Orthogonal Standing-wave Fields Research Articles

High-precision three-dimensional atom localization in a microwave-driven atomic system

We demonstrate the behavior of three-dimensional (3D) atom localization in a four-level Y-type atomic system driven by a microwave field. The position information of the atom can be obtained by measuring the position-dependent probe absorption when the atom interacts with three orthogonal standing-wave fields. It is found that the precision of the atom localization depends sensitively on the probe detuning and the strength of the microwave field. Remarkably, the localization precision can be significantly improved by increasing the amplitude of the microwave field, and the localization position will be changed by adjusting the relative phase between the standing-wave, microwave, and control fields.

Localization of cold [formula omitted] atom simulated by a three-level quantum system within half-wavelength domain

Simulating the cold R87b atom with a three-level quantum system interacting with two orthogonal standing-wave fields, the localization within half-wavelength domain in the x-y plane is achieved by monitoring the probe absorption. Within the half-wavelength domain, the single absorption peak increases from 0.2 to 1.0 via the spontaneously generated coherence (SGC), while the diameters of the single absorption peaks are diminished by the increasing incoherent pumping field. Our scheme provides the flexible parameters manipulating manner for the localization of cold R87b atom.

Dual peaks evolving into a single-peak for sub-wavelength 2-D atom localization in a V-type atomic system

The atom localization of a V-type atomic system is discussed by the detunings associated with the probe and the two orthogonal standing-wave fields, and by the spontaneously generated coherence (SGC). Within the half-wavelength domain in the 2-dimensional (2-D) plane, the atom localization depicted by the probe dual absorption peaks is achieved when the detunings are tuned. However, the dual peaks change into a single-peak when the SGC arises. The single-peak 2-D localization demonstrated the advantage for atom localization achieved by the flexible manipulating parameters in our scheme.

Two-dimensional electromagnetically induced grating in coherent atomic medium

We propose a scheme for effectively creating a type of all optical device called electromagnetically induced two-dimensional grating by utilizing a four-level coherent atomic medium, which is coherently driven by two orthogonal standing-wave fields. With a far-off resonant trigger field, a spatially modulated cross-phase modulation takes place accompanied by vanishing absorption. The resulting phase grating can diffract the probe beam into high-order directions. When a resonant trigger field is applied on the atoms, the probe obtains gain without inversion due to the atomic coherence effect. And then a gain-phase grating is formed. The diffraction efficiency can be significantly improved compared with that of phase grating. The results show that the diffraction efficiencies attainable by the gratings strongly depend on the interaction length, coherent field intensity, probe field detuning and coherent field detuning. Therefore, the proposed gratings can be used as two-dimensional multi-channel beam splitter which have potential application in optical networking and communication.

Two-dimensional localization of an atom with sub-half-wavelength spatial resolution via coherently controlled spontaneous emission

We propose a scheme for two-dimensional sub-half-wavelength atom localization using two lasers with equal frequencies, and obtain the analytical expression of conditional position probability (CPP) using a spontaneous-emission spectrum for a four-level atom which passes through two-dimensional orthogonal standing-wave fields. The quantum interference effect between two decay channels leads to extreme spectral narrowing and quenching of spontaneous emission in some regions of the standing-wave field, which results in the appearance of a high-spatial-resolution localization peak. The two-dimensional sub-half-wavelength atom localization is obtained with high precision and high spatial resolution by adjusting the relative phase and detuning.

Two-dimensional gain cross-grating based on spatial modulation of active Raman gain**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274112 and 11347133).

Based on the spatial modulation of active Raman gain, a two-dimensional gain cross-grating is theoretically proposed. As the probe field propagates along the z direction and passes through the intersectant region of the two orthogonal standing-wave fields in the x–y plane, it can be effectively diffracted into the high-order directions, and the zero-order diffraction intensity is amplified at the same time. In comparison with the two-dimensional electromagnetically induced cross-grating based on electromagnetically induced transparency, the two-dimensional gain cross-grating has much higher diffraction intensities in the first-order and the high-order directions. Hence, it is more suitable to be utilized as all-optical switching and routing in optical networking and communication.

Two-dimensional Sub-wavelength Atom Localization of a Four-Level $$\varLambda$$ Λ -type Atomic System with two Adjacent Lower Levels Via Probe Absorption

Two-dimensional atom localization of a four-level \(\varLambda\)-shaped atom with two adjacent lower levels interacting with two orthogonal standing wave fields is considered. By measuring the probe field absorption, spatial information of position of a moving atom is obtained in \(x - y\) plane. The position of atom through two-dimensional standing wave field strongly depends on the intensity of standing waves, detuning of the probe and standing wave fields. Choosing the appropriate controlling parameters, the two-dimensional atom localization through the standing wave fields in a sub-wavelength domain will be achieved.

Two-dimensional electromagnetically induced grating via gain and phase modulation in a two-level system

A scheme for two-dimensional (2D) electromagnetically induced grating via spatial gain and phase modulation is presented in a two-level atomic system. Based on the interactions of two orthogonal standing-wave fields, the atom could diffract the weak probe beam into high-order directions and a 2D diffraction grating is generated. It is shown that the diffraction efficiency of the grating can be efficiently manipulated by controlling the Rabi frequencies of control fields, the detunings of the control and probe fields, and interaction length. Different from 2D cross-grating via electromagnetically induced transparency in a four-level atomic system, the present scheme results from the spatial modulation of gain and phase in a simple two-level system, which could lead to 2D gain-phase grating with larger diffraction intensities in the diffraction directions. The studies we present may have potential applications in developing photon devices for optical-switching, optical imaging and quantum information processing.

Three-Level &#923-Type Atomic System Localized by the Parameters of the Two Orthogonal Standing-Wave Fields

Localization of the three-level Λ-type atomic system interacting with two orthogonal standing-wave fields is proposed. Two equal and tunable peaks in the 2D plane are obtained by the detunings corresponding to the two orthogonal standing-wave fields when the decreasing intensities of spontaneously generated coherence (SGC) arise in the three-level Λ-type atomic system, while one circular ring with shrinking radii in the 2D plane is obtained by the adjusted phases and wave vectors of the standing-wave fields when the increasing intensities of SGC occur in the three-level Λ-type atomic system. 2D atom localization with the single ring with shrinking radii realized by the multiple parametric manipulations demonstrated the flexibility for our scheme.

Resonance fluorescence based two- and three-dimensional atom localization

Two- and three-dimensional atom localization in a two-level atom–field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.

Phase control of three-dimensional atom localization in a four-level atomic system in Lambda configuration

A scheme of phase-sensitive three-dimensional atom localization (3DAL) is presented based on absorption measurement of the weak probe field in a driven four-level Λ-type atomic system with twofold lower levels in which the atom interacts with three orthogonal standing wave fields. Because of the space-dependent coupling of the atom field in three dimensions, the position probability distribution of the passer atom through the standing wave fields can be straightforwardly assessed by gauging the resultant absorption spectra. It is found that, by appropriately tuning the system parameters, various 3D periodic isosurface patterns of localization including polyhedrons, waves, cylinders, diamonds, lattices, bowling pins, tetrahedrons, cubes, and spheres can be formed and the high-precision and high-resolution 3DAL can be manipulated. Because of the closed-loop structure in this atomic system, the probe absorption is dependent on the relative phase of applied fields. The phase dependence of 3DAL in also discussed.

Realization of position-dependent absorption based on biexciton coherence in a Quantum Dot Nanostructure

In this letter, the two-dimensional (2D) spatial-dependent of probe absorption based on biexciton coherence is investigated by monitoring the probe absorption spectra in a Quantum Dot (QD) Nanostructure. We find that due to the quantum interference which is set up by two control pulses that couples to a resonance of the biexciton, the 2D spatial distribution of probe absorption spectrum can be controlled via adjusting the system parameters. We study the effect of controlling parameters of the QD system on spatial distribution of the probe field absorption for two different cases in which the QD interacts with the standing-wave laser fields; first, when two laser fields which couple to a biexciton state, correspond to the two orthogonal standing-wave fields and couple the different transitions. Second, when only one of laser fields correspond to the combination of two orthogonal standing-wave fields, while the other one corresponds to a traveling-wave field. Results exhibit different interesting 2D absorption patterns.

2D spatial distribution of probe absorption in a triple semiconductor quantum well nanostructure

We investigate the two-dimensional (2D) position-dependent probe absorption in a triple semiconductor quantum well (SQW) structure driven coherently by two orthogonal standing-wave fields. Under weak probe field approximation and utilizing the density matrix approach, an analytical solution is presented for the probe linear susceptibility which clarifies directly the spatial-dependent nature of the probe absorption. Then, the distribution of probe absorption in 2D is numerically explored. It is found that 2D absorption spectra are very sensitive to the intensity and frequency detuning of standing-wave fields which can result in various 2D localization structures in one period of standing waves in the x–y plane.

2D isotropic negative permeability in a Λ-type three-level atomic system

An approach for two-dimensional (2D) negative permeability in a Λ-type three-level atomic system interacting with a magnetic probe and the superposition of two orthogonal standing-wave fields is proposed. Through theoretical analysis and numerical simulation, two equally and tunable peak maxima of negative magnetic responses are observed in the x-y plane, and around the peak maxima region the negative permeability is isotropic. A new avenue to 2D isotropic negative permeability in isotropic applications, via the quantum optics method, is achieved in our scheme.

Two-dimensional atom localization via phase-sensitive absorption-gain spectra in five-level hyper inverted-Y atomic systems

A scheme for realizing two-dimensional atom localization in the sub-wavelength domain is proposed in a microwave-driven five-level hyper inverted-Y atomic system in which the atom interacts with a weak probe field, two control fields together with two orthogonal standing-wave fields. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be extracted directly from the absorption and gain spectra of a weak probe field. It has been found that the probe detuning, the intensities of two control fields, and the relative phase of the driving fields can significantly improve the localization precision. Moreover, the maximal probability of finding the atom at an expected position in the sub-wavelength domain of the standing-wave field can reach unity via properly adjusting the system parameters.

2-D isotropic negative refractive index in a N-type four-level atomic system

Abstract 2-D(Two-dimensional) isotropic negative refractive index (NRI) is explicitly realized via the orthogonal signal and coupling standing-wave fields coupling the Ntype four-level atomic system. Under some key parameters of the dense vapour media, the atomic system exhibits isotropic NRI with simultaneous negative permittivity and permeability (i.e. left-handedness) in the 2-D x-y plane. Compared with other 2-D NRI schemes, the coherent atomic vapour media in our scheme may be an ideal 2-D isotropic NRI candidate and has some potential advantages, significance or applications in the further investigation.

Two-Dimensional Atom Localization via Controlled Spontaneous Emission in a Coupled Cavity Waveguide

A scheme of atom localization based on controlled spontaneous emission is proposed, in which the atom is embedded in a coupled cavity waveguide with two orthogonal standing-wave fields. We can achieve high-precision and high-resolution atom localization by properly adjusting the system parameters. It is shown that the localization is significantly improved due to the strong coupling effect between the atom and a coupled cavity waveguide.

Efficient two-dimensional atom localization via an external coherent magnetic field

The primary objective of this study was to investigate the two-dimensional (2D) atom localization via a coherent magnetic field in a closed three-level atomic system. Two-dimensional (2D) atom localization in multi-level atomic systems has been studied in recent years because of its unique properties and extensive applications. However, to the best of our knowledge, no further theoretical or experimental work has been carried out to study such 2D atom localization in a closed three-level atomic system in the presence of the coherent magnetic field that motivates the current work. As for 2D atom localization, the conditional position probability distribution, i.e., the probability of finding the atom at the position in the two orthogonal standing-wave fields when the atom is found in its internal excited state. In this paper, 2D atom localization is obtained via measuring the population in the excited state, which is solved via the density-matrix equations in dipole and rotating-wave approximations. Results The precision and spatial resolution of the 2D atom localization are improved via properly adjusting the controllable parameters of the system such as the detunings and intensities of the corresponding applied fields as well as the collective phase of the probe and standing-wave fields. Due to the position-dependent atom-field interaction, the position information of the atom in the standing-wave fields can be obtained by means of the phase-sensitive excited state population. More importantly, the maximal probability of finding an atom within the sub-half-wavelength domain of the standing waves can reach 100 %. Thus, our scheme may be helpful in observing precision quantum measurement and computation for quantum information processing.

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

By using two orthogonal coupling standing-wave fields, we propose a scheme for a two-dimensional electromagnetically induced cross-grating (EICG) in a four-level tripod-type atomic system. Based on the electromagnetically induced transparency, the probe field will be diffracted and form the two-dimensional EICG through the interaction of the two coupling standing-wave fields. It is shown that the first-order diffraction intensity of the two-dimensional EICG depends observably on the detuning of the probe field and the Rabi frequencies of the two coupling standing-wave fields. The results may be used to develop novel photonic devices for use in quantum information processing, quantum networking and optical imaging.

Efficient two-dimensional localization effect in a semiconductor quantum well

The behavior of the two-dimensional (2D) localization effect is explored by monitoring the excitonic population in a three-level semiconductor quantum well under the action of two orthogonal standing-wave fields. Owing to the position-dependent quantum interference, the localization behavior is significantly improved due to the joint quantum interference induced by the standing-wave and pumping fields. Most importantly, the electron can be localized at a particular position and the maximal probability of finding the electron in one period of the standing-wave fields reaches unity by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve a high-precision and high-resolution 2D localization effect in a solid.