Multi-photon Resonance Condition Research Articles

Spatially dependent optical bistability

The effect of the orbital angular momentum (OAM) of light beams on the optical bistability (OB) phenomenon has been investigated in a three-level quantum system. In a first step, we consider a Λ -type configuration in which the coupling field is assumed as a Laguerre–Gaussian (LG) beam. It is shown that the OB strength spatially depends on the intensity profile as well as the topological charge (TC) of the light beam. In a second scheme, we apply a strong microwave field to the lower level transition and obtain an analytical expression for the OB behavior of the probe field in the presence of an LG field in the multi-photon resonance condition. We analytically obtain a generalized input–output bistability relation for the systems containing the LG beam. More complicated phase-dependent OB profiles can be obtained for higher order LG modes due to the OAM transfer and classical interference between the generated field and applied fields. The results of this paper may provide a potential application of OB in generating simultaneously reconfigurable sets of various optical logic gates in the same structure, as well as in enhancing the capacity of fast volatile bit-level optical memories.

Achieving colossal Kerr nonlinearity via multiphoton atomic coherence in a five-level Λ − Ξ system

We propose to utilize a five-level Λ − Ξ system to achieve large self-Kerr nonlinearity under multiphoton resonance conditions. Using a density matrix formulation along with an iterative perturbation technique, analytic expressions of linear and nonlinear susceptibilities are derived for stationary as well as for moving atoms. Variation of first- and third-order susceptibilities with respect to frequency and intensity of switching field is then discussed. The dressed-state picture is employed to explain the amplitude and position of each peak in linear and nonlinear absorption profiles. It is found that under slow light conditions, large controllable Kerr nonlinearity with reduced linear and nonlinear absorption is achieved by properly adjusting the strength and detunings of strong electromagnetic (e.m.) fields. Our numerical results also reveal that the Kerr nonlinear index of our considered system is greater than that of existing three-level Λ and four-level N systems. Finally, it is substantiated that self-Kerr nonlinearity is proliferated by taking the Doppler effect into account.

Atom localization using Laguerre–Gaussian beams

Use of the Laguerre–Gaussian (LG) beams in an atom-light interaction makes the linewidth of the optical spectrum narrow. We exploit this fact for providing the ability to accomplish simultaneous ultra-high precision and spatial resolution atom localization in a double-Λ atomic system; under multi-photon resonance condition, the resolution of the localization is remarkably improved so that the atom can be localized in a region smaller than λ/100 × λ/100. Most prominently, the probability of finding the atom at a particular position is always 100%, when a photon with certain frequencies is absorbed or amplified. Such features are mainly attributed to radial dependence associated with the LG beams in a spatially dependent atom-light interaction.

Giant Goos-Hänchen shift in two different enantiomers' chiral molecules via quantum coherence.

The Goos and Hänchen (GH) shifts in reflected and transmitted probe light through a cavity mixture of left- and right-handed chiral molecules into two enantiomer states are investigated. Due to the broken mirror symmetry of the left- and right-handed chiral molecules in the presence of cyclic population transfer, such quantum systems can be selectively excited because of the coexistence of one- and two-photon transitions. With the help of coupling Rabi frequency and damping effects due to scattering processes, the generated GH shifts accompanied by simultaneously negative and positive lateral shifts in reflected and transmitted probe lights are greatly enhanced. It is found that the large negative and positive GH shifts are available in the presence of multiphoton resonance and off-resonance conditions for two different enantiomers' chiral molecules. Moreover, the switching between superluminal and subluminal light propagation is extremely dependent on choosing the left- and right-handed chiral molecules. Furthermore, the effects of pulse shape and mode of Laguerre-Gaussian probe light on the GH shifts that lead to a switch between negative and positive shift are also studied. The negative and positive GH shifts in a reflected and transmitted probe beam for an incident Gaussian and different mode of Laguerre-Gaussian shaped beam with various widths by the use of two different enantiomers' chiral molecules are also discussed.

Electromagnetically induced grating based on Zeeman coherence oscillations in cases beyond the multi-photon resonance condition

We present a theoretical study on the generation of an electromagnetically induced grating (EIG), based on Zeeman coherence oscillations, in a duplicated two-level atomic system. We show that the pure amplitude grating is obtained in the resonance case of multi-photon detuning. In this system, transferring of light energy from the zero order to the first order occurs by tuning the intensity and detuning of the coupling field. Physical mechanisms of the results are discussed using cases beyond the multi-photon resonance condition. Additionally, in the duplicated two-level system, we can create a two-dimensional EIG by splitting the coupling field into two orthogonal components. Optical properties of the proposed two-dimensional grating are also controlled by the intensity and detuning of the coupling field.

Transverse magnetic field effect on the giant Goos–Hänchen shifts based on a degenerate two-level system

We study the effect of the Goos–Hänchen (GH) shifts through a cavity with degenerate two-level systems in the line of . For this purpose, we focus on the transverse magnetic field (TMF) in a Floquet frame to obtain the giant GH shifts. Physically, the collisional effects of TMF lead to increasing the population trapping in the ground state. However, we demonstrate that the population trapping generates the large negative or positive GH shifts and simultaneously switches from superluminal to subluminal (or vice versa). Also, we investigate the other optical properties such as the longitudinal magnetic field (LMF), which plays an important role in the control of the GH shifts and leads to the generation of new subsystems. In the next step, we evaluate the GH shifts beyond the multi-photon resonance condition by the control of TMF. Moreover, we compute the appearance of negative and positive GH shifts by setting the width of the incident Gaussian beams in the presence of a multi-photon resonance condition. Our results show that superluminal or subluminal light propagation can be simultaneously controlled by adjusting the rates of the TMF and LMF. The significant effects of these factors on the degenerate two-level systems provide different applications such as slow light, optical switches and quantum information storage.

Multiphoton-resonance-induced fluorescence of a strongly driven two-level system under frequency modulation

We study the fluorescence spectrum of a strongly driven two-level system (TLS) with modulated transition frequency, which is a bichromatically driven TLS and has multiple resonance frequencies. We are aiming to provide a reliable description of the fluorescence in a regime that is difficult to tackle with perturbation theory and the rotating-wave approximation (RWA), and illustrate the spectral features of the fluorescence under off- and multiphoton-resonance conditions. To go beyond the RWA, we use a semianalytical counter-rotating-hybridized rotating-wave method that combines a unitary transformation and Floquet theory to calculate the two-mode Floquet states and quasienergies for the bichromatically driven TLS. We then solve the master equation accounting for the spontaneous decay in the bases of the two-mode Floquet states, and derive a physically transparent fluorescence spectrum. In comparison with the numerically exact spectrum from the generalized Floquet-Liouville approach, the present spectrum is found to be applicable in a wide range of the parameters where the RWA and the secular approximation may break down. We find that the counter-rotating (CR) terms of the transverse field omitted in the RWA have non-negligible contributions to the spectrum under certain conditions. Particularly, at the multiphoton resonance the width of which is comparable with the Bloch-Siegert shift, the RWA and non-RWA spectra markedly differ from each other because of the CR-induced shift. We also analyze the symmetry of the spectrum in terms of the transition matrix elements between the two-mode Floquet states. We show that the strict symmetry of the spectrum cannot be expected without the RWA but the almost symmetric spectrum can be obtained at the single-photon resonance that takes the Bloch-Siegert shift into account if the driving is moderately strong and at the multiphoton resonance with a sufficiently weak transverse field.

Floquet exceptional points and chirality in non-Hermitian Hamiltonians

Floquet exceptional points correspond to the coalescence of two (or more) quasi-energies and corresponding Floquet eigenstates of a time-periodic non-Hermitian Hamiltonian. They generally arise when the oscillation frequency satisfies a multi-photon resonance condition. Here we discuss the interplay between Floquet exceptional points and the chiral dynamics observed, over several oscillation cycles, in a wide class of non-Hermitian systems when they are slowly cycled in opposite directions of parameter space.

Four-Wave Mixing-Induced Maximal Entanglement in Superconducting Phase Quantum Circuits

We are interested in studying the entanglement of an array of superconducting phase quantum circuits and external magnetic fluxes. It is shown that in a four-level cascade type quantum system, the degree of entanglement increases by generation of fourth microwave pulse, in multi-photon resonance condition. We achieve the maximal entanglement induced via four-wave mixing in our model. Moreover, it is demonstrated that the population distribution of the dressed states approaches to be uniform as the degree of entanglement becomes maximum. We can control the entanglement of the composite system by changing amplitudes of the applied magnetic fluxes. Our results can be used in quantum information processing via superconducting quantum circuits.

Coherent control of multiphoton dynamics and high-order-harmonic generation driven by two frequency-comb fields with a relative envelope delay

We present a theoretical investigation of the coherent control of multiphoton dynamics and a high-order-harmonic generation (HHG) process driven by two frequency-comb fields, via the interference of multiphoton transition paths by tuning the relative envelope delay between fields. The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and frequency-comb laser fields. The case of two frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental and second harmonics, respectively, is considered. Due to the coupling of the second harmonic controlling the frequency-comb laser field, multiphoton transitions involving both fundamental- and second-harmonic photons occur. Different multiphoton transition paths can be superpositioned when the matching condition for carrier-envelope-phase shifts is satisfied, offering the possibility of coherent control of HHG power spectra via the interference of paths by tuning the relative envelope delay between fields. The calculated HHG power spectra present both sub-cycle oscillation and multi-cycle modulation behavior when the relative envelope delay is varied. It is also found that, under the condition of multiphoton resonance, the HHG power spectra can be further enhanced by about 10 times via the interference of multiphoton transition paths by tuning the relative envelope delay.

Phase-controlled optical trap potential in a closed-loop atomic system

The optical trap potential is studied in a four-level double-Λ closed-loop atomic system in the multiphoton resonance condition. We apply four femtosecond Gaussian laser beams to generate a closed-loop configuration. It is shown that the induced optical dipole force on the system dramatically depends on the relative phase of applied fields, and it switches from focusing to defocusing in the transverse direction, simply by properly changing the relative phase. Through special switching of the relative phase, the trapping potential splits into two positions, which has novel applications in trapping and manipulating the particles. Moreover, it is further demonstrated that trap depth can be manipulated by the relative phase. Finally, a maximum coherent population transfer is achieved for a special value of the relative phase of applied fields.

Atom–photon entanglement beyond the multi-photon resonance condition

Atom---photon entanglement between the dressed atom and its spontaneous emission is studied in a near-degenerate three-level V-type atomic system in multi-photon resonance condition and beyond it. Taking into account the quantum interference due to the spontaneous emission, the density matrix equations of motion are numerically calculated in two-photon resonance condition and beyond it. The dynamical behavior of these two subsystems is investigated by using the von Neumann entropy. We apply the Floquet decomposition to the equations of motion to solve this time-dependent problem and identify the contribution of the different scattering processes to the atom---photon entanglement. In addition, the impact of the various nonlinear effects on the atom---photon entanglement is introduced in two-photon resonance condition. It is shown that the degree of entanglement (DEM) can be controlled via the intensity and the detuning of the coupling field as well as the quantum interference induced by spontaneous emission. We find that vacuum-induced interference has a major role in phase sensitivity of the DEM; however, beyond the two-photon resonance condition the DEM does not depend on the relative phase of the applied fields. Our results can be used for quantum information processing via entanglement.

Maximal atom–photon entanglement in a double- $$\Lambda $$ Λ quantum system

The atom---photon entanglement of a dressed atom and its spontaneous emission in a double-$$\Lambda $$? closed-loop atomic system is studied under multi-photon resonance condition. It is shown that even in the absence of quantum interference due to the spontaneous emission, the von Neumann entropy is phase-sensitive and it can be controlled by either intensity or relative phase of the applied fields. It is demonstrated that for the special case of Rabi frequency of the applied fields, the system is maximally entangled. Moreover, an open-loop configuration is considered, and it is shown that the degree of entanglement can be controlled by intensity of the applied fields. Furthermore, in electromagnetically induced transparency condition, the system is disentangled. Such a system can be used for quantum information processing via entanglement using optical switching.

Multilevel interference resonances in strongly driven three-level systems.

We study multiphoton resonances in a strongly driven three-level quantum system, where one level is periodically swept through a pair of levels with constant energy separation E. Near the multiphoton resonance condition nℏω=E, where n is an integer, we find qualitatively different behavior for n even or odd. We explain this phenomenon in terms of families of interfering trajectories of the multilevel system. Remarkably, the behavior is insensitive to fluctuations of the energy of the driven level, and survives deep into the strong dephasing regime. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in strongly driven double quantum dots.

Phase-controlled optical bistability via electromagnetically induced absorption

The optical properties of a four-level double-V-type closed-loop system is studied in the multiphoton resonance condition. It is shown that the phase-dependent electromagnetically induced transparency (EIT) window is established and by changing the relative phase of the applied fields, EIT switches to electromagnetically induced absorption. Moreover, the optical bistability (OB) behavior of the system is studied, and it is demonstrated that the cross-Kerr-effect-induced OB depends on the relative phase of the applied fields, and it can be controlled by either intensity or relative phase of laser fields. By applying a microwave field to drive the hyperfine transition between two lower states, the optical properties change and OB switches to optical multistability. This can be used for detection of longer wavelengths than visible light.

Amplification without inversion, fast light and optical bistability in a duplicated two-level system

The optical properties of a weak probe field in a duplicated two-level system are investigated in multi-photon resonance (MPR) condition and beyond it. It is shown that by changing the relative phase of applied fields, the absorption switches to the amplification without inversion in MPR condition. By applying the Floquet decomposition to the equations of motion beyond MPR condition, it is shown that the phase-dependent behavior is valid only in MPR condition. Moreover, it is demonstrated that the group velocity of light pulse can be controlled by the intensity of the applied fields and the gain-assisted superluminal light propagation (fast light) is obtained in this system. In addition, the optical bistability (OB) behavior of the system is studied beyond MPR condition. We apply an indirect incoherent pumping field to the system and it is found that the group velocity and OB behavior of the system can be controlled by the incoherent pumping rate.

Phase-controlled atom—photon entanglement in a three-level Λ—type closed-loop atomic system

We study the entanglement of dressed atom and its spontaneous emission in a three-level Λ-type closed-loop atomic system in a multi-photon resonance condition and beyond it. It is shown that the von Neumann entropy in such a system is phase-dependent, and it can be controlled by either the intensity or relative phase of applied fields. It is demonstrated that for the special case of the Rabi frequency of applied fields, the system is disentangled. In addition, we take into account the effect of Doppler broadening on the entanglement and it is found that a suitable choice of laser propagation direction allows us to obtain the steady state degree of entanglement (DEM) even in the presence of the Doppler effect.

Basis dependence of approximative energy levels in a strongly driven two-level system

We introduce the diabatic and the adiabatic bases of a strongly driven superconducting two-level system. The multiphoton resonance conditions, the Rabi couplings, and the energy levels are calculated in both bases using the rotating wave approximation, and the results are compared with the corresponding numerical values. We show the basis dependence of the approximate energy levels and deduce the validity regions for both bases. We demonstrate a parameter region where neither of the bases is sufficient for calculations in the rotating wave approximation.

Phase and amplitude control of optical bistability in the three-coupled quantum wells

We investigate the optical properties of a weak probe field in a ladder-type configuration in an asymmetric semiconductor three-coupled quantum well system. It is shown that the dispersion, absorption and optical bistability behavior of the system can be controlled by both the amplitude and relative phase of applied fields. The phase dependence arises from a scattering of the pumping and signal fields into the probe field mode at a frequency which in multi-photon resonance condition is the same as the probe field frequency. Moreover, it is demonstrated that in the gain region of the absorption spectrum, considerable output is obtained for zero input.

Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

We investigate the optical bistability behavior of a three-level closed-loop atomic system beyond the multi-photon resonance condition. Using the Floquet decomposition, we solve the time-dependent equations of motion, beyond the multi-photon resonance condition. By identifying the different scattering processes contributing to the medium response, it is shown that in general the optical bistability behavior of the system is not phase-dependent. The phase dependence is due to the scattering of the driving and coupling fields into the probe field at a frequency, which, in general, differs from the probe field frequency.