Four-level Atom Research Articles

Microwave field sensor based on cold cesium Rydberg three-photon electromagnetically induced spectroscopy

Abstract We present the electromagnetically induced transparency (EIT) spectra of cold Rydberg four-level cascade atoms consisting of the 6S1/2 → 6P3/2 → 7S1/2 → 60P3/2 scheme. A coupling laser drives the Rydberg transition, a dressing laser couples two intermediate levels and a weak probe laser probes the EIT signal. We numerically solve the Bloch equations and investigate the dependence of the probe transmission rate signal on the coupling and dressing lasers. We find that the probe transmission rate can display an EIT or electromagnetically induced absorption (EIA) profile, depending on the Rabi frequencies of the coupling and dressing lasers. When we increase the Rabi frequency of the coupling laser and keep the Rabi frequency of the probe and dressing laser fixed, flipping of the EIA to EIT spectrum occurs at the critical coupling Rabi frequency. When we apply a microwave field coupling the transition 60P3/2 → 61S1/2, the EIT spectrum shows Autler–Townes splitting, which is employed to measure the microwave field. The theoretical measurement sensitivity can be 1.52 × 10−2 nV⋅cm−1⋅Hz−1/2 at the EIA–EIT flipping point.

Surface plasmon polariton excitation and propagation in metal tripod systems

Through the activation of a planar gaseous medium consisting of four-level tripod atoms, our approach provides a mechanism to generate the Surface Plasmon Polariton (SPP). We investigate a three-layer structure in which the bottom layer is composed of atoms arranged in a tripod configuration, a metal film is layered in the middle, and a transparent layer of either air or vacuum resides on top. The bottom layer facilitates SPP excitation via amplification in the atom arrangement, caused by three laser beams: control, weak probe, and signal. The electromagnetically induced transparency effect, which can be seen in atoms, compensates for the momentum difference between light and SPP. We can coherently change SPP propagation length by altering control field strength, resonance, and off-resonant detuning. SPP optical gain power, propagation length, penetration depth, and metal thickness effects are also examined. Our method to generate SPPs may find use in lithography, sensors, polarizers, along with photodetectors.

Spontaneous emergence of temporal structures in a continuously driven many-body system

Abstract The spontaneous emergence of temporal structures challenges the conventional understanding that systems governed by time-invariant laws remain unchanged over time. Recent experiments have observed this time translation symmetry breaking in quantum atomic systems that either exhibit strong atom-atom interactions or have low dissipation rates. While current theoretical frameworks reveal the importance of strong atom-atom interactions, they fall short in explaining this phenomenon observed in low-dissipation atomic systems. Here, we present a theoretical study on the spontaneous breaking of time translation symmetry in materials with low
dissipation rates. By constructing phase diagrams for a system of four-level atoms driven by a continuous-wave optical field, we identify the essential requirements for self-sustained temporal motions. These include a driven open system, nonlinear interactions, and sufficient degrees of freedom that facilitate competing processes. Our findings contribute to a better understanding of the emergence of spontaneous time translation symmetry breaking in these materials.

Fast simulation for interacting four-level Rydberg atoms: electromagnetically induced transparency and Autler-Townes splitting

Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4 N × 4 N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.

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.

Surface plasmon induced quantum interference at meta-material interface

In this work we investigate quantum interference in a four-level atom coupled to a negative index meta-material (NIMM) anisotropic plasmonic environment that supports both TE and TM polarized surface plasmons (SP). The analysis confirms the creation of the anisotropic environment and two dipoles can interfere with each other even if they are orthogonal by sharing such SP modes. The NIMM/plasmonic environment provides more options to control SP interaction with emitters and their spontaneous emission decays and spectrum. The spectrum depends critically on structure parameters, mode frequency, frequency dependent electric permittivity and magnetic permeability, and the location of the atom etc. We observe orders of magnitudes enhancement in the plasmonic-modified decays and spectrum compared to free space case.

Controllable nonreciprocal single-photon frequency converter via a four-level system

We propose an efficient, nonreciprocal single-photon device that achieves single-photon routing and frequency conversion through chiral coupling of two one-dimensional waveguides with a four-level atom. Photons incoming from one port can be definitely directed to another port. However, the photon frequency conversion has been achieved only when the single photons are transferred from one waveguide to the other, and its probability can reach unity. Applied the on-demand classical field to drive an atom, the transmission quantum tunneling path can be turned off and on by exploiting the Autler–Townes splitting mechanism. Our results illustrate the potential of our device for applications in a quantum network.

Interaction of a four-level atom with a quantized field in the presence of a nonlinear Kerr medium

Quantum entanglement and atomic coherence are examined for a system consisting of a four-level atom (FLA) interacted with a nonlinear quantum field. We assume that the FLA-field coupling, Kerr medium and quantified field are all f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f$$\\end{document}-deformed with full nonlinear formalism. We consider N-configuration and cascade (C)-configuration of the FLA. We explore the impact of field deformation and Kerr medium on the dynamics of the quantumness measures when the quantized field is initially prepared in a deformed coherent state without and with Kerr medium effect. Moreover, we examine the statistical properties of the radiation field using the second order correlation function. The results indicate how the considered quantumness measures in the FLA–field system can be manipulated and controlled through the parameters of the quantum model.

Realization of an inherent time crystal in a dissipative many-body system

Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.

Rydberg-atom-based measurements of microwave electric fields with cavity quantum electrodynamics

A scheme for enhancing the measurement of microwave electric (MW E) fields based on a cavity-quantum-electrodynamics (CQED) system consisting of an optical resonator coupled with four-level cold Rydberg atoms is analyzed in the paper. The strong collective coupling of the CQED cavity compresses the linewidth of the electromagnetically induced transparency signal substantially, which can be used to enhance the measurement. Our simulation results show that the minimum detectable strength of MW E-field can be enhanced by 196.7 and 26.2 times smaller than the separate atomic medium scheme and the weak coupling scheme, respectively. The detectable minimum strength in the present work can reach as low as 396.5nVcm−1. In addition, compared with the other two schemes, our work can increase the spectrum resolution respectively by about 216 and 10 times. The proposed scheme shows a broadband tunability and can be used in a broad detection range.

State transfer and entanglement between two- and four-level atoms in a cavity

Qudits with a large Hilbert space to host quantum information are widely utilized in various applications, such as quantum simulation and quantum computation, but the manipulation and scalability of qudits still face challenges. Here, we propose a scheme to directly and locally transfer quantum information from multiple atomic qubits to a single qudit and vice versa in an optical cavity. With the qubit–qudit interaction induced by the cavity, our scheme can transfer quantum states efficiently and measurement-independently. In addition, this scheme can robustly generate a high-dimensional maximal entangled state with asymmetric particle numbers, showing its potential in realizing an entanglement channel. Such an information interface for qubits and qudit may have enlightening significance for future research on quantum systems in hybrid dimensions.

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.

Quantum entanglement and coherence in a system of four-level atom interacting with a nonlinear field

Entanglement and atomic coherence are investigated for a system that consists of a four-level atom (FLA) coupled with a nonlinear field. We explore the influence of field deformation and photon transition on the dynamical behavior of the quantum measures when the quantized field is initially in a coherent state or in a Schrödinger cat state with and without energy dissipation. The results indicate that the entanglement and coherence in the FLA–field system can be controlled and manipulated through the nature and initial state of the quantized field.

Depiction of an external classical field effects on a four-level W-configuration atom embedded in a coherent cavity field

This paper examines the dynamics of a W-configuration four-level atom in a quantized cavity field and the system driven by an external classical field. By applying some canonical transformations, we derive analytical solutions to the Schrödinger equation for the corresponding Hamiltonian. We have analyzed the impact of the external field and detuning parameters on the system’s relative entropy of coherence, Wigner function, and Pancharatnam phase. Our findings suggest that the external field parameter greatly affects the coherence of the system, whereas the detuning parameters may increase its maximum bounds. Furthermore, we have utilized the Wigner function as a tool to measure the quantumness and classicality of the system in its phase space. Our results indicate that the external field has a greater impact on the classicality of the system than the detuning parameters. Additionally, we have observed rapid oscillations in the dynamics of the Pancharatnam phase for large detuning values. It is worth noting that the external field reduces the number of phase jumps in the system.

Theoretical Investigation on the Mechanism and Law of Broadband Terahertz Wave Detection Using Rydberg Quantum State

The bandwidth and sensitivity of traditional terahertz detection devices are limited by material properties and working temperature. Here, we proposed a four-level Rydberg atom detection method, which can realize real-time detection for the absolute strength of the terahertz electric field under room temperature with the detection bandwidth of 0-5 THz. By theoretical analysis and formula derivation, the relation among the terahertz electric field strength, excitation energy level, coupling photoelectric field strength, gas cell temperature and electromagnetically induced transparency (EIT) signal are studied in detailed. The NEP of this method is proven to be 10^−17 W/Hz^1/2 in the range of 0-1 THz, which is three orders of magnitude smaller than that of the traditional optimal thermal detection system. This research has important reference value for the later high-sensitivity detection and application development of terahertz waves

A deformed model for N-type four-level atom and a single mode field system in the presence of the Kerr medium

The aim of this paper is to study the interaction between a single mode field and four-level atom in N - configuration under nonlinear medium effect. The non-resonance case and the deformation forms in the coupling interaction between the field and the atom are included. The wave function of the proposed system is obtained when the atom is prepared initially in its excited state while the field is prepared in a coherent state. The effect of the deformation and nonlinear medium on the temporal behavior of collapse-revival, field entropy and geometric phase of the system are examined. The results show that the presence of the intensity of the coupling interaction and the non-linear medium have an important influence on the properties of these phenomena.

Dispersion Relation for a Four-Level Atom with an Equidistant Energy Spectrum at a High Excitation Level

Dispersion Relation for a Four-Level Atom with an Equidistant Energy Spectrum at a High Excitation Level

Autler-Townes splitting of three-photon excitation of cesium cold Rydberg gases.

We demonstrate the three-photon Autler-Townes (AT) spectroscopy in a cold cesium Rydberg four-level atom by detecting the field ionized Rydberg population. The ground state |6S1/2〉, two intermediate states |6P3/2〉 and |7S1/2〉 and Rydberg state |60P3/2〉 form a cascade four-level atomic system. The three-photon AT spectra and AT splittings are characterized by the Rabi frequency Ω852 and Ω1470 and detuning δ852 of the coupling lasers. Due to the interaction of two coupling lasers with the atoms, the AT spectrum has three peaks denoted with the letters A, B and C. Positions of the peaks and relative AT splittings, γAB and γBC, strongly depend on two coupling lasers. The dependence of the AT splitting, γAB and γBC, on the coupling laser detuning, δ852, and Rabi frequency, Ω852 and Ω1470 are investigated. It is found that the AT splitting γAB mainly comes from the first photon coupling, whereas the γBC mainly comes from the second photon coupling with the atom. The three-photon AT spectra and relevant AT splittings are simulated with the four-level density matrix equation and show good agreement with the theoretical simulations considering the spectral line broadening. Our work is of great significance both for further understanding the interaction between the laser and the atom, and for the application of the Rydberg atom based field measurement.

Influence of an External Classical Field on a ♢ Four-Level Atom Inside a Quantized Field

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dressed states, the exact solution of the Schrödinger equation is obtained. The occupation of atomic levels and statistical population inversion is studied. Our results show that the classical field parameter dissolved the collapse periods and increased the maximum bounds of the upper state, while decreasing the lower bounds of the lower state. The detuning parameters reduce the minimum bounds of atomic levels and their inversion. On the other hand, the linear entropy and l1 norm of coherence are employed to measure the temporal evolution of the mixedness and coherence. It is found that the driven classical field improves the temporal evolution of the mixedness and lower bounds of coherence. However, the detuning parameters have a destructive effect on the mixedness and lower bounds of coherence. The intensity of the external classical field is regarded as a control parameter with different values of detuning parameters.

Sensitive detection of radio-frequency field phase with interacting dark states in Rydberg atoms.

An efficient scheme of phase measurement of a radio-frequency (RF) field is proposed by interacting dark states. Under the condition of electromagnetically induced transparency (EIT), the four-level Rydberg atom exhibits two windows. Compared with the transmission spectrum on resonance, the linewidths of absorption peaks off resonance are very narrow due to the interaction of double dark states. It is interesting to find that the distance of absorption peaks shifts approximately linearly with the phase of an RF field, which can be used to measure the RF field phase. Simulation results show that the linewidth of an absorption peak can be narrowed by more than one order of magnitude, and a narrow linewidth improves the detectable minimum phase difference by more than six times. It helps to reduce analyzation complexity and increase sensing resilience. The dependence of phase measurement on the control field and RF field is also investigated.