Mode Of Electromagnetic Field Research Articles

Controlled spontaneous nuclear γ decay: Theory of controlled excited and radioactive nuclei γ decay

A general theory of controlling and changing the spontaneous nuclear \ensuremath{\gamma} decay is proposed. The phenomenon of nuclear decay controlling is a result of the interaction of the excited nucleus with zero-energy electromagnetic modes, which in turn interact with the controlling screen. In the general case the spontaneous decay probability with the presence of adjacent material bodies always differs from the corresponding probability for free space. It is shown for the first time that the decay parameters greatly depend on the sign and magnitude of the radiation shift (radiation correction) of the resonance level position (nuclear analog of the Lamb shift for atom electrons). This shift is determined by processes of nucleus interaction with all zero-energy electromagnetic field modes (the lowest by energy or ground). It was shown that the resonant screen effect in all cases appears to be more significant than for the nonresonant one. The most influence on the nucleus spontaneous decay process will be realized in the case when the modes of the electromagnetic field in the zero-energy state, which interact with the nucleus, occur to be mutually synchronized. For this case the radiative lifetime may be increased by many orders of magnitude.

Quantum-statistical properties of two coupled modes of electromagnetic field

Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components ${q}_{1}$ and ${q}_{2}$ is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.

Probing evanescent modes from near-field optical microscopes:: propagation into anisotropic media

We describe how to probe the amplitude and polarization of the evanescent modes of light emanating from near-field scanning optical microscopes and Bethe–Bouwkamp holes by placing these structures near anisotropic dispersive media. Evanescent modes have different cut-offs for propagation inside the anisotropic medium as a function of the angles made by their wave vectors and the optic axes of the medium. The electromagnetic field mode amplitudes near the tip can be obtained by varying the orientation of the optic axes relative to the tip.

Features of the photon statistics of two coupled electromagnetic field modes under the conditions of strong mode coupling

The probabilities of transitions between the Fock states of two electromagnetic field modes under the influence of coupling between modes of finite duration are investigated. It is shown that the transition probability is a strongly oscillating function of the mode numbers of the photons. Under conditions in which the coupling frequency exceeds the geometric mean of the mode frequencies (strong coupling), large numbers of photons are excited in the mode with the lower frequency. The excitation of a two-dimensional radiation field oscillator and the “red” asymmetry of the transition probabilities can be attributed to instability of the classical two-dimensional oscillator with strong mode coupling.

Squeezing of light by a collection of atoms

We study squeezing in electromagnetic field quadrature components, produced by a collection of A two-level atoms interacting with a single mode of a strong electromagnetic field. We present analytic results both for short and long interaction times. At short times, squeezing grows with the number of atoms for a given initial number of photons. The maximum squeezing which can be achieved in a strong-field case is 66%. At long interaction times, collective effects increase the quadrature fluctuations, compared to the single-atom case. However, for a given number of atoms A, any initial pure atomic state exhibits squeezing when the mean photon number of the initial coherent field satisfies the condition n-bar>(2A${)}^{4}$ . At times close to the first revival, strong squeezing can be achieved for special initial atomic conditions.

Quantum coherence in a dissipative-driven system and the optical Stern-Gerlach experiment

The quantum coherence of a single mode electromagnetic field in a cavity is analysed when a linear pumping is considered together with the damping mechanism of the cavity. An expression for the decoherence time of the field is estimated and it turns out to be independent of the pumping process. An interesting situation occurs in the long time limit when the action of the pumping is shown to induce a finite degree of quantum coherence in the stationary state of the field. For specific values of the parameters involved in the problem this state is very close to a coherent state and is considered in the realization of the optical Stern-Gerlach experiment. Other particular cases are also investigated.

Phase distribution and superstructures on the phase correlation of copropagating electromagnetic fields

Abstract The phase distribution and phase correlation of two initially coherent electromagnetic field modes copropagating through a lossless nonlinear medium are investigated. We show that the number of distinguishable components in the phase distribution depends on the set of nonlinear parameters through a simple relation and that it is connected with the number of entangled field states as well as the number of components that a single field state acquires after propagating through the medium. The phase correlation between the two field modes is shown to exhibit a rich pattern of collapses and revivals, similar to those observed in the quantum inversion of several generalizations of the Jaynes-Cummings model and is related to beats of the various eigenstates of the total Hamiltonian.

CAVITY QUANTUM ELECTRODYNAMICS OF COMPETING ONE AND TWO PHOTON PROCESSES

We consider a new model of cavity quantum electrodynamics consisting of the interaction of a single mode of electromagnetic field with two non-identical two-level atoms undergoing one and two photon transition respectively in an ideal cavity. The exact analytic results for the vacuum Rabi splitting and the dynamical evolution of the model are given.

Probability distributions for the phase difference.

In this work we analyze the quantum phase properties of pairs of electromagnetic field modes. Since phases differing by 2\ensuremath{\pi} are physically indistinguishable, we propose a general procedure to obtain the correct mod(2\ensuremath{\pi}) probability distributions for the phase difference. This allows us to investigate the properties of a number of phase approaches. This procedure provides deeper insight into the quantum nature of the phase difference. We relate this problem to the representation of nonbijective canonical transformations in quantum mechanics. \textcopyright{} 1996 The American Physical Society.

Modulation of the vacuum field in the beam splitter and mirror system

We present modulation of the vacuum field with a single mirror placed close to an unused port of a beam splitter. The electromagnetic field modes of the vacuum fluctuation near the mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence upon the distance from the mirror. If we combine this spatially amplitude-modulated vacuum field mode and a coherent local oscillator with a beam splitter, we may obtain squeezed states of light in a homodyne detection scheme. We show that the amplitude fluctuation of the combined light can be reduced by a factor of\(\sqrt 2 \) below that of the coherent light and the fluctuations of the intensity difference of the two beams can be also reduced.

One-dimensional coherent-state representation on a circle in phase space.

The representation of the states of a single electromagnetic field mode by coherent states of an identical mean number of photons, i.e., the representation on a circle in phase space, is presented. The connection between the circle representation and the analytic representation is given.

Scattering of atoms by light: probing a quantum state and the variance of the phase operator

An experiment is proposed to study the quantum state and the variance of the phase operator by measuring the momentum distribution of the atoms resulting from the interaction of an atomic beam with a single mode electromagnetic field via a two-photon interaction. A comparison of the results with those obtained for a one-photon interaction is made. Advantages in using the two-photon interaction are pointed out.

Quantization of electromagnetic fields in cavities and spontaneous emission.

The normal modes of electromagnetic fields satisfying three different boundary conditions are constructed systematically. For each of these cases, cavity quantization of the electromagnetic fields is carried out explicitly. It is possible, using normal modes, to perform a unitary transformation of the minimal-coupling Hamiltonian of an atom inside the cavity to a multipolar form. It is shown that the boundary condition plays an important role in the transition rates for the spontaneous emission by the atom. Some explicit calculations are carried out for several different boundary conditions. These results become consistent with those for free space in the large-box limit.

Decay of a single mode electromagnetic field inside a cavity in the presence of an even coherent field

An equation of motion for the reduced density matrix, describing the decay of a single mode field inside a cavity in the presence of an even coherent field, has been derived. With the help of this equation, it is predicted that such an even coherent field can play an important role in the enhancement of steady state squeezing for the degenerate parametric oscillator.

Squeezing an harmonic oscillator with a sawtooth pulse

In recent years there has been a marked interest in quantum-system states called squeezed and correlated (in particular, electromagnetic-field modes), differently named in [1-5]. The history of the question and its present status are treated in various surveys and conference proceedings (we mention here only the latest ones [6, 7]). Squeezed states of an harmonic cavity oscillator (which include in the final analysis practically all the physical systems investigated in this connection) are the natural result of parametric excitation. The actual excitation mechanisms can vary. Quantum optics deals most frequently with various nonlinear interactions of several modes in crystals (see, e.g., the articles in [8-10]). Other possible mechanisms, for example, are variation of the boundary conditions in the cavities [11, 12] or collisions [13]. The main features of the phenomenon, however, are best understood and analyzed within the framework of a model of an oscillator with a specified time dependence of the natural frequency. The parametric quantum oscillator problem was first solved by Husimi [14] who devised Gaussian wave packets and an analog of Fock states for an oscillator with a time-dependent frequency, and also found the amplitudes of transitions between energy levels corresponding to a stationary oscillator (albeit only in series form). His results were obtained and generalized in [15-18] by a simpler procedure, based on the method of time dependent operator integrals of motion, an expanded exposition of which can be found in [19]. It turns out that all the quantities indicative of the behavior of a quantum oscillator (transition probabilities, variances, etc.) can be expressed in terms of the trajectory parameters of a corresponding classical oscillator. The explicit forms of classical trajectories are known, however, only for certain special time dependences of the oscillator frequency. It is easy to obtain solutions for a jump change of the frequency [20-22] and also for a delta-function pulsed frequency perturbation [23]. Exact solutions for a frequency that varies exponentially with time were obtained in [24]. Some other dependences of the frequency on the time, which admit of both exact and approximate solutions, were investigated in [6]. The aim of the present article is an examination of the case of a sawtooth time dependence of an oscillator frequency so as to obtain an exact solution. A sawtooth pulse simulates an experimental situation of interest and makes it possible to consider, in limiting cases, both a delta-function excitation and a slow variation of the frequency. For completeness, we shall repeat in the next section the approach based on the method of timedependent integrals of motion [15-19]. In Sec. 3 we solve the classical equations of motion for a parametric oscillator with a sawtooth time dependence of the frequency, in a form convenient for finding the transition amplitudes of a quantum oscillator. In Sec. 4 we find in explicit form, in the framework of the approach developed in [15:19], the transition amplitudes in the case of a sawtooth pulse. In Sec. 5. we investigate the excitation of an oscillator from an initial thermal-equilibrium state. The analysis of the results is presented in Sec. 6.

Conceptions of quantum optical phase

Much confusion has resulted from the failure to recognise the different concepts embodied in the single word "phase" as applied to a quantized electromagnetic field mode. In this paper we describe three conceptions of phase and the connections between them.

CAVITY QUANTUM ELECTRODYNAMICS AT OPTICAL FREQUENCIES

Quantum electrodynamics (QED) tells us that the electromagnetic field is, on a mode-by-mode basis, quantized according to the harmonic oscillator model. Each mode is ascribed a lowest energy (or dark) state possessing one half quanta of non-removable energy plus an infinite ladder of equally spaced excited states accessed through the addition or removal of energy quanta from the mode. In the optical regime and under normal thermal conditions, electromagnetic field modes are typically in their dark state. Nevertheless, a residual dark-state atom-field coupling remains, and it is this coupling that mediates shifts and spontaneous radiative decay of atomic states. The experimental reality of dark-state atom-field coupling is frequently interpreted as proof of the quantum description of light.

Trapping states in a three-level Λ system

We study the temporal evolution and the stationary regime of an electromagnetic-field mode interacting with three-level \ensuremath{\Lambda}-type atoms in a lossless microwave cavity. We find that under certain conditions the field evolves to the recently defined tangent or cotangent states [J. J. Slosser and P. Meystre, Phys. Rev. A 41, 3867 (1990)]. In particular, in this system number states can be generated for any value of the atomic-upper-level population. In addition, a strong squeezing in the quadrature fluctuations is found.

Interaction of a charged harmonic oscillator with a single quantized electromagnetic field mode.

The interaction of an atomic system with a single mode of a quantized electromagnetic field is investigated in the dipole approximation. Two approximations that are almost always made in this analysis are the neglect of the diamagnetic term in the Hamiltonian and the dropping of the rotating-wave approximation (RWA) terms that correspond to processes that do not conserve energy. Both approximations involve the neglect of terms that are of the same order of magnitude so that consistency demands that they be considered together. It is demonstrated that, in the dipole approximation, a minor modification of the usual application of quantum electrodynamics to any atomic system can exactly incorporate the effects of the diamagnetic term into a new frequency of the electromagnetic cavity mode; this frequency is slightly different from that of the empty cavity. This result is then applied to the specific case of a charged harmonic oscillator interacting with a single mode. For this simple model an analytic solution can then be found that includes the effects of the diamagnetic term and does not use the RWA. It is found that, for off resonance, the normal modes of the coupled system oscillate at shifted frequencies which are in agreement with the second-order perturbation-theory calculation of the Lamb shift. When the cavity mode is tuned to the atomic oscillator frequency, the perturbation-theory Lamb-shift calculation is no longer valid, and the exact solution derived in this paper predicts a resonant Lamb shift that is significantly larger than the off-resonant single-mode Lamb shift. Furthermore, the frequency spectrum is qualitatively changed from the single frequency of the free atomic system to a doublet spectrum. An analytic solution of this harmonic-oscillator problem can also be found when the RWA terms are dropped from the Hamiltonian. Comparison of the two solutions reveals that the RWA terms contribute a frequency shift of magnitude independent of the field intensity in the simple case of a charged harmonic oscillator.When trajectories of the exact and RWA solutions are compared in phase space, it is found that one effect of the RWA terms is to lift a twofold degeneracy of the phase-space orbits that occurs when the RWA terms are neglected. The harmonic-oscillator problem has several features in common with the interaction of a two-level atom with a single quantized field mode. Both Hamiltonians exhibit inversion symmetry and hence have parity as a good quantum number. Both Hamiltonians contain RWA terms. When these RWA terms are neglected, both Hamiltonians have a new constant of motion that can be identified with the total number of excitations in the combined system.

Quantum Effects in the Interaction of an Anharmonic Oscillator with Binomial and Squeezed Coherent Fields

Abstract We show that a single mode of an electromagnetic field in the binomial state or in the squeezed coherent state, propagating in a non-absorbing nonlinear medium modelled as an anharmonic oscillator, gives rise to interesting quantum effects such as collapses and revivals in the energy exchange between the field and the medium. Analytic expressions are obtained for the energy exchange variable. We have exploited the characteristics of the binomial state which provides a means of systematic study of the collapses and revivals with variation in the field statistics from Poissonian to sub-Poissonian. Effects of variation in initial squeezing in the field are also included.