Four-level Atomic System Research Articles

Coherent control of dressing interaction of sequential-doubly-dressed four-wave mixing

Abstract We investigate the coherent control of dressing interaction in four-wave mixing (FWM) in a Y-type four-level atomic system based on the dressed states theory. We study the density matrix equation acted by two dressing fields simultaneously governing FWM signal intensity and the eigenvalues under the dressed state formalism. It is shown that the peak position and intensity of Autler–Townes splitting both originate from the dressing interaction as the detuning of the probe field is scanned. Moreover, it is observed that the interaction could be controlled by the dressing fields. Such flexibly controlled nonlinear signal has potential applications in optical communication and quantum information processing.

Two-channel optical bistability and multistability in a degenerate four-level atomic medium under a static magnetic field

In this paper, we study the formation of optical bistability (OB) and optical multistability (OM) in a degenerate four-level atomic system by an external magnetic field that is excited by a probe laser field, a coupling laser field and a signal laser field. The coupling field can cause electromagnetically induced transparency (EIT) for the probe field in the atomic medium, while the signal field and/or external magnetic field can switch between single-EIT and two-EIT regimes. Based on these properties, OB and OM effects can be formed at two different frequency regions of the probe field (two channels). By adjusting the magnetic field or the intensity and the frequency of laser fields, the threshold intensity and the width of OB or OM can also be changed simply. The model can be useful for experimental observations and applications in modern photonic devices.

Spontaneously generated structured light

We suggest a method for spontaneous emission in a four-level atomic system driven by vortex light beams that generates structured light. The atom in consideration has two excited states that are closely spaced and linked to the ground state by two control fields. The excited states have the ability to spontaneously decay into a fourth level, known as a metastable state. We demonstrate that in such configuration the orbital angular momentum (OAM) of the vortex pumping light beams can be transferred from both control fields to the spontaneously emitted photons by analyzing the spontaneously generated output spectrum. Furthermore, we discover that by spontaneous emission, the azimuthal phase dependency may be used to develop different kinds of structured light, the spatial intensity distribution of which can be significantly modified by varying the OAM of the control fields. The concept we propose could indeed have significant implications in fields such as optical communication and optical storage, where structured light plays a crucial role.

Diffractionless transmission of optical beams through a four-level atomic system affected by a plasmonic nanostructure

A nondiffracting propagation of an optical beam through a four-level double-V-type quantum system near a plasmonic nanostructure is investigated. We study the linear absorption and dispersion properties of the quantum system as it interacts with two laser fields. We discuss the effect of the control beam with a Laguerre-Gaussian (LG) profile on the focusing of the probe beam in the presence of a plasmonic nanostructure. An appropriately selected control beam excites one transition of the atomic system and generates a spatially varying refraction index modulation for a weak probe beam that couples to the other transition. We demonstrate that placing a plasmonic nanostructure at a nanometer distance from the atomic system and using a control field with the spatial structure leads to the diffraction-less propagation of the probe beam through the atomic system. Also, it is shown that the optical properties and probe beam focusing can be controlled by adjusting the distance of the plasmonic nanostructure from the atomic system. The proposed all-optical waveguide with high contrast and transmission can be used to implement applications such as image transfer through the medium and image processing.

Switching between slow light and fast light by static magnetic field in a degenerate four-level atomic system at room temperature

The optical response of a magnetic-degenerated four-level atom system to the two left and right circular polarization components of the probe field is represented at room temperature. The absorption spectrum and group index for the two polarization components of the probe field are controlled according to the static magnetic field and the coupling field under electromagnetically induced transparency condition. By varying the strength of the static magnetic field, the optical response of the atomic medium can be changed from transparency to absorption or vice versa and hence the amplitude of group index also changes from positive extreme to negative extreme or vice versa. The same phenomenon also occurs when changing the coupling field intensity. In addition, temperature also significantly influence on the optical response of the atomic medium, which changes not only the amplitude but also the sign of the group index as the temperature increases. Our analytical results can be useful for experimental observation and related applications of light group index/velocity at room temperature.

Effect of relaxation on the transfer of orbital angular momentum via four-wave mixing process in the four-level double lambda atomic system

In this work, we have theoretically studied the resonant four-wave mixing (FWM) in a four-level double Lambda (Λ) atomic system in connection with orbital angular momentum (OAM) transfer from probe to generated signal beam. The effect of the relaxation process is studied in the forward as well as backward FWM. Based on the semiclassical model, our analysis shows a strong dependence of conversion efficiency on spontaneous decay and decoherence rates. From the intensity and phase profile, we have confirmed the OAM nature of the generated signal beam. The physical explanation is given for the dependence of efficiency on the decay rate of the excited atomic state. We have shown that decoherence present in the system always leads to a deleterious effect on conversion efficiency. Our presentation treats forward and backward FWM in a unified way in the context of OAM transfer and sheds light on the parameter dependence of conversion efficiency.

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.

Double electromagnetically induced transparency in a four-level lambda atomic system with doppler broadening

In this paper, we study the formation of two electromagnetically induced transparency (EIT) windows in a four-level lambda atomic system with Doppler broadening. The depth and the width of the EIT windows are easily changed by adjusting the intensity of the controlling laser fields. Meanwhile, the position of the EIT windows is also easily shifted by changing the frequency of the laser fields. In particular, by turning on or off one of the two coupling laser fields, the probe field response can be switched between one or two EIT window regimes, i.e., it is possible to switch between absorption and transparency regimes, and vice versa. In addition, our analytical model also allows one to investigate the influence of temperature (or Doppler width) on EIT windows, which is necessary for experimental observations as well as related applications at room temperature.

Formation and manipulation of optical soliton pulse in a self- and cross-phase modulated four-level inverted Y-type system

We have proposed a theoretical model for controllable optical soliton pulse formation in a magnetic-field-assisted four-level inverted Y-type atomic system. The probability amplitudes of the pertinent levels are used to analyze the contrast between self- and cross-phase modulated probe absorption signals. The absorption profiles obtained from the probability amplitudes and the zeroth-order of the pulse propagation constant in the Taylor series are appropriately congruent. The nonlinear Schrödinger equation derived from the Maxwell–Bloch equation determines the respective bright and dark soliton conditions with positive and negative values of the pulse shape parameter. It is demonstrated that the coupling laser field strengths, laser frequency detunings, and the external magnetic field’s direction are the controlling parameters to produce both bright and dark optical soliton pulses. Alongside, the shape of the optical soliton pulses in self- and cross-phase modulation is influenced by the polarization angle of the probe and coupling fields. It is also found that the variation of coupling field strengths may be used to regulate the group velocity of the soliton probe pulse from superluminal to subluminal modes or vice-versa.

Absorption spectra and enhanced Kerr nonlinearity in a four-level system

In a coherent system, enhanced nonlinearity can be reached via far-detuned coupling fields in the presence of Autler--Townes splitting. We explore the absorption spectra and the Kerr nonlinearity of the coherent system via the interaction between a four-level atomic system and triple fields. We obtain the absorption spectra with double, triple and even quadruple peaks which depend on both the magnitude and the difference of the coupling fields. The Kerr nonlinearity always remains reversely correlated with the absorption spectra. We find that the large coupling detunings can lead to a significant growth of the Kerr nonlinearity and the degenerate four-wave mixing. Both the Kerr nonlinearity and the four-wave mixing can be managed by adjusting the detunings of the coupling fields.

Controlling magnon-magnon entanglement and steering by atomic coherence.

Here we show that it is possible to control magnon-magnon entanglement in a hybrid magnon-atom-cavity system based on atomic coherence. In a four-level V-type atomic system, two strong fields are applied to drive two dipole-allowed transitions and two microwave cavity modes are coupled with two dipole forbidden transitions as well as two magnon modes simultaneously. It is found that the stable magnon-magnon entanglement, one-way steering and two-way EPR steering can be generated and controlled by atomic coherence according to the following two points: (i) the coherent coupling between magnon and atoms is established via exchange of virtual photons; (ii) the dissipation of magnon mode is dominant over amplification since one of the atomic states mediated one-channel interaction always keeps empty. The coherent control of magnon-magnon correlations provides an effective approach to modify macroscopic quantum effects using the laser-driven atomic systems.

Controlling optical bistability, multistability and all-optical switching through multi-photon excitation process

We present a theoretical study on optical bistability (OB), optical multistability (OM) and tunable all-optical switching in a four-level cascade type atomic system. The density matrix formalism is used to find out the response of the probe laser field. We explore OB and OM under unidirectional optical ring cavity configuration. A comparison between the effects of electromagnetically induced transparency and electromagnetically induced absorption windows on OB is presented. The threshold of OB and the hysteresis width can be tuned effectively by adjusting the applied coherent fields. A transition from OB to OM and vice-versa can be easily achieved by tuning the field parameters and the atomic cooperation parameter. Dynamic control of the probe laser propagating through the medium has been investigated. We also demonstrate conversion of a continuous wave input probe field into output switched pulse. The ON/OFF time of the switched probe pulse can also be controlled by tuning the field parameters.

Sagnac interferometry and self-Kerr nonlinearity dependent photon drag

We present a theoretical investigation of the photon drag by incorporating self-Kerr nonlinearity (SKN) in a Sagnac interferometer featuring a four-level atomic system. By introducing SKN in the system, we demonstrate significant improvements in the photon drag angles, ranging from ±10 micro-radians to ±1 centi-radians. Additionally, the presence of SKN leads to electromagnetically induced transparency (EIT), reduced group velocities, and a positive group index enhancement within the system. Conversely, in the absence of SKN, a negative group index is observed, accompanied by larger group velocities and minimal photon drag angles. The results obtained may have potential applications in various fields, such as slow-light detection, controlled image coding/design, efficient light modulators, and phase-matching in Brillouin scattering.

Coherent control of light-induced torque on four-level tripod atom systems

This paper investigates the manipulation of induced torque on a four-level tripod atom system through the interaction with two vortex probe beams featuring spatial inhomogeneity, along with a non-vortex control beam. The study explores both the linear and nonlinear regimes of torque induction. In the linear regime, where the intensity of the vortex beams is weaker than that of the control field, effective control over the induced torque is demonstrated by adjusting parameters such as magnetic field strength, control field intensity, detuning, and dephasing terms between relevant atomic levels. The analysis highlights the significant contribution of the Zeeman shift-induced magnetic field, which enhances the torque and exhibits a distinct sharp peak. Furthermore, higher-order contributions to the induced torque are discussed as the intensity of the probe fields approaches that of the control field, resulting in further enhancement of the induced torque. These findings offer opportunities for precise control over the rotational motion of atoms within the system, with potential applications in precision measurement, quantum information processing, and quantum control.

Reconstruction of the high-fidelity vortex wavefront via double dark resonances in a four-level atomic medium

Recent years have seen vast progress in the generation and detection of vortex light, with potential applications in classical and quantum optics. However, it is still a challenge to efficiently generate high-fidelity vortex wavefronts in practical applications. Here, we propose a scheme to reconstruct the high-fidelity vortex wavefront via double dark resonances in a four-level atomic system. It is shown that, owing to a microwave field which interacts with magnetic or electric dipole moments of relevant atomic transitions, thereby generating spatially varying double dark resonances which in turn lead to the reconstruction of the incident probe field. In addition, to gauge the quality of the reconstructed probe field in comparison to the incident probe field, we study the fidelity of the reconstructed probe field and find that the reconstructed mode has a fidelity of more than 90% under the double-dark resonant condition. This study would be helpful to demonstrate optical vortex manipulation in atomic media.

Quantum Langevin theory for two coupled phase-conjugated electromagnetic waves

While loss-gain-induced Langevin noises have been intensively studied in quantum optics, the effect of a complex-valued nonlinear coupling coefficient on the noises of two coupled phase-conjugated optical fields has never been questioned before. Here, we provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-$\Lambda$ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. Finally, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

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.

Light drag in an optically dense left-handed atomic medium

In this paper, we investigate the light drag in an optically dense negative refractive index medium. Our model is a four-level atomic system in which we demonstrate an enhancement of the light drag while keeping the negative refraction condition. Furthermore, we control the shift in the light drag by tuning both the strong coupling field and the detuning. Hence, we observe that the light drag in the negative refractive index material can be controlled to switch from subluminal to superluminal at various ranges of the detuning. Our system suggests a straightforward technique for realizing and controlling light dragging in materials with negative refractive indices, or ‘NRI,’ which might open the way for more efficient use of left-handedness in atomic systems.

Spontaneously generated coherence in a four-level atomic system under induced chirality: Quantum control of the Casimir force

In this work, we investigate the coherent control of the Casimir force (CF) in a four-level atomic system under electromagnetically induced chirality. Therefore, we consider two parallel slabs of finite length in a quantum vacuum composed of ensembles of cesium vapor atoms in a four-level double Λ-type atomic configuration. By the use of the quantum interference (QI) effect which arises from the cross-coupling between the different spontaneous emission pathways, we demonstrate that it is possible to fully control the CF in the system via the spontaneously generated coherence (SGC) and the relative phase between the electromagnetic fields. In fact, we first show that the chirality in the atomic system can be induced by the SGC and the probe detuning, satisfying the passivity conditions. Next, we manipulate and control the QI in the system by changing the angle between the dipole moments, as the SGC is sensitive to their relative orientations. Besides, we explore the dependence of the Casimir interaction energy on the relative phase of the control fields. Finally, we observe that the Casimir interaction energy can be switched from negative to positive for a specific given phase value.

Two-dimensional electromagnetically induced grating via phase regulation in a closed-loop four-level atomic system

We proposed a theoretical scheme for two-dimensional (2D) electromagnetically induced grating (EIG) in a closed-loop four-level atomic system driven by a weak probe field, a traveling-wave control field, two orthogonal standing-wave fields and a microwave field. Due to low amplitude modulation accompanied with large phase modulation, EIG can be obtained and the probe energy can be diffracted into first-order and even high-order directions with high efficiency. The results show that the diffraction pattern and efficiency of the EIG could be adjusted effectively by the probe field detuning, the coherent field intensity, the interaction length. Meanwhile, the quantum interference between the amplitude modulation and phase modulation can be manipulated by the relative phase, which can be used to regulate the diffraction pattern and efficiency of the 2D EIG. Our scheme of 2D EIG may be useful in beam splitting and all-optical switching.