Identical Three-level Atoms Research Articles

Power and efficiency of a thermal engine with a coherent bath.

We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalization temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalization, therefore increasing the output power and the engine efficiency only when the thermalization temperature is reduced; revealing a more nuanced perspective of coherence as a resource. This allows us to optimize the output power by adjusting the coherence and relative stroke durations.

Coherent control of cooperative spontaneous emission from two identical three-level atoms in a photonic crystal

The coherent control of cooperative spontaneous emission from two identical non-overlapping three-level atoms in the V-configuration located within a photonic band gap (PBG) material with two resonant frequencies near the upper band edge of the PBG and confined to a region small in comparison to their radiation wavelengths but still greater than their atomic sizes is investigated. The dependencies of cooperative effects in which a photon emitted by one atom is reabsorbed by the other atom on the inter-atomic separation, on the initial state of the two-atom system, on the strength of the driving control laser field, and on the detuning of the atomic resonant frequencies from the upper band edge frequency is analyzed so as to identify the conditions for which these cooperative effects are enhanced or inhibited. Cooperative effects between atoms are shown to be influenced more by the PBG than by the nature of the atomic transitions involved. Excited state populations as well as coherences between excited levels are expressed in terms of time-dependent amplitudes which are shown to satisfy coupled integro-differential equations for which analytic solutions are derived under special conditions. Unlike for the case of one atom in a PBG where the fractional non-zero steady state populations on the excited levels as well as the coherence between the excited levels are constants independent of time, in the case of two atoms in PBG these quantities continuously oscillate as a manifestation of beating due to the continuous exchange between the two atoms of the photon trapped by the PBG. The values of these quantities as well as the amplitudes and frequencies of their oscillations depend of the parameters of the system, providing different ways of manipulating the system. The general formalism presented here is shown to recapture the special results of investigations of similar systems in free space when the non-Markovian memory kernels of the PBG are replaced by delta function dependent Markovian memory kernels.

Generation and nonclassicality of entangled states via the interaction of two three-level atoms with a quantized cavity field assisted by a driving external classical field

The interaction of two identical three-level atoms of the types $$V,\,\varXi $$V,? and $$\varLambda $$? with a quantized cavity field as well as a driving external classical field is studied. Under two certain unitary transformations, the system is converted to a typical form of the Jaynes---Cummings model for two three-level atoms. The exact analytical solutions of the wave function for different considered atom---field systems are exactly obtained with the help of the Laplace transform technique, when the atoms are initially prepared in the topmost excited state and the quantized field is in a coherent state. In order to examine the nonclassicality features of the deduced states, the dynamics of the entanglement between subsystems is discussed via two well-known measures, namely, von Neumann entropy of the reduced state and negativity. In addition, we pay attention to the temporal behavior of quantum statistics of the photons of the field and squeezing phenomenon. Meanwhile, the influence of the external classical field on the latter physical quantities is analyzed in detail. The results show that the mentioned quantities can be sensitively controlled via the external classical field. Also, numerical computations imply the fact that the nonclassicality features in $$\varXi $$?-type three-level atomic system is more visible than the other two configurations. In addition, it is shown that in the particular case of $$\varLambda $$?-type atomic system, the rank of the reduced density matrix of the three-level atoms is no larger than three, so that negativity fully captures the entanglement of this system and that such entanglement is distillable.

Derivation of a generalized double-sine-Gordon equation describing ultrashort-soliton propagation in optical media composed of multilevel atoms

We consider the propagation of ultrashort optical solitons in media described by a general Hamiltonian of multilevel atoms. Assuming that all transition frequencies of the medium are well below the typical wave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wave approximation and a rigorous application of the reductive perturbation formalism to derive a cumbersome coupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems. The rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation for a special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system of coupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showing the formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalized double-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.

Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics

We propose an interesting scheme for distributed orbital state quantum cloning with atomic ensembles based on the quantum Zeno dynamics. These atomic ensembles which consist of identical three-level atoms are trapped in distant cavities connected by a single-mode integrated optical star coupler. These qubits can be manipulated through appropriate modulation of the coupling constants between atomic ensemble and classical field, and the cavity decay can be largely suppressed as the number of atoms in the ensemble qubits increases. The fidelity of each cloned qubit can be obtained with analytic result. The present scheme provides a new way to construct the quantum communication network.

Speed Geometric Quantum Logical Gate Based on Double-Hamiltonian Evolution under Large-Detuning Cavity QED Model

We introduce the double-Hamiltonian evolution technique approach to investigate the unconventional geometric quantum logical gate with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms for the large-detuning interaction of the atoms with the cavity mode. The main advantage of our scheme is of eliminating the photon flutuation in the cavity mode during the gating. The corresponding analytical results will be helpful for experimental realization of speed geometric quantum logical gate in real cavities.

Implementation of quantum search scheme by adiabatic passage in a cavity–laser–atom system

This paper proposes a scheme for implementing the adiabatic quantum search algorithm of different marked items in an unsorted list of N items with atoms in a cavity driven by lasers. N identical three-level atoms are trapped in a single-mode cavity. Each atom is driven by a set of three pulsed laser fields. In each atom, the same level represents a database entry. Two of the atoms are marked differently. The marked atom has an energy gap between its two ground states. The two different marked states can be sought out respectively starting from an initial entangled state by controlling the ratio of three pulse amplitudes. Moreover, the mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided since the dynamics follows the dark state. Furthermore, this paper extends the algorithm with m (m > 2) atoms marked in an ideal situation. Any different marked state can be sought out.

Analog Grover search by adiabatic passage in a cavity-laser-atom system

A physical implementation of the adiabatic Grover search is theoretically investigated in a system of $N$ identical three-level atoms trapped in a single-mode cavity. Some of the atoms are marked through the presence of an energy gap between their two ground states. The search is controlled by two partially delayed lasers which allow a deterministic adiabatic transfer from an initially entangled state to the marked states. Pulse schemes are proposed to satisfy the Grover speedup either exactly or approximately, and the success rate of the search is calculated.

Effect of Cavity Decay on Entanglement of Ladder-Type Three-Level Atoms and a Two-Mode Cavity Field

Considering the adiabatical approximation and the large detuning condition, we give the effective Hamiltonian of a ladder-type three levels atom interacting with a bimodal cavity field. If two identical three-level atoms are sent through the cavity one by one, a two-atom entangled state can be generated. With the choice of the appropriate interaction time, a maximally entangled state of two atoms can be obtained if decoherence effect is ignored. Moreover, we discuss the effect of cavity decay on four physical quantities including atomic population probability, residual entanglement of the first atom and the cavity field, concurrence between the two atoms, and fidelity for generating atomic EPR state, all of which decrease with the increase of cavity decay when the other parameters are fixed.

Generation of field cluster states through collective operation of cavity QED disentanglement eraser

We investigate effects of a collective disentanglement eraser performed over states of two pairs of pre-entangled cavities tagged independently with two identical three-level atoms. It is shown that the collective disentanglement operation ensures not only the recovery of initial coherence but also its extension from the initial two to four qubits, generating four-qubit field cluster states. We also propose a cavity QED scheme to generate an arbitrary field graph state by means of a collective operation of disentanglement erasers.

Adiabatic Quantum Search Scheme With Atoms In a Cavity Driven by Lasers

We propose an implementation of the quantum search algorithm of a marked item in an unsorted list of N items by adiabatic passage in a cavity-laser-atom system. We use an ensemble of N identical three-level atoms trapped in a single-mode cavity and driven by two lasers. In each atom, the same level represents a database entry. One of the atoms is marked by having an energy gap between its two ground states. Appropriate time delays between the two laser pulses allow one to populate the marked state starting from an initial entangled state within a decoherence-free adiabatic subspace. The time to achieve such a process is shown to exhibit the square root N Grover speedup.

Influence from cavity decay on geometric quantum computation in the large-detuning cavity QED model

We introduce a general displacement operator to investigate the unconventional geometric quantum computation with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms, based on a previous scheme [S.-B. Zheng, Phys. Rev. A 70, 052320 (2004)] for the large-detuning interaction of the atoms with the cavity mode. The analytical results we present will be helpful for experimental realization of geometric quantum computation in real cavities.

Dynamic Behavior of Lambda-Type Three-Level Atoms andTwo-Mode Cavity Field

A system comprising of Lambda-type three-level atoms and the two-modecavity field is considered in this paper. Under the adiabaticalapproximation and the large detuning condition, the effectiveHamiltonian of the system in the interaction picture can be givenout. If the two identical three-level atoms pass through thecavity in turn, the entangled state atoms can be generated. Whenthe interaction time is taken to an appropriate value, the maximallyentangled states are created. At the same time, the dynamic behaviorsof the system are studied in detail.

Strong-driving-assisted unconventional geometric logic gate in cavity QED

We propose a potential scheme for carrying out two-qubit unconventional geometric logic gates on two identical three-level atoms in a cavity, strongly driven by a resonant classical field. Compared to a previous scheme [S. B. Zheng, Phys. Rev. A 70, 052320 (2004)] based on the large-detuning interaction of the two identical three-level atoms with the cavity mode, our scheme can, in principle, achieve a faster gating because of the resonant coupling of the atoms to the classical field. We present the two-qubit unconventional geometric phase gates in both an ideal cavity and a real cavity with decay. Discussions about the fidelity and the success probability of the proposed scheme as well as the experimental feasibility are made in detail.

Can the kicked top be realized?

Collections of identical two-level atoms can give rise to (quantum) chaotic behaviour if non-resonantly coupled to a resonator mode and periodically driven. Observation of such chaos would require a new generation of experiments on microwave superradiance, or optical variants thereof which would exploit the strong coupling characteristic of very small cavities. Similarly, collections of identical three-level atoms non-resonantly coupled to two cavity modes could provide ‘SU(3) laboratories’, capable of realizing the semiclassical and classical limits of SU(3) dynamics, both integrable and chaotic. Some of the more interesting modes of behaviour of such systems are discussed.

Cooperative two-photon interaction with nonclassical light

The two-photon interaction process of N identical three-level atoms with squeezed light is considered. The dependence of the absorption process on the squeezed fluctuations of light is studied. It is shown that the absorption rate of phase squeezed light is larger than the absorption rate of amplitude squeezed light. If the amplitude of the fluctuations is approximately equal to the average value of the electromagnetic field intensity, the quantum fluctuations can stop the two-photon nutation in the system. The possibility of a first-order phase transition in the system composed by the atoms and the external electromagnetic field is discussed.

Nonlinear Susceptibilities in a Three-Level Atomic System

We have studied the effect of the propagation of two strong fields of different frequencies on the nonlinear susceptibility in a medium composed of identical stationary three-level atoms in V-configuration. In particular, we show that each field influences the steady-state susceptibility, absorption and refractive-index change experienced by the other field. At large field strengths of one field, the second field experiences less absorption and an enhanced refractive index change.

Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities: II. Stimulated three-photon processes

We have studied stimulated three-photon processes arising from the interaction of a system of two-identical three-level atoms with a strong pump field and a weak signal field simultaneously. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole and cooperative radiative interactions, respectively. The strong laser field, whose frequency mode ω b is initially populated, depletes the metastable state by bringing the electrons into the excited state from where the electrons emit photons and decay through the signal field into the lower ground states of the system. Using the Green function method in the limit of high photon densities of the laser field, the spectral functions for the signal field have been calculated describing stimulated three-photon processes of the symmetric and antisymmetric modes, respectively, which arise from the dipole-dipole and cooperative radiative interactions between the atoms. The stimulated three-photon excitations near the frequency ω≈ ω 21 − 2 ω b describe physical processes where one-photon of the signal field with frequency ω 21 is absorbed while simultaneously two photons of the laser field are emitted. At resonance and in the absence of the dipole-dipole interaction, the spectra consist of a doublet whose peaks are symmetrically located from frequency ω = ω 21 − 2 ω b, while the magnitude and sign of the intensity of the peaks depend on the value of the relative Rabi frequency η b. For η b = 3, the intensity of the doublet takes negative values and it becomes positive for η b⩾5. As the value of η b increases the magnitude of the intensity of the doublet decreases and it becomes nearly constant for values of η b between 50 and 100. The single atom spectra consist of a doublet having a constant negative intensity independent of η b. The difference between the single and two-atom spectra is attributed to the cooperative radiative interaction between the two atoms. In the presence of detunings, the symmetry in the positions and intensities of the two sidebands vanishes. In the presence of the dipole-dipole interaction and at resonance, the spectra consist of three sidebands whose position, line shape, and sign as well as magnitude of the intensities depend entirely on the strength of the dipole-dipole interactions between the atoms. In the presence of detunings, asymmetries arise, enhancing certain spectral peaks while diminishing the intensity of others. The computed spectra are graphically presented for different values of η b, dipole-dipole interactions, and detunings. Comparison between the single and two-atom spectra is made and discussed in detail.

Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities: I. Stimulated one-photon spectra

We have considered the stimulated one-photon spectra for a system consisting of two identical three-level atoms interacting simultaneously with a strong pump field and a weak signal field. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole interaction and radiate to each other as well. The strong laser field depletes one of the lower ground states (metastable state) by bringing the electrons into the excited state from where the electrons decay through the signal field into the lower ground states of the system. Using the Green function formalism in the limit of high photon densities of the laser field, the spectral function for the signal field which describes the stimulated one-photon process of the symmetric and antisymmetric modes arising from the dipole-dipole and cooperative radiative interactions between the two atoms, has been calculated and compared with that of the single atom. In the absence of the dipole-dipole interaction between the atoms, the spectra consist of the main peak at the frequency of the signal field and two pairs of sidebands, which are symmetrically located from the position of the main peak. In this case, the difference between the single and two-atom spectra is caused by the cooperative radiative interaction between the atoms and amounts: i) to increase the lifetime of the main peak by a factor of two from that of the single atom; ii) to split the one pair of sidebands of the single atom spectrum into two pairs of sidebands; iii) to cause the intensity of the two pairs of sidebands to vary as a function of the Rabi frequency of the laser field; and iv) to induce strong asymmetries in the lineshapes of the sidebands. In the presence of the dipole-dipole interaction, the spectra consist of a main peak at the frequency of the signal field shifted by the magnitude of the dipole-dipole interaction and six sidebands whose positions and intensities are governed by the strength of the dipole-dipole interactions between the atoms. The lineshapes of all peaks are described by asymmetric Lorentzian lines and the extent of the asymmetry depends on the strength of the dipole-dipole interaction. The relative intensity of the main peak and those of the sidebands are either positive or negative depending on the strength of the dipole-dipole interaction. The amplification of the sidebands is found to be more pronounced in the two-atom spectra than in that of the single atom. The computed spectra are presented graphically for different values of the Rabi frequencies, dipole-dipole interactions and for different detunings.

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

Numerical calculations are presented for the excitation spectrum of two identical three-level atoms interacting with a strong resonant laser field. The atoms interact through their dipole-dipole interaction and radiate to each other as well. The spectrum of the symmetric and antisymmetric modes due to the radiative decay from the higher to the lower excited state of the interacting atoms is considered without and with taking into account the effects of the strong pumping process. In the absence of strong pumping, the dipole-dipole interaction in the spectrum of the symmetric modes gives rise to an asymmetric doublet whose ratio of intensities is 2:1, while the spectrum of the antisymmetric modes consists of two peaks one of which represents a stable mode indicating the trapping of a photon between the atoms and a radiative one which has a lifetime one-half that of the isolated atom. In the presence of strong pumping, asymmetries due to the dipole-dipole interaction arise enhancing certain peaks while diminishing the intensity of others and a new pair of sidebands is induced as well. The computed spectra are presented graphically for different values of the Rabi frequencies and the dipole-dipole interaction, respectively.