Four-level N-type Atomic System Research Articles

Amplified Nonreciprocal Reflection in a Uniform Atomic Medium with the Help of Spontaneous Emissions

It is important to elaborate on versatile strategies for achieving the perfect nonreciprocal reflection amplification, which is the key technology of high-quality nonreciprocal photonic devices. In this work, we ingeniously design a coherent four-level N-type atomic system to harness the nonreciprocal light amplification, in which the uniform distribution of atoms is driven by two strong coupling fields and a weak probe field. In our regime, the strength of the two control fields is designed with linear variation along the x direction to destroy the spatial symmetry of the probe susceptibility, leading to the nonreciprocity of the reflection. In particular, the closed-loop transitions to amplify the probe field are due to the combined effect of the control fields and spontaneous emissions. The numerical simulation indicates that the perfect nonreciprocal reflection amplification can be realized and modulated by the appropriate settings of the control fields and the detuning, Δc. Our results will open a new route toward harnessing nonreciprocity, which can provide more convenience and possibilities in experimental realization.

Generation of optical -antisymmetry in a coherent N-type atomic medium

We have proposed two schemes to exhibit -antisymmetry in a four-level N-type atomic system interacting with two strong driving fields and a weak probe field. For both the schemes, the required spatially modulated coherence rendering -antisymmetry is achieved by employing a double-channel Gaussian beam for one driving field with a single channel for the other driving field in different field configurations. In each scheme, for equal and opposite detunings of the double-channel Gaussian beam, -antisymmetry can be obtained in the spatial domain. Such a way of control is unique to this model. Using the present method, it is possible to obtain -antisymmetry for both the homogeneously and inhomogeneously broadened atoms.

The steady-state of probe susceptibility in a four-level N-type atomic system with a squeezed vacuum field

The gain, absorption and dispersion properties of a probe field for a four level N-type atomic system with a normal vacuum and a squeezed vacuum fields is studied. Under such conditions that normal and squeezed vacuum-induced interference among decay channels is significant. Our study also reveals that the quantum interference will produce a remarkable effect on the absorption and dispersion properties of the system. A single squeezed vacuum is coupled to three transitions. Numerically the effect of the squeezing vacuum field parameters and the relative phases between the squeezed vacuum and the probe (strong) fields on the index of refraction is analyzed.

Electromagnetically induced grating via Kerr nonlinearity and spontaneously generated coherence in a Doppler broadened four-level N-type atomic system

We study the electromagnetically induced grating in a four-level N-type atomic system in the presence of Kerr field, spontaneously generated coherence (SGC), and Doppler broadening. The transmission and diffraction intensity of the probe light is controlled through the Kerr field and the SGC. The gradual increase of the Kerr field and the SGC in the presence of a Doppler broadened medium leads to the enhanced multiple transmission and intensity peaks of the probe light. The electromagnetically induced grating may find applications in a quantized probe field, all-optical switching, routing, and light storage devices.

An analytical model for cross-Kerr nonlinearity in a four-level N-type atomic system with Doppler broadening

We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening. The model is applied to 87Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor. The analysis shows that in the absence of electromagnetically induced transparency (EIT) the cross-Kerr nonlinear coefficient is zero, but it is significantly enhanced when the EIT is established. It means that the cross-Kerr effect can be turned on/off when the external light field is on or off. Simultaneously, the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field. The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases. The analytical model can be convenient to fit experimental observations and applied to photonic devices.

Enhanced cross-Kerr nonlinearity induced -symmetry in optical lattices

We propose a physical scheme to realize optical lattices that are symmetric under a combination of parity and time () reversal. The -symmetric structures can be constructed with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system under the effects of cross-Kerr nonlinearity and Doppler broadening. The atoms are considered in the Gaussian density distribution loaded into the dipole traps of one- and two-dimensional optical lattices. The spatial modulation of the probe field susceptibility is achieved by a proper combination of standing wave strong control fields. With proper detunings and coupling field Rabi frequencies, we find the conditions of achieving -symmetry in optical lattices of nonlinear atoms. We show that the -symmetry can be realized when the cross-Kerr nonlinearity is significantly enhanced, and further demonstrate that it survives the Doppler broadening. Our model is based on experimentally observable and effectively controllable scheme which may find potential applications in optical information processing.

Controllable two- and three-dimensional atom localization via spontaneously generated coherence

A scheme for two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level N-type atomic system is proposed. The scheme is based on the probe absorption measurement when the atom passes through the orthogonal standing-wave fields. Using the electromagnetically induced transparency, we prove that the probe field absorption is spatially localized in sub-wavelength domain. We also show that the spatial resolution of 2D and 3D atom localization strongly depends on the probe field detuning, the quantum interference parameters induced by spontaneous emission, and the relative phase between the driving fields.

Complex conductivity-dependent two-dimensional atom microscopy

A two-dimensional atom microscopy is investigated using the absorption spectrum under the effect of complex conductivity in a four-level inverted N-type atomic system. Sharp localized peaks are noticed in one wavelength domain in 2D inverse space $ -\pi\leq kx\leq\pi$ and $ -\pi\leq ky\leq\pi$. Four, three, two and even single localized peaks having high precise position, minimum uncertainty and significant probability are measured in the proposed model. The localized probability is enhanced or degraded with the application of complex conductivity. The phase and amplitude of complex conductivity significantly influence the atom microscopy for useful technological applications. The results may be helpful to advance laser cooling and trapping.

Effect of the atomic dipole relaxation and the pulse width on temporal cloaking

We investigated the effect of atomic dipole relaxation on temporal cloaking in a four-level N-type atomic system. Due to dipole relaxation rates, significant variation in the group index and in the advance/delay time of the probe pulse is noted. Temporal gaps of the order of nanoseconds are opened. Furthermore, multiple temporal gaps are created in a comparatively narrow probe pulse, whose quality is modified due to the width of the probe pulse and with the dipole relaxation rates. The results of this article will play a vital role in secure transmission and storage of information.

Switching from EIT to EIA in a four-level N-type atomic system

We study the optical properties of a four-level N-type system theoretically for $$^{87}$$ Rb atoms using density matrix formalism. Electromagnetically induced transparency and electromagnetically induced absorption (EIA) are two extensively studied two-photon coherence phenomena. EIA can be observed as a result of the transfer of coherence and transfer of population between the atomic levels. A narrow absorption is observed at the resonance frequency for moving atoms. Enhanced transmission and absorption lead to sub-luminal and super-luminal light propagation, respectively. It is observed that the third field in N-type system causes switching from transmission to absorption. We also discuss group index changes with coupling field strength.

Efficient images storage via modulating the atomic spin coherence in a N-type system

A four-level N-type cold atomic system is proposed for optimizing images storage based on the electromagnetically induced transparency (EIT). Both analytical analysis and numerical simulation clearly show that the application, during the storage time, of an additional intensity-modulated signal field and an additional microwave field can impose an intensity and a phase-dependent factors on the atomic spin coherence in a controlled manner, then the amplitude of the retrieved images can be increased or decreased with an enhancement in the visibility. Our results are very promising for the realization of all-optical information processing of images coherently stored in EIT media in the future.

Some phenomena in susceptibility of atomic medium via the phases and direction of the Gaussian near-field

We display the phenomena of dark state, vanishing absorption and dispersion as well as the up-conversion and large refractive index with low absorption in a Doppler broadened four-level N-type atomic system which interacts with three fields. We take three cases for the field which representing by the spontaneously generated coherence and Gaussian near-field. The effect of the relative phase of the fields and the Gaussian field parameter on the spectrum of the probe field in the three cases of the field are discussed. The direction and magnitude of the pump field have an important role when we discuss these phenomena. The chance of obtaining the large refractive index with low absorption is achieved at specific conditions. Then the interesting results can be observed on the spectrum of the probe field depending on kind of the field.

Enhancement of cross-Kerr nonlinearity in four-level N-type atomic sysem based on electromagnetically induced transparency

We study enhancement of cross-Kerr nonlinearity in four-level N-type atomic system by the analytical method. The results apply to the 87Rb atoms and show that in the presence of the EIT effect (i.e., the presence of coupling laser field), the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-6 cm2/W) around the EIT window. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Analytical results are useful for experimental observation and related applications.

Double-cavity optical bistability and all-optical switching in four-level N-type atomic system

We analyze the absorptive and hybrid absorptive–dispersive double-cavity optical bistability behavior in a four-level N-type atomic system driven by two optical fields circulating inside two independently unidirectional ring cavities and a trigger field outside the cavities. In this system, the two-photon absorption and cross Kerr nonlinearity play significant roles in the formation of bistability and can be controlled efficiently due to the quantum interference effect, and then the resulting nonlinear behavior exhibits different features from the two/three-level schemes. It is shown that the threshold values and hysteresis cycle width of the bistable curve can be manipulated via the adjustment of the system parameters. Meanwhile, we also obtain double-beam optical multistability. When adding positive and negative pulses to the cavity input, all-optical steady-state switching for the two cavity outputs can be achieved simultaneously. Therefore, the proposed scheme may have potential applications in all-optical communication and computing.

An absorption-free and Doppler-improved optical waveguide for diffractionless light propagation

We propose a novel scheme to realize an optical waveguide induced by an active Raman gain (ARG) process in a four-level N-type atomic system. Because of the nature of the ARG, there are two distinct features related to the waveguide: i) It is not absorptive, on the contrary, weak gain is presented; ii) It can be improved by the Doppler effect in the sense that the dispersion is enhanced while the gain is further reduced. This is in sharp contrast to the previously considered schemes where usually the optical induced waveguide is passive and is severely attenuated by the Doppler effect. We then study the paraxial light propagation in the waveguide which shows that the propagation dynamics is lossless and diffractionless.

Study on probe field propagation in the presence of control and coupling fields through a four-level N-type atomic system

The absorption features of a probe field propagating through a four-level N-type atomic system in the presence of two coherent radiation fields is studied analytically by using a density matrix formulation. The system has two ground levels and two excited levels. A weak probe laser couples the upper ground level to the lower excited level whereas a strong control field connects the lower ground level to the lower excited level. The coupling field acts between the upper ground level and the upper excited level. The transition parameters of the 87Rb D1 line have been used to simulate the probe response. The simulated probe absorption shows a gain-like structure depending on the relative field intensities. The spectral features of the probe response exhibit substantial differences under thermal averaging as compared to a Doppler-free condition. The splitting of simulated probe absorption can be explained by the dressed state model. Electromagnetically induced absorption (EIA) is observed in the simulated probe response curve when the spontaneous decay of the population from the uppermost excited state to the lower ground state is absent.

Induced dual EIT and EIA resonances with optical trapping phenomenon in near/far fields in the N-type four-level system

The optical trapping phenomenon is investigated in the probe absorptive susceptibility spectra, during the interaction of four-level N-type atomic system with three transverse Gaussian fields, in a Doppler broadened medium. The system was studied under different temperature settings of 87 Rb atomic vapor as well as different non-radiative decay rate. The system exhibits a combination of dual electromagnetically induced transparency with electromagnetically induced absorption (EIA) or transparency (EIT) resonances simultaneously in near/far field. Also, the optical trapping phenomenon is considerably affected by the non-radiative decay rate.

Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices

We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.

Two-dimensional electromagnetically induced cross-grating in a four-level N-type atomic system

We propose a scheme for a two-dimensional (2D) electromagnetically induced cross-grating (EICG) in a four-level N-type atomic system. By employing standing-wave fields interacting with the atomic system, the absorption and dispersion of the probe field will change with the spatial periodical modulation. The first-order diffraction intensity sensitively depends on the parameters (the probe detuning, and the amplitude and detuning of the standing-wave fields), and can reach its maximum on varying the system parameters. The present studies may be instructive to design new devices in all-optical switching and optical imaging.

Reversible self–Kerr nonlinearity in an N-type atomic system through a switching field

We investigate the self–Kerr nonlinearity of a four-level N-type atomic system in Rb and observe its reversible property with a unidirectional increase in the switching field. For a laser arrangement in which the probe field interacts with the middle two states, the slope and the sign of the self–Kerr nonlinearity around the atomic resonance not only can be changed from negative to positive but also can be changed to negative again with a unidirectional increase in the switching field. Numerical simulations are consistent with the experimental results, and dressed state analysis is presented to explain the experimental results.