Single-mode Radiation Field Research Articles

Entangled two two-level atoms interacting with a cavity field in the presence of the stark shift terms

The general solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a cavity single-mode radiation field in the presence of the Stark shift terms is obtained. The temporal evolution of the atomic inversion for the single-atom case, the entropy squeezing and the atomic variances squeezing are studied. We use the linear entropy and von Neumann entropy to measure the degree of entanglement between the atoms and the field. It has shown that an increase in the value of the Stark shift parameter leads to an increase in the degree of entanglement. These aspects are sensitive to changes in the Stark shift parameter.

Two coupled oscillators in the form of a frequency converter in interaction with a single atom via two-photon processes

We consider the problem of a two-level atom with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric frequency-converter term. A Hamiltonian representing such a system contains three time-dependent coupling parameters. We obtain an exact solution of the wave function in the Schrodinger picture, using the canonical transform and under a certain choice of the coupling parameters. We use the results obtained to discuss the atomic inversion as well as the linear entropy in addition to both the variance and entropy squeezing. We show that the system at a certain time is sensitive to variations in both the detuning parameter Δ and the ratio of the coupling parameter g.

Quantum Otto engine of a two-level atom with single-mode fields

We establish a quantum Otto engine (QOE) of a two-level atom, which is confined in a one-dimensional (1D) harmonic trap and is coupled to single-mode radiation fields. Besides two adiabatic processes, the QOE cycle consists of two isochoric processes, along one of which the two-level atom as the working substance interacts with a single-mode radiation field. Based on the semigroup approach, we derive the time for completing any adiabatic process and then present a performance analysis of the heat engine model. Furthermore, we generalize the results to the performance optimization for a QOE of a single two-level atom trapped in a 1D power-law potential. Our result shows that the efficiency at maximum power output is dependent on the trap exponent θ but is independent of the energy spectrum index σ.

Amplification of nonclassical light in phase space

The scale transformation acting on P-functions associated with density operators of light is introduced as an amplification process for single-mode radiation fields. The P-amplification does not always yield a physical state out of the given nonclassical state; in particular, there are some restrictions on the degree of amplification that depend on how nonclassical the initial state is. The exact constructions of P-amplified density operators for two- and three-dimensional Hilbert spaces are carried out explicitly.

Performance analysis of a two-state quantum heat engine working with a single-mode radiation field in a cavity

We present a performance analysis of a two-state heat engine model working with a single-mode radiation field in a cavity. The heat engine cycle consists of two adiabatic and two isoenergetic processes. Assuming the wall of the potential moves at a very slow speed, we determine the optimization region and the positive work condition of the heat engine model. Furthermore, we generalize the results to the performance optimization for a two-state heat engine with a one-dimensional power-law potential. Based on the generalized model with an arbitrary one-dimensional potential, we obtain the expression of efficiency as η=1-E(C)/E(H), with E(H) (E(C)) denoting the expectation value of the system Hamiltonian along the isoenergetic process at high (low) energy. This expression is an analog of the classical thermodynamical result of Carnot, η(c)=1-T(C)/T(H), with T(H) (T(C)) being the temperature along the isothermal process at high (low) temperature. We prove that under the same conditions, the efficiency η=1-E(C)/E(H) is bounded from above the Carnot efficiency, η(c)=1-T(C)/T(H), and even quantum dynamics is reversible.

Homodyne estimation of quantum state purity by exploiting the covariant uncertainty relation

We experimentally verify the uncertainty relations for the mixed states in tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of a single-mode radiation field are discussed in detail as a paradigm of the mixed quantum state. On considering the connection between generalized uncertainty relations and optical tomograms, it is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critically on the purity of the information carrier states. In this context, the homodyne detector becomes an easy-to-handle purity-meter for the state on line with a running quantum information protocol.

A progressive diagonalization scheme for the Rabi Hamiltonian

A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.

Entropic uncertainty in two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier

The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.

Effect of cavity dissipation on the emission spectrum of an atom interacting with a field in the dispersive approximation

The emission spectrum of a two-level atom interacting dispersively with a single mode radiation field in the dissipative cavity is investigated. A general expression for the emission spectrum is derived. The numerical results for the initial field in coherent state are calculated. It is found that the spectrum structure is influenced significantly by the cavity damping constant κ, and the spectrum structure is dependent on the interaction time T when the cavity dissipation is present. Only one peak located at ωa appears in the atomic spectra for larger T.

Interaction of a Two-Level Atom with the Morse Potential in the Framework of Jaynes–Cummings Model

A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes–Cummings model (JCM) is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.

New classes of nonlinear vector coherent states of generalized spin–orbit Hamiltonians

This paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau–Klauder type associated with generalized spin–orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their ‘dual’ counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S3 sphere has been identified without making use of the annihilation operator.

Quantum thermodynamic cycles and quantum heat engines. II.

We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.

A scheme for amplification and discrimination of photons

A scheme for exploring photon number amplification and discrimination is presented based on the interaction of a large number of two-level atoms with a single-mode radiation field. The fact that the total number of photons and atoms in the excited states is a constant under time evolution in the Dicke model is exploited to rearrange the atom–photon numbers. Three significant predictions emerge from our study: threshold time for initial exposure to photons, time of perception (time of maximum detection probability) and discrimination of first few photon states.

The general velocity and current modulation linear transfer matrix of FEL and control over SASE power in the collective regime

We present the general linear transfer matrix of FEL in the collective regime in terms of a single-mode radiation field amplitude and e-beam current and velocity modulation parameters. The formulation is useful to account for composite configurations of the FEL, including non-radiating sections, and is employed to demonstrate the possibility to control the SASE radiation power (including its substantial reduction for facilitating coherent emission with seed radiation amplification) by varying the space-charge parameter in a drift section.

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes–Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.

Effect of field quantization on Rabi oscillation of equidistant cascade four-level system

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed using a six-parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally, we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.

A Class of Quasi-exact Solutions of RabiHamiltonian

A class of quasi-exactsolutions of the Rabi Hamiltonian, which describes a two-level atominteracting with a single-mode radiation field via a dipoleinteraction without the rotating-wave approximation, are obtained byusing a wavefunction ansatz. Exact solutions for part of thespectrum are obtained when the atom-field coupling strength and thefield frequency satisfy certain relations. As an example, the lowestexact energy level and the corresponding atom-field entanglement atthe quasi-exactly solvable point are calculated and compared toresults from the Jaynes–Cummings and counter-rotating cases of theRabi Hamiltonian.

Wave packet dynamics of entangled two-mode states

We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ‘overlap fidelity’ of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher order squeezing. The power spectra of the time series generated by the mean photon number are presented for initial states corresponding, respectively, to a coherent state and a photon-added coherent state. When the nonlinearity in the Hamiltonian is weak, these show signatures of quasiperiodicity.

Robust generation of entanglement in Bose-Einstein condensates by collective atomic recoil

We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits of {\em high-Q cavity} and {\em bad-cavity}, the latter corresponding to the so-called superradiant regime, both in the quasi-classical and quantum regimes. We found that three-mode entanglement as well as two-mode atom-atom and atom-radiation entanglement is generally robust against losses and decoherence,thus making the present system a good candidate for the experimental observation of entanglement in condensate systems. In particular, steady-state entanglement may be obtained both between atoms with opposite momenta and between atoms and photons.

Radiation to atom quantum mapping by collective recoil in a Bose–Einstein condensate

We propose a scheme to realize radiation to atom continuous variable quantum mapping, i.e., to teleport the quantum state of a single mode radiation field onto the collective state of atoms with a given momentum out of a Bose–Einstein condensate. The atoms-radiation entanglement needed for the teleportation protocol is established through the interaction of a single mode with the condensate in the presence of a strong far off-resonant pump laser, whereas the coherent atomic displacement is obtained by the same interaction with the radiation in a classical coherent field.