We devise an ab initio formalism for the quantum dynamics of Auger decay by laser-dressed atoms which are inner-shell ionized by extreme ultraviolet (XUV) light. The optical dressing laser is assumed to be sufficiently weak such that ground-state electrons are neither excited nor ionized by it. However, the laser has a strong effect on continuum electrons which we describe in strong-field approximation with Volkov waves. The XUV light pulse has a low peak intensity and its interaction is treated as a one-photon process. The quantum dynamics of the inner-shell hole creation with subsequent Auger decay is given by equations of motion (EOMs). For this paper, the EOMs are simplified in terms of an essential-states model which is solved analytically and averaged over magnetic subshells. We apply our theory to the M_4,5 N_1 N_2,3 Auger decay of a 3d hole in a krypton atom. The orbitals are approximated by scaled hydrogenic wave functions. A single attosecond pulse produces 3d vacancies which Auger decay in the presence of an 800nm laser with an intensity of 10^13 W / cm^2. We compute the Auger electron spectrum and assess the convergence of the various quantities involved.
We have unveiled coherent multiphoton interferences originating from different quantum paths taken by the Auger electron induced by a high-intensity x-ray/XUV pulse under the presence of a strong optical field. These interferences give rise to a clear signature in the angle-resolved Auger electron spectrum: an asymmetry with respect to the energy of the Auger decay channel. In order to illustrate this effect we have considered the resonant Auger decay of the transition $2p^{5} \!\leftrightarrow\! 1s^{-1}2p^{6}$ in Ne$^{+}$. The simulations show that these interferences are very sensitive to th…
Single photon laser enabled Auger decay (spLEAD) has been redicted theoretically [Phys. Rev. Lett. 111, 083004 (2013)] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we have detected the process and coherently controlled the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems.
A generalization of non-perturbative QED model for high harmonic generation is developed for the multi-mode optical field case. By introducing classical-field-dressed quantized Volkov states analytically, a formula to calculate HHG for hydrogen-like atom in ultrashort intense laser pulse is obtained, which has a simple intuitive interpretation. The dressed state QED model indicates a new perspective to understand HHG, for example, the presence of the weak even-order harmonic photons, which has been verified by both theoretical analysis and numerical computation. Long wavelength approximation a…
We explore the possibility of retrieving Auger spectra with FEL radiation. Using a laser pulse of 260 eV photon energy, we study the interplay of photo-ionization and Auger processes following the initial formation of a 2p inner-shell hole in Ar. Accounting for the fine structure of the ion states we demonstrate how to retrieve the Auger spectrum of $\mathrm{Ar^{+}\rightarrow Ar^{2+}}$. Moreover, considering two electrons in coincidence we also demonstrate how to retrieve the Auger spectrum of $\mathrm{Ar^{2+}\rightarrow Ar^{3+}}$.
Photoelectron emission from excited states of laser-dressed atomic helium is analyzed with respect to laser intensity-dependent excitation energy shifts and angular distributions. In the two-color XUV (exteme ultra\-violet) -- IR (infrared) measurement, the XUV photon energy is scanned between \SI{20.4}{\electronvolt} and the ionization threshold at \SI{24.6}{\electronvolt}, revealing electric dipole-forbidden transitions for a temporally overlapping IR pulse ($\sim\!\SI{e12}{\watt\per \centi\meter\squared}$). The interpretation of the experimental results is supported by numerically solving t…
Using attoscience, we study the electron correlations responsible for Auger decay in krypton atoms. The Auger decay is induced by a pulse train or a twin pulse composed of subpulses of attosecond duration. During the Auger decay an optical dressing laser may be present. Interference effects between the ejected Auger electron wave packets are predicted.
We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbatio…
Light-induced states are commonly observed in the photoionization spectra of laser-dressed atoms. The properties of autoionizing polaritons, entangled states of light and Auger resonances, however, are largely unexplored. We employ attosecond transient-absorption spectroscopy to study the evolution of autoionizing states in argon, dressed by a tunable femtosecond laser pulse. The avoided crossings between the $3s^{-1}4p$ and several light-induced states indicates the formation of polariton multiplets. We measure a controllable stabilization of the polaritons against ionization, in excellent ag…
We demonstrate a technique for precisely measuring hyperfine intervals in alkali atoms. The atoms form a three-level $Λ$ system in the presence of a strong control laser and a weak probe laser. The dressed states created by the control laser show significant linewidth reduction. We have developed a technique for Doppler-free spectroscopy that enables the separation between the dressed states to be measured with high accuracy even in room-temperature atoms. The states go through an avoided crossing as the detuning of the control laser is changed from positive to negative. By studying the separa…
We propose a theoretical approach for the interpretation of pump-probe measurements where an attosecond pulse is absorbed in the presence of an intense laser pulse. This approach is based on abstractly defined dressed bound states, which capture the essential aspects of the interaction with the laser pulse and facilitate a perturbative description of transitions induced by the attosecond pulse. Necessary properties of dressed bound states are defined and various choices are discussed and compared to accurate numerical solutions of the time-dependent Schroedinger equation.
Photoelectron spectroscopy of 3s3p doubly excited helium dressed with strong near-infrared laser fields
Nagoya University（名古屋大学）；RIKEN, SPring-8 Center（理化学研究所 SPring-8 中心）；Fu-Jen Catholic University（辅仁大学）；Japan Synchrotron Radiation Research Institute（日本同步辐射研究机构）；University of Toyama（富山大学）
We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7 kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at $< 1 μK$. By increasing the density to $1 \times 10^{12} \rm{cm^{-3}}$, we show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable l…
The theory of resonant Auger decay of atoms in a high intensity coherent X-ray pulse is presented. The theory includes the coupling between the ground state and the resonance due to an intense X-ray pulse, taking into account the decay of the resonance and the direct photoionization of the ground state, both populating the final ionic states coherently. The theory also considers the impact of the direct photoionization of the resonance state itself which typically populates highly-excited ionic states. The combined action of the resonant decay and of the direct ionization of the ground state i…
Using extreme-ultraviolet attosecond-pulse-trains, we investigate the photoionization dynamics of a Helium atom in the presence of moderately-strong (~10^12 W/cm^2) femtosecond laser pulses. The electronic structure of a laser-dressed atom is traced in real-time through precision measurements of ion-yields and photo-electron angular distributions. Quantum interferences between photo-excitation paths are interpreted using the Floquet formalism. As the laser pulse intensity ramps on femtosecond timescales, we observe transitions between ionization channels mediated by different atomic resonances…
X-ray refraction and absorption by neon atoms under the influence of an 800 nm laser with an intensity of 10^13 W/cm^2 is investigated. For this purpose, we use an ab initio theory suitable for optical strong-field problems. Its results are interpreted in terms of a three-level model. On the Ne 1s --> 3p resonance, we find electromagnetically induced transparency (EIT) for x rays. Our work opens novel perspectives for ultrafast x-ray pulse shaping.
We discuss harmonic generation in the case of laser field-dressed Hamiltonians that are invariant under so-called dynamical symmetry operations. Examples for such systems are molecules which exhibit a discrete rotational symmetry of order N (e.g. benzene with N=6) interacting with a circularly polarized laser field and single atoms in a bichromatic field, with the two lasers having circular polarizations. Within a general group theory approach we study the harmonics one obtains from the interaction of a laser pulse and a circular molecule. When the system is in a pure field-dressed state the k…
We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different parameters of the FEL pulse, allows us to identify the most efficient parameters of the FEL pulse for obtaini…
The derivation of approximate wave functions for an electron submitted to both a coulomb and a time-dependent laser electric fields, the so-called Coulomb-Volkov (CV) state, is addressed. Despite its derivation for continuum states does not exhibit any particular problem within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. Indeed the natural way of translating the unperturbed momentum by the laser vector potential is no longer possible since a bound state does not exhibit a plane wave form including explicit…
We study the effects of field fluctuations on the total yields of Auger electrons, obtained in the excitation of neutral atoms to a core-excited state by means of short-wavelength free-electron-laser pulses. Beginning with a self-contained analysis of the statistical properties of fluctuating free-electron-laser pulses, we analyse separately and in detail the cases of single and double Auger resonances, focusing on fundamental phenomena such as power broadening and ac Stark (Autler-Townes) splitting. In certain cases, field fluctuations are shown to influence dramatically the frequency respons…
Cavity electromagnetically induced transparency in a coherently prepared cavity-atom system is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. We show that with a resonant pump laser coupling the cavity-confined four-level atoms from free space, the narrow transmission peak of the cavity EIT is split into two peaks. The two peaks represent the dressed intra-cavity dark states and have a frequency separation approximately equal to the Rabi frequency of the free-space pump laser. We observed experimentally the dressed intra-cavity dark states in cold …
We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom r…
We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and …
We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first…
We study the interaction of xenon with an 850 eV photon energy FEL pulse. We do so by employing a Monte-Carlo technique. We compute the single-photon ionisation cross sections and Auger rates, used in the Monte-Carlo technique, by adopting to atoms a formalism we previously developed for diatomic molecules. We determine the yields of the ion states of driven xenon and compare with previously obtained experimental results. To better understand the yields obtained, we identify the prevalent pathways leading to the formation of each final ion state of xenon. We gain further insight into the high …
We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic groundstate of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between groundstate atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the Bose-Einstein condensate undergoes a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the a…
Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving it in inherently unstable states that decay on femtosecond timescales. As the relaxation occurs primarily via Auger emission, excited state observations are constrained by Auger decay. In situ measurement of this process is therefore crucial, yet it has thus far remained elusive at XFELs due to inherent timing and phase jitter, which can be orders of magnitude larger than the timescale of Auger decay. Here, we develop a new approach termed self-referenced attosecond streaking, based upon simultaneous measurements of …
An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected elec…
We investigated the complex index of refraction in the x-ray regime of atoms in laser light. The laser (intensity up to 10^13 W/cm^2, wavelength 800nm) modifies the atomic states but, by assumption, does not excite or ionize the atoms in their electronic ground state. Using quantum electrodynamics, we devise an ab initio theory to calculate the dynamic dipole polarizability and the photoabsorption cross section, which are subsequently used to determine the real and imaginary part, respectively, of the refractive index. The interaction with the laser is treated nonperturbatively; the x-ray inte…
An extreme ultraviolet (EUV) single attosecond pulse passing through a laser-dressed dense gas is studied theoretically. The weak EUV pulse pumps the helium gas from the ground state to the 2s2p(1P) autoionizing state, which is coupled to the 2s2(1S) autoionizing state by a femtosecond infrared laser with the intensity in the order of 10^{12} W/cm2. The simulation shows how the transient absorption and emission of the EUV are modified by the coupling laser. A simple analytical expression for the atomic response derived for delta-function pulses reveals the strong modification of the Fano lines…
We theoretically analyze the interactions and decay rates for atoms dressed by multiple laser fields to strongly interacting Rydberg states using a quantum master equation approach. In this framework a comparison of two-level and three-level Rydberg-dressing schemes is presented. We identify a resonant enhancement of the three-level dressed interaction strength which originates from cooperative multiphoton couplings as well as small distance dependent decay rates. In this regime the soft-core shape of the potential is independent of the sign of the bare Rydberg-Rydberg interaction, while its s…
A new version of the R-matrix Floquet theory for laser-assisted electron-atom scattering is presented. The theory is non-perturbative and applicable to a non-relativistic many-electron atom or ion in a homogeneous linearly polarized field. It is based on the use of channel functions built from field-dressed target states, which greatly simplifies the general formalism.
We present the experimental realization and characterization of a Ramsey interferometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly-excited Rydberg state. We show that the observed interference signals can be used to precisely measure the Rydberg atom-light coupling strength as well as the population and coherence decay rates of the Rydberg-dressed states with sub-kilohertz accuracy and for Rydberg state fractions as small as one part in $10^{6}$. We also demonstrate an application for measuring small,…
We explore the formation by Free-Electron-Laser radiation of Ar hollow states with two or three inner-shell holes. We find that even charged Ar ion states can be more populated than odd charged Ar ion states. This depends on the pulse intensity and the number of energetically accessible inner- shell holes. Fully accounting for fine structure, we demonstrate that one electron spectra bare the imprints of Ar hollow states with two inner-shell holes. Moreover, we show how the Auger spectra of these hollow states can be extracted from two-electron coincidence spectra.
We investigate the formation of multiple-core-hole states of molecular nitrogen interacting with a free-electron laser pulse. We obtain bound and continuum molecular orbitals in the single-center expansion scheme and use these orbitals to calculate photo-ionization and Auger decay rates. Using these rates, we compute the atomic ion yields generated in this interaction. We track the population of all states throughout this interaction and compute the proportion of the population which accesses different core-hole states. We also investigate the pulse parameters that favor the formation of these…
We present analytical and numerical results of the relativistic calculation of the transition matrix element $S_{fi}$ and differential cross section for Mott scattering of initially polarized Dirac particles (electrons) in the presence of strong laser field with linear polarization. We use exact Dirac-Volkov wave functions to describe the dressed electrons and the collision process is treated in the first Born approximation. The influence of the laser field on the degree of polarization of the scattered electron is reported.
A tenet of time-resolved spectroscopy is -faster laser pulses for shorter timescales- . Here we suggest turning this paradigm around, and slow down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.
Multiple electron processes occur widely in atoms, molecules, clusters, and condensed matters when they are interacting with energetic particles or intense laser fields. In this work, a unified and accurate theoretical formalism is proposed on the direct multielectron processes of atoms including the multiple Auger decay and multiple ionization by an impact of an energetic electron or a photon based on the atomic collision theory described by a correlated many-body Green's function. Such a practical treatment is made possible due to different coherence features of the particles (matter waves) …
Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the vibrational motion of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. …
Bifurcation of laser-dressed band extrema in solids under intense low-frequency fields
Voronezh State University（沃罗涅日国立大学）；Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences（中国科学院西安光学精密机械研究所）；Peking University（北京大学）；A.V. Gaponov-Grekhov Institute of Applied Physics, Russian Academy of Sciences（俄罗斯科学院阿·瓦·加波诺夫-格列霍夫应用物理研究所）
We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar equal to the mixed product formed with the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transit…
We propose a laser cooling technique in which atoms are selectively excited to a dressed metastable state whose light shift and decay rate are spatially correlated for Sisyphus cooling. The case of cooling magnetically trapped (anti)hydrogen with the 1S-2S-3P transitions using pulsed ultra violet and continuous-wave visible lasers is numerically simulated. We find a number of appealing features including rapid 3-dimensional cooling from ~1 K to recoil-limited, millikelvin temperatures, as well as suppressed spin-flip loss and manageable photoionization loss.
We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. We model a realistic architecture, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B…
We study the electron scatter from the freely movable spin-$\frac{1}{2}$ particle in the presence of a linearly polarized laser field in the first Born approximation. The dressed state of electrons is described by a time-dependent wave function derived from a perturbation treatment (of the laser field). With the aid of numerical results we explore the dependencies of the differential cross section on the laser field properties such as the strength, the frequency, as well as on the electron-impact energy, etc. Due to the targets are movable, the DCS of this process reduced comparing to the Mott…
Electron-positron pair creation by multiphoton absorption in the collision of a relativistic electron with a strong laser beam is calculated within laser-dressed quantum electrodynamics. Total production rates, positron spectra, and relative contributions of different reaction channels are obtained in various interaction regimes. We study the process in a manifestly nonperturbative domain which is shown accessible to future experiments utilizing the electron beamlines at novel x-ray laser facilities or all-optical setups based on laser acceleration. Our theory moreover allows us to add further…
We theoretically examine neon atoms in ultrashort and intense x rays from free electron lasers and compare our results with data from experiments conducted at the Linac Coherent Light Source (LCLS). For this purpose, we treat in detail the electronic structure in all possible nonrelativistic cationic configurations using a relativistic multiconfiguration approach. The interaction with the x rays is described in rate-equation approximation. To understand the mechanisms of the interaction, a path analysis is devised which allows us to investigate what sequences of photoionization and decay proce…
In dense atomic gases the interaction between transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged forces. Despite decades of research, a full understanding of this paradigmatic many-body problem is still lacking. Here, we put forward and explore a scenario in which a dense atomic gas is weakly excited by an off-resonant laser field. We develop the theory for describing such dressed many-body ensembles and show that collective excitations are responsible for the emergence of many-body interactions, i.e. effective potentials that …
We develop the research achievement of recent work [M. Gärttner, et.al., Phys. Rev. Letts. 113, 233002 (2014)], in which an anomalous excitation enhancement is observed in a three-level Rydberg-atom ensemble with many-body coherence. In our novel theoretical analysis, this effect is ascribed to the existence of a quasi-dark state as well as its avoided crossings to nearby Rydberg-dressed states. Moreover, we show that with an appropriate control of the optical detuning to the intermediate state, the enhancement can evoke a direct facilitation to atom-light coupling that even breaks through the…
We demonstrate the trapping of cold $^{87}Rb$ atoms in a toroidal geometry using a radio frequency (rf) dressed quadrupole magnetic trap formed by superposing a strong rf-field on a quadrupole trap. This rf-dressed quadrupole trap has the minimum potential away from the quadrupole trap centre on a circular path which facilitates trapping in toroidal geometry. In these experiments, the laser cooled atoms were first trapped in a quadrupole trap, then cooled evaporatively using a weak rf-field, and finally trapped in an rf-dressed quadrupole trap. The radius of the toroid could be varied by varyi…
We investigate the creation of double K-shell holes in N2 molecules via sequential absorption of two photons on a timescale shorter than the core-hole lifetime by using intense x-ray pulses from the Linac Coherent Light Source free electron laser. The production and decay of these states is characterized by photoelectron spectroscopy and Auger electron spectroscopy. In molecules, two types of double core holes are expected, the first with two core holes on the same N atom, and the second with one core hole on each N atom. We report the first direct observations of the former type of core hole …
Metastable pionic helium ($π{\rm He}^+$) is a three-body atom composed of a helium nucleus, an electron occupying the $1s$ ground state, and a negatively charged pion $π^-$ in a Rydberg state with principal- and orbital angular momentum quantum numbers of $n\sim \ell+1\sim 16$. We calculate the spin-independent energies of the $π{\rm ^3He}^+$ and $π{\rm ^4He}^+$ isotopes in the region $n=15$--19. These include relativistic and quantum electrodynamics corrections of orders $R_{\infty}α^2$ and $R_{\infty}α^3$ in atomic units, where $R_{\infty}$ and $α$ denote the Rydberg and fine structure const…
Dynamic control of atomic dressing to the highly-excited Rydberg state in multi-level systems has special appeals owing to the development of flexible and precise measurement. In this study we develop an experimentally-accessible proposal to robustly control the dressing probability via a three-step cascaded excitation with double electromagnetically induced transparency (EIT) technique. The system can function as an optical switch where the third addressing laser serving as the control knob can switchably engineer the dressing probability with time. Differing from a conventional two-photon EI…
We have studied the absorption of a weak probe beam through cold rubidium atoms in a magneto-optic trap. The absorption spectrum shows two peaks with the smaller peak having linewidth as small as 28% of the natural linewidth. The modification happens because the laser beams used for trapping also drive the atoms coherently between the ground and excited states. This creates ``dressed'' states whose energies are shifted depending on the strength of the drive. Linewidth narrowing occurs due to quantum coherence between the dressed states. The separation of the states increases with laser intensi…
