Atom-field Detuning Research Articles

Note on the emission spectrum and trapping states in the Jaynes–Cummings model

The emission of light from an atom represents a fundamental process that provides valuable insights into the atom–light interaction. The Jaynes–Cummings model is one of the simplest fully quantized models to deal with these interactions, allowing for an analytical solution, while exhibiting notable nontrivial effects. We explore new, to our knowledge, features in the fluorescence emission spectrum for initial “trapping states,” which suppress the atomic population inversion. Despite the seemingly dormant activity of the atom, the resulting emission spectra exhibit rich features, and using a dressed-state coordinates formalism, we are able to quantitatively explain the different profiles in the spectrum. We generalize the trapping conditions for nonzero atom-field detuning and also unveil two types of trapping states that lead to spectra with three peaks, in contrast to previously known states: a center peak and one secondary peak on each side. These are a trapping state formed by a Schrödinger cat state with Poissonian statistics (Yurke–Stoler state) and also a different type of “perfect trapping state.”

Injected coherence and phase control in the tunneling of ultra slow three-level atoms

Our research aims to investigate the impact of injecting atomic coherence on the phase tunneling time of ultra slow cascade three-level atoms traversing through high-quality cavities. Prior to interacting with the cavity in the Fock state, the atoms are initially prepared in a superposition of the two upper levels. Our study has demonstrated that the coherence of the injected atoms can be tuned to control the phase time. Specifically, we have observed that the injected coherence can regulate the peak values and sub-superclassical nature of the traversal time. Moreover, we have investigated how the number of superclassical peaks and resonances in the tunneling time curve can be influenced by the cavity length and de Broglie waves of the atom. Additionally, we have discovered that the phase time behavior is not only affected by the center-of-mass (CM) motion but also by the atom–field detuning and the final internal state of the transmitted atoms. These findings have potential implications for developing and controlling ultracold atom-based technologies, such as quantum sensors, quantum information processing, and quantum simulation.

Dynamics of entanglement of atoms with two-photon transitions induced by a thermal field

In this paper, we investigate the entanglement between two two-level atoms non-resonantly in-teracting with a thermal field of a lossless one-mode resonator via degenerate two-photon transi-tions. On the basis of the exact solution of the time-dependent density matrix we calculate the negativity as a measure of atomic entanglement. We show that for separable initial atomic states a slight atom-field detuning may generate the high amount of atom-atom entanglement. The re-sults also show that for non-resonant atom-field interaction the entanglement induced by nonlin-ear two-photon interaction is smaller than that induced by one-photon interaction in contrast to the resonant interaction situation. For a Bell-type entangled initial atomic state we obtain that if the detuning increases, there is an appreciable decrease in the amplitudes of the negativity oscilla-tions. The results also show that elimination of the sudden death of entanglement for non-resonant two-photon atom-field interaction may take place.

Electro-optomechanical switch via tunable bistability and four-wave mixing

We investigate the tunable bistable behavior of a hybrid nano-electro-optomechanical system (NEOMS) composed of S-shaped in the presence of two-level atoms, trapped inside a Fabry–Pérot cavity, and driven by a strong driving field and a weak probe field. The bistable behavior of the steady-state photon number and the mechanical steady-state positions are discussed. Further, we tune bistability by tuning all the coupling frequencies involved in the system and amplitude of the driving field. The present study provides the possibility of realization of a controllable optical switch depending on atom-field coupling, optomechanical coupling, electrostatic Coulomb coupling, and threshold power. In addition, we discuss that the non-linear effect of the hybrid NEOMS generates the four-wave mixing (FWM) process. Moreover, we show that the FWM process can be suppressed by the atom-field detuning and cavity-field detuning, which exhibits low photon transmission.

Optomechanical cooling and self-trapping of low field seeking point-like particles

Atoms in spatially dependent light fields are attracted to local intensity maxima or minima depending on the sign of the frequency difference between the light and the atomic resonance. For light fields confined in open high-Q optical resonators the backaction of the atoms onto the light field generates dissipative dynamic opto-mechanical potentials, which can be used to cool and trap the atoms. Extending the conventional case of high field seekers to the regime of blue atom-field detuning, where the particles are low field seeking, we show that inherent nonlinear atom field dynamics still can be tailored to cool and trap near zero field intensity. Studying field intensity, particle localization and kinetic energy for cavity driving or pumping the particle from the side, we identify optimal parameter regimes, where sub-Doppler cooling comes with trapping and minimal atomic saturation.

The Effect of Internal Dynamics on the Motion of Cold Atoms in 2D Optical Lattices with Interfering Laser Beams

We show theoretically and numerically that cold two-level atoms demonstrate unexpectedly complicated motion in an absolutely rigid two-dimensional optical lattice with interfering laser beams. The point-like atoms can move there in a chaotic way resembling motion of particles in a random potential. Chaos arises if the laser frequency is close to the atomic transition frequency where one should take into account the excitation of internal atomic states by the laser field. After loading cold atoms to the lattice, their induced electric dipole moments interact with a spatially inhomogeneous electric field of the two-dimensional standing laser wave. We find the range of the atom–field detuning where the synchronized (with the laser field) component of the atomic dipole moment changes in a random-like manner just after crossing the nodal lines of the standing wave where the electric field is zero. It, in turn, causes irregular changes in the momentum of atoms, leading eventually to chaotic walking of cold atoms in a deterministic potential. We show that adjusting the single control parameter, the atom–field detuning, it is possible to switch between regular and chaotic regimes of motion.

Entanglement transfer in a noisy cavity network with parity-deformed fields

We investigate the effects of parity-deformed radiation fields on the dynamics of entanglement transfer to distant noninteracting atom qubits. These qubits are embedded in two separated lossy cavities connected by a leaky fiber, which acts as a cavity buffer with delocalized modes. The process is studied within a single-excitation subspace, the parity-deformed cavity photons allowing the introduction of static local classical fields which function as a control. The mechanism of state transfer is analyzed in comparison to the uncontrolled case. We find that the transfer evolution exhibits an asymmetry with respect to atom-field detuning, being sensitive to the sign of the detuning. Under a linear interaction controlled by the local classical fields, we show that the entanglement distribution can be both amplified and preserved against the noise. These results motivate developments towards the implementation or simulation of the purely theoretical model employing parity-deformed fields.

Controlling tunneling of ultracold three-level atoms through a two-photon mazer cavity via the atom-field detuning

We study the tunneling and traversal of ultracold three-level atoms through a high- Q microwave cavity. In particular, we analyzed effects of the atom-field detuning on the tunneling time of ultracold atoms through a two-photon mazer cavity. Here, photons are emitted and absorbed in pairs; therefore, the nature of the interaction is quite different from a single photon mazer. It is found that when an appropriate detuning is introduced, one may obtain alternate positive and negative values of the phase time of tunneling with increasing centre-of-mass energies of the incident atoms. Further, phase time can be switched between the sub- and super-classical characters, and its peak value may be smartly controlled by adjusting the atom-field detuning. More interestingly, we find that phase time rigorously depends on the internal degree of freedom of the interacting atoms, i.e. the final state in which the atoms are exiting the cavity.

RETRACTED: Superluminal effect in a hybrid nano-electro-optomechanical system

Abstract We theoretically investigate the phenomenon of superluminosity of the transmission probe field under the effect of a strong driving field in a hybrid nano-electro-optomechnical system comprising two coupled charged mechanical end resonators connected by bias voltages. The first mechanical charged mirror is connected to the optical field, while the second charged mirror is coupled by Coulomb coupling. We find that the superluminal behavior of the transmitted probe field can be switched by adjusting the cavity field detuning and atom field detuning. The present study extends the previously developed simple optomechanical and nano-electro-optomechanical system (Ma et al., 2014)[62]. Moreover, the group delay of the pulse advancement can be controlled by adjusting the electrostatic Coulomb coupling and the power of the driving field. We explain the effect of atomic field detuning on the superluminal behavior in the regimes of anti-Stokes sidebands, i.e. Δ a = − ω 1 .

Pump-probe response sensitive to atomic excitation in a hybrid optomechanical system

We study the pump-probe response in an optomechanical cavity accommodating an ensemble of two-level atoms interacting with a cavity mode, which is pumped by a strong driving field and probed by a weak signal field. The atomic excitation is examined without taking any approximations and may be in any regimes ranging from the low limit to the high limit for a given collective coupling constant between the atomic ensemble and the cavity mode. This then results in different absorption and dispersion spectra (such as optomechanically induced transparency, Fano-resonance, normal-mode splitting) when the excitation transfer from cavity mode to atomic ensemble is controlled to change from ineffective to effective. This indicates that a hybrid optomechanical response is indeed determined by the excitation of the atomic ensemble embedded in the optomechanical cavity. It is also of interest that the output signal component and the inside atomic polarization show either synchronous or asynchronous behaviors depending on how the atom-field detuning is chosen, i.e. equal to the mechanical resonator frequency or its negative. Such features may open up an effective avenue in coherently manipulating the internal atomic polarization via the external signal field, and vice versa.

Stimulated radiation characteristics and quantum phase transition for two-component Bose-Einstein condensate in optical cavity

Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

Optical-response properties in levitated optomechanical systems beyond the low-excitation limit

We investigate the optical-response properties of a levitated optomechanical cavity coupled to a higher order excited atomic medium. The cavity field driven through the atom-field interaction is responsible for trapping a dielectric nanosphere, whose steady-state position is biased by the Coulomb force between the nanosphere and the cavity wall. We show that the phenomena of optomechanically induced transparency (OMIT) and amplification can be generated from the output probe field in the presence of an effective optomechanical coupling between the nanosphere and the cavity field. Further, the width of the transparency window increases with increasing strength of the effective optomechanical coupling, which is controlled easily by varying the Coulomb interaction and the radius of the nanosphere. In particular, when the higher order excitation of the atomic medium is included, a large driving of the atomic ensemble but a relatively small atom-field detuning can be applied to help observe the OMIT behavior in the hybrid system.

Double-electromagnetically induced transparency in a Y-type atomic system

We study the absorption and dispersion properties of a weak tunable probe field in a four-level Y-type atomic system driven by two strong laser (coupling) fields within the framework of density matrix formalism. It is found that the probe absorption profile displays double-electromagnetically induced transparency (double-EIT) and it is shown how to control it by changing the Rabi frequencies as well as the atom field detuning of the coupling fields.

Phase transition for coupled atom-light states in the presence of optical collisions

The problem of photon phase transition in a system of two-level atoms interacting with a quantized single-mode electromagnetic field in the presence of optical collisions is discussed. The photon field is shown to undergo a high-temperature second order phase transition into the coherent (superradiant) state at large negative values of atom-field detuning and under the condition of thermalization of coupled atom-light states.

Wave-vector mismatch effects in electromagnetically induced transparency inY-type systems

We study electromagnetically induced transparency (EIT) of a probe field in a four-level Y-type atomic system driven by two strong laser (coupling) fields. Both homogeneously (radiative) and Doppler broadened systems are considered. The effect of residual Doppler broadening on EIT is demonstrated for various wave-vector mismatches occurring when the frequency of coupling fields is equal (${k}_{c}$ $=$ ${k}_{p}$), higher (${k}_{c}>{k}_{p}$), or lesser (${k}_{c}<{k}_{p}$) than that of the probe field frequency. Contrary to usual belief it is found that for the ${k}_{c}>{k}_{p}$ wave-vector mismatch case, the probe absorption profile displays very wide and almost complete single or double EIT windows whose width, depth, and location depend upon the wave-vector mismatch, Rabi frequencies, and atom field detuning of the coupling fields. Analytical results are also obtained to explain these interesting features.

Chaotic walking and fractal scattering of atoms in a tilted optical lattice

We consider analytically and numerically chaotic walking of cold atoms in a tilted optical lattice created by two counter-propagating running waves with an additional external field in the semiclassical and Hamiltonian approximations. The effect consists in random-like changing the direction of atomic motion in a rigid lattice under the influence of a constant force due to a specific behavior of the atomic dipole-moment component that changes abruptly in a random-like manner while atoms cross standing-wave nodes. Chaotic walking generates a fractal-like scattering of atoms that manifests itself in a self-similar structure of the scattering function in the atom–field detuning in the position and momentum spaces. We show that the probability distribution function of the scattering time decays in a non-exponential way with a power-law tail.

High fidelity and flexible quantum state transfer in the atom-coupled cavity hybrid system

We investigate a system composed of N coupled cavities (linear array) and two-level atoms interacting one at a time. Adjusting appropriately the atom-field detuning, and making the hopping rate of photons between neighboring cavities, A, greater than the atom-field coupling g (i.e. A ? N 3/2 g), we can eliminate the interaction of the atom with the non-resonant normal modes reducing the dynamics to the interaction of the atom with only a single-mode. As an application of this interaction, we propose a two-step protocol for quantum communication of an arbitrary atomic quantum state between distant coupled cavities. In the ideal case, the coupled cavities system acts as a perfect quantum bus and we obtain a flexible and perfect quantum communication for any N. Considering the influence of dissipation, an interesting parity effect emerges and we still obtain a high fidelity quantum state transfer for an appreciable number of cavities with current experimental parameters. We also studied important sources of imperfections during the procedure.

Entanglement of two distant qubits driven by thermal environments

A model of entanglement generation of two initially disentangled qubits, each coupled to a separate cavity with the cavities connected by a fiber, is considered. The creation and evolution of the atomic entanglement are studied in the framework of the microscopic master equation capable of describing an open quantum system. The cavities and fiber are coupled to their own thermal environment. In these conditions, we compute the concurrence as a measure of the atomic entanglement and study the contribution of the environments at finite temperature to the dynamics of entanglement. As a result, one finds interesting effects where the thermal baths stimulate the generation of the entanglement in a given range of temperatures and the effect could be seen especially at some stage of the entanglement evolution. The range of temperatures at which entanglement increases is limited by some optimal values, depending on the physical characteristics of the system, such as operating cavity/fiber frequencies, atom–field detuning and couplings, and loss rates.

Implementation of quantum controlled phase gate and preparation of multiparticle entanglement in cavity QED

Schemes are presented for realizing quantum controlled phase gate and preparing an N-qubit W-like state, which are based on the large-detuned interaction among three-state atoms, dual-mode cavity and a classical pulse. In particular, a class of W states that can be used for perfect teleportation and superdense coding is generated by only one step. Compared with the previous schemes, cavity decay is largely suppressed because the cavity is only virtually excited and always in the vacuum state and the atomic spontaneous emission is strongly restrained due to a large atom—field detuning.