute mF states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme mF states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.

Quantum criticality induced strong coupling between resonant modes

We propose a scheme to achieve a strong interaction between an optical cavity and a single polariton mode of an optomechanical cavity, despite a weak initial coupling between the two. This interaction is made possible by quantum criticality, and the coupled system comprising two optical cavities and an optomechanical cavity displays a phenomenon similar to the concepts of electromagnetically induced transparency (EIT) and Autler–Townes splitting in atomic physics.

Classic analogue of Autler–Townes-splitting transparency using a single magneto-optical ring resonator

We show that an optical transparency can be obtained by using only one single magneto-optical ring resonator. This effect is based on the splitting of counterclockwise and clockwise modes in the ring resonator. Within a proposed resonator-waveguide configuration the superposition between the two degeneracy broken modes produces a transparency window, which can be closed, open, and modified by tuning the applied magnetic field. This phenomenon is an analogue of Autler–Townes splitting, and the magnetic field is equivalent to the strong external pump field. We provide a theoretic analysis on the induced transparency, and numerically demonstrate the effect using full-wave simulation. Feasible implication of this effect and its potential applications are also discussed.

Perspective on electromagnetically induced transparency vs Autler–Townes splitting

Electromagnetically induced transparency and Autler–Townes splitting are two distinct yet related effects. These phenomena are relevant to quantum technologies, including quantum memory, quantum switching, and quantum transduction. Here, the similarities and differences between these phenomena along historical and conceptual lines are discussed and their realizations on various physical platforms including atomic gases, superconducting circuits, and optomechanics are elaborated. In particular, the author clarifies two approaches to assessing which phenomenon is observed based on a black-box approach of modeling the output, given a particular input vs analyzing the underpinning physics. Furthermore, the author highlights the ability to effect a continuous transition between the two seemingly disparate phenomena.

Quantum Control of a Single Magnon in a Macroscopic Spin System.

Nonclassical quantum states are the pivotal features of a quantum system that differs from its classical counterpart. However, the generation and coherent control of quantum states in a macroscopic spin system remain an outstanding challenge. Here we experimentally demonstrate the quantum control of a single magnon in a macroscopic spin system (i.e., 1mm-diameter yttrium-iron-garnet sphere) coupled to a superconducting qubit via a microwave cavity. By tuning the qubit frequency insitu via the Autler-Townes effect, we manipulate this single magnon to generate its nonclassical quantum states, including the single-magnon state and the superposition of single-magnon state and vacuum (zero magnon) state. Moreover, we confirm the deterministic generation of these nonclassical states by Wigner tomography. Our experiment offers the first reported deterministic generation of the nonclassical quantum states in a macroscopic spin system and paves a way to explore its promising applications in quantum engineering.

Rydberg-State Engineering: Investigations of Tuning Schemes for Continuous Frequency Sensing

On-resonance Rydberg atom--based radio-frequency- (rf) electric-field sensing methods remain limited by the narrow frequency-signal detection bands available from resonant transitions. An additional rf tuner field can be used to dress or shift a target Rydberg state to return a detuned signal field to resonance and thus dramatically extend the frequency range available for resonant sensing. Here we investigate three distinct tuning-level schemes based on adjacent Rydberg transitions, which are shown to have distinct characteristics and can be controlled with the frequency or the strength of the tuning field. We further show that a two-photon Raman peak can be used as an effective tuning feature separate from conventional Autler-Townes splitting. We compare our tuning schemes with ac Stark effect--based broadband rf-field sensing and show that although the sensitivity is diminished with tuning away from a resonant state, it nevertheless can be used in configurations where there is a low density of Rydberg states, which would result in a weak ac Stark effect.

Memory and Transduction Prospects for Silicon T Center Devices

The T center, a silicon-native spin-photon interface with telecommunication-band optical transitions and long-lived microwave qubits, offers an appealing new platform for both optical quantum memory and microwave-to-optical telecommunication-band transduction. A wide range of quantum memory and transduction schemes could be implemented withT center ensembles with sufficient optical depth, with advantages and disadvantages that depend sensitively on the ensemble properties. In this work we characterize T center spin ensembles to inform device design. We perform the first T ensemble optical depth measurement and calculate the improvement in center density or resonant optical enhancement required for efficient optical quantum memory. We further demonstrate a coherent microwave interface by coherent population trapping and Autler-Townes splitting. We then determine the most promising microwave and optical quantum memory protocol for such ensembles. By estimating the memory efficiency both in free space and in the presence of a cavity, we show that efficient optical memory is possible with reasonable optical density forecasts. Finally, we formulate a transduction proposal and discuss the achievable efficiency and fidelity.Received 13 September 2022Accepted 13 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020308Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoherent population trappingElectromagnetically induced transparencyQuantum information with hybrid systemsQuantum information with solid state qubitsQuantum interconnectsQuantum memoriesQuantum networksQuantum repeatersQuantum InformationAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect

A novel version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time varying, spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the 2-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric AB effect and the AC Stark effect.

Extending bandwidth sensitivity of Rydberg-atom-based microwave electrometry using an auxiliary microwave field

We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.

Autler–Townes splitting in the trap-loss fluorescence spectroscopy due to single-step direct Rydberg excitation of cesium cold atomic ensemble

We experimentally investigate trap-loss spectra of the cesium 6S1/2(F = 4) → 71P3/2 Rydberg transition by combining the cesium atomic magneto-optical trap with the narrow-linewidth, continuously tunable 318.6 nm ultraviolet laser. Specifically, the atoms in the magneto-optical trap are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which leads to the reduction of atomic fluorescence. Based on the trap-loss spectroscopy technology, the Autler–Townes (AT) splitting due to a strong cooling laser is observed, and the parameter dependence of the AT splitting interval of trap-loss spectroscopy is investigated. The effective temperature of cold atoms is measured by using simplified time-of-flight fluorescence imaging. In addition, closed-loop feedback power stabilization of 318.6 nm ultraviolet laser is carried out. This lays the foundation for further experimental research related to the Rydberg atoms using ultraviolet lasers, which is of great significance for the development of quantum computing and quantum information.

Spectroscopic study of the F[formula omitted] outer well state in H2, HD and D2

Two-photon UV-photolysis of hydrogen sulfide molecules is applied to produce hydrogen molecules in highly excited vibrational levels in the X1Σg+ electronic ground state, up to the dissociation energy and into the quasibound region. Photolysis precursors H2S, HDS and D2S are used to produce vibrationally hot H2, HD and D2. The wave function density at large internuclear separation is excited via two-photon transitions in the F1Σg+ - X1Σg+ system to probe ro-vibrational levels in the first F1Σg+ outer well state of gerade symmetry. Combining with accurate knowledge of the X1Σg+ (v,J) levels from advanced ab initio calculations, energies of rovibrational levels in the F1Σg+ state are determined. For the H2 isotopologue a three-laser scheme is employed yielding level energies at accuracies of 4×10−3 cm−1 for F(v=0,J) up to J=21 and for some low J values of F(v=1). A two-laser scheme was applied to determine level energies in H2 for F(v=0−4) levels as well as for various F levels in HD and D2, also up to large rotational quantum numbers. The latter measurements in the two-laser scheme are performed at lower resolution and the accuracy is strongly limited to 0.5 cm−1 by ac-Stark effects. For H2 a new quasibound resonance X1Σg+ (v=6, J=23) is detected through the Q(23) and O(23) transitions in the F0-X6 band. Also a quasi-bound resonance in D2 is assigned, for the first time in this species: X1Σg+ (v=17 , J=15). The experimental results on F(v,J) level energies are compared with previously reported theoretical results from multi-channel quantum-defect calculations as well as with results from newly performed non-adiabatic quantum calculations.

Multichannel Six‐Wave Mixing with Spatial Multimode and Squeezing via Atomic Coherence

AbstractMultimode properties, based on nonlinear parametric processes, have potential research value on entanglement imaging. This paper studies the spatial and frequency multimode from dressing parametric‐amplified six‐wave mixing (PA‐SWM) process with three entangled signals. The S1 signal contains fifth‐order nonlinearity, the S2 signal contains electromagnetically induced absorption and fifth‐order nonlinearity, and the S3 signal contains Autler–Townes splitting (AT), second‐ and fifth‐order nonlinearity. The frequency multimode is attributed to dressing energy level splitting in spontaneous SWM (SSWM) process. The spatial multimode is due to frequency multimode and beam splitting via Kerr nonlinearity. In the spatial domain, it finds the optimal conditions of intensity difference squeezing (IDS) and spatial imaging along with their competitive relationship. On the one hand, the light spots with single spatial mode are contributed to the maximum IDS but not conducive to entanglement imaging; on the other hand, the light spots with multiple spatial modes are instrumental in entanglement imaging but not appropriate for the IDS. This research has potential applications in squeezed light sources for quantum metrology, and correlated imaging of spatial signals.

Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields

We show that two seemingly unrelated problems—the trapping of an atom in an optical superlattice (OSL) and the libration of a planar rigid rotor in combined electric and optical fields (PR) – have isomorphic Hamiltonians. Formed by the interference of optical lattices whose spatial periods differ by a factor of two, OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect. The PR system, also known as the generalized planar pendulum, is realized by subjecting a planar rigid rotor to combined orienting and aligning interactions due to the coupling of the rotor’s permanent and induced electric dipole moments to the combined fields. The PR system belongs to the class of conditionally quasi-exactly solvable problems and exhibits intriguing spectral properties that have been established in our previous work Becker et al (2017 Eur. Phys. J. D 71 149). Herein, we make use of both the PR OSL mapping and the quasi-exact solvability of the PR system to treat ultracold atoms in an OSL as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained previously for the PR system as solutions of the Whittaker-Hill equation. These solutions characterize both the squeezing and the tunneling of atoms trapped in an OSL and pave the way to unraveling their dynamics in analytic form. Furthermore, the PR OSL mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other.

Atomic mixer based on phase control without ac Zeeman shift

Atom-based mixers have been shown to be very useful in performing the absolute measurement of the magnitude of a radio-frequency (rf) field by using Autler-Townes (AT) splitting. However, there has been less success in measuring the phase of a rf field with the AT splitting in a magnetic-resonance system. The phase of the rf magnetic field plays a very important role in imaging applications. Here, we design an atomic mixer for measuring the phase of the rf field by detecting the transmission spectra of a laser-detected magnetic-resonance system based on the interference between Raman and cascade two-photon processes for ${F}_{g}=4$ of the ${D}_{1}$ line of cesium atoms. A scheme of measuring the rf phase can be realized with the elimination of the ac Zeeman shift of the system by adjusting the amplitude ratio of a transverse fundamental-wave field and its third-harmonic field. Theoretical and experimental results show that the scheme with cancellation of the ac Zeeman shift is superior in linear measurement of the longitudinal rf component. Our results provide schemes for a magnetic sensor based on quantum interference of nonlinear processes for the absolute measurement of the relative phase of rf fields.

Observation of the transition from inverted coupled-resonator-induced transparency to inverted Autler-Townes splitting

Inverted coupled-resonator-induced transparency eliminates amplification as a result of destructive interference between two competing excitation pathways and induces a ``nonamplifying'' transparency window in an otherwise strongly amplifying spectral region. Using coupled ring resonators as a model system, we systematically examined the transition from inverted induced transparency to Autler-Townes splitting (ATS) by controlling the coupling strength between two resonators. The inverted induced transparency spectrum transitioned into different ATS spectra depending on the parameters of the resonators. We also examined the transition that occurs when the second resonator has gain. In this case, the system showed enhanced transparency, in which the intensity of the induced window was much greater than the incident laser level.

Improving the spectral resolution and measurement range of quantum microwave electrometry by cold Rydberg atoms

We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler–Townes splitting (EIT-AT splitting). In cold atoms, a spectral linewidth of ∼500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e. by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity (E MW) that can be measured is 430 µV cm−1, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if E MW is so large that the EIT-AT splitting interval exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ω p ). Moreover, EIT-AT splitting can be observed if exceeds the natural linewidth of the intermediate states while scanning the coupling laser (ω c ) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ω c , the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV cm−1, nearly three times higher than that of 6.8 mV cm−1 while scanning ω p . The results indicate that the linear range of E MW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.

Atom-based sensing technique of microwave electric and magnetic fields via a single rubidium vapor cell.

We present an atom-based approach for determining microwave electric and magnetic fields by using a single rubidium vapor cell in a microwave waveguide. For a 87Rb cascade three-level system employed in our experiment, a weak probe laser driving the lower transition, 5S1/2→5P3/2, is first used to measure the microwave magnetic field based on the atomic Rabi resonance. When a counter-propagating strong coupling laser is subsequently turned on to drive the Rydberg transition, 5P3/2→67D5/2, the same probe laser is then used as a Rydberg electromagnetically induced transparency (EIT) probe to measure the microwave electric field by investigating the resonant microwave dressed Autler-Townes splitting (ATS). By tuning the hyperfine transition frequency of the ground state using an experimentally feasible static magnetic field, we first achieved a measurement of the microwave electric and magnetic field strength at the same microwave frequency of 6.916 GHz. Based on the ideal relationship between the electric and magnetic field components, we obtained the equivalent microwave magnetic fields by fitting the inversion to the measured microwave electric fields, which demonstrated that the results were in agreement with the experimental measurement of the microwave magnetic fields in the same microwave power range. This study provides new experimental evidence for quantum-based microwave measurements of electric and magnetic fields by a single sensor in the same system.

Tunable high-Q resonance and abnormal phase-shift in P T-symmetric meta-molecules

We analyze the optical response of a parity-time ( P T ) symmetric diatomic meta-molecular array. We show that the P T symmetry can transform an initial dark antisymmetric mode of the diatomic meta-molecule into bright, featured by a high-Q peak in the scattering spectrum. The Q factor is tunable by managing the magnitudes of the gain and loss. Furthermore, around this high-Q resonance an abnormal phase-shift is obtained, which persists even at exceptional point. We also show that the effective dielectric constant of the P T -symmetric meta-molecular array can be modeled by an anomalous doubly-resonant Lorentz oscillator, which is different from that in electromagnetically induced transparency and Autler-Townes splitting. This study contributes to the advances of non-Hermitian optics and slow light.