Relaxation of a two-level system coupled to a Bose gas with Einstein spectrum

This note contains the exact diagonalisation of the Hamiltonian describing a two-level system coupled to a Bose gas with an Einstein spectrum (Sections II–IV). In Sections VI and VII we calculate the decay in time of different initial situations of the system.     

Time dependence of absorption lineshapes

We study the dependence of the absorption lineshape on the time of interaction with the electromagnetic field, taking into account the finite lifetime of the excited state. We find important deviations from the lorentzian lineshape (broadening of the central peak and oscillatory structures) when the interaction time is comparable with the natural lifetime. Experimental implications are discussed.     

Effects of spatial dispersion on exciton absorption

The exciton absorption is studied in the spatially dispersive case. The energy propagation properties of the medium are used to define an appropriate absorption coefficient. The specific example of PbI₂ is considered in order to display the role of spatial dispersion.     

Two-photon interband transitions in semiconductors in a static magnetic field. Nonlocal effects

Summary It is shown that in the presence of a static magnetic field, the electronic states in the effective-mass approximation are described by a Hamiltonian containing a nonlocal potential. In order to preserve the gauge invariance of the transition rates, the interaction between the electrons and the radiation has to be modified. For ZnS, the transition rate between two particular levels is evaluated by showing a difference of more than one order of magnitude when compared with the transition rate previously calculated. Partially supported by the Italian Research Council (C.N.R.) through G.N.S.M.     

Quantum theory of polaritons with spatial dispersion: Exact solutions

Summary We give the exact solution of the quantum polariton problem with spatial dispersion. The exact polariton eigenstates are obtained in terms of photon and polariton states. For all values ofk a nonlinear contribution of the photon and polarization states is present in the polariton wave function. Two- and three-photon components are explicitly singled out.

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Riassunto Si presentano le soluzioni esatte del problema quantistico del polaritone con dispersione spaziale. Gli autostati polaritonici esatti sono ottenuti come combinazioni di stati fotonici e di stati di polarizzazione. Contributi non lineari di fotoni e di quanti di polarizzazione sono presenti a tutti i valori dik. Componenti a due fotoni e a tre fotoni sono date in forma esplicita.

     

On the Green's function technique for the study of multiphoton transitions in atoms

Summary The Green's function method for implicitly evaluating the sums over intermediate states occurring in the study of multiphoton processes is revisited. Partieular emphasis is given to bound-bound transitions and to the numerical techniques used to implement the method. This is also extended to the important case in which the sum over intermediate states must be performed with respect to an incomplete set. The accuracy of the method is tested against very precise results on atomic hydrogen obtained by direct summation over intermediate states.

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Riassunto Si riesamina il metodo della funzione di Green per calcolare implicitamente le somme di stati intermedi che compaiono nello studio dei processi a molti fotoni. L'enfasi é posta su transizioni discreto-discreto e sulle tecniche numeriche utilizzate. Il metodo é anche esteso al caso in cui si debba sommare su un insieme incompleto di stati intermedi. La precisione del metodo è verificata nel caso dell'idrogeno confrontandone i risultati con quelli otenuti mediante una somma accurata sugli stati intermedi.

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Резюме Заново исследуется метод функций Грина для явного вычисления сумм по промежуточным состояниям, которые появляются при рассмотрении многофотонных процессов. Особое внимание уделяется переходам из связаннного в связанное состояние и использованной вычислительной технике. Предложенный метод также обобщается на важный случай, в котором суммирование по промежуточным состояниям должно быть проведено по неполной системе состояний. Точность предложенного метода проверяется посредством сравнения с точными результатами для атома водорода, полученными прямым суммированием по промежуточным состояниям.

     

Longitudinal-transverse splitting in Wannier excitons and polariton states

Summary In the theory of Wannier excitons, the long-range nonanalytical part of the exchange interaction is usually expressed in terms of the dipole matrix element between Wannier functions. We show that it can be expressed in terms of the dipole matrix element between zone-centre Bloch functions, without any assumption on the localization of Wannier functions. We obtain an expression for the longitudinal-transverse splitting in terms of the dipole matrix element between the crystal ground state and the excition state. This is required in order to prove that the transverse upper polariton is degenerate with the longitudinal exciton in the limitk _ex→0. A new expression for the short-range part of the exchange interaction is also obtained, which is more suitable for microscopic calculations and which is evaluated for the case of CuCl. The resulting exchange parameter isΔ _ex = 12.6 meV, which compares well with the experimental value.

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Riassunto Nella teoria degli eccitoni di Wannier, la parte a lungo raggio e non analitica dell’interazione di scambio è generalmente espressa in termini dell’elemento di matrice di dipolo fra funzioni di Wannier. Noi mostriamo che può invece essere espressa in termini dell’elemento di matrice di dipolo fra funzioni di Bloch al centro della zona di Brillouin, senza assumere che le funzioni di Wannier siano localizzate. Otteniamo quindi un’espressione per lo splitting longitudinale-trasverso in termini dell’elemento di matrice di dipolo fra stato fondamentale del cristallo e stato eccitonico. Ciò è necessario per dimostrare che il polaritone trasverso del ramo superiore è degenere con l’eccitone longitudinale nel limitek _ex→0. Otteniamo inoltre una nuova espressione per la parte a corto raggio dell’interazione di scambio, che è più appropriata per un calcolo microscopico e che calcoliamo nel caso del CuCl. Otteniamo un parametro di scambioΔ _ex = 12.6 meV, in buon accordo col valore sperimentale.

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Резюме В теории экситонов Ваннье дальнодействуйщая неаналитическая часть обменного взаимодействия обычно выражается через дипольный матричный элемент между функциями Ваннье. Мы показываем, что эта часть обменного взаимодействия может быть выражена через дипольный матричный элемент между функциями Б=qlоха без каких-либо предположений о локализации функций Ваннье. Мы получаем выражение для продольно-поперечного расщепления в терминах дипольного матричного элемента между основным состоянием кристалла и экситонным состоянием. Это выражение требуется, чтобы доказать, что поперечный поляритон является вырожденным с продольным экситоном в пределеk _ex→0. Получается новое выражение для короткодействующей части обменного взаимодействия, которое более удобно для микроскопических вычислений и которое оценивается для случая CuCl. Вычисляется обменный параметрΔ _ex = 12.6 мэВ, который хорошо согласуется с экспериментальной величиной.

     

Construction of grating profiles yielding prescribed diffraction efficiencies

We present a numerical iteration procedure for the (re)construction of perfectly conducting gratings that yield prescribed (or measured) diffraction efficiencies. Prior knowledge of the approximate grating profile is not required. The method is not limited to shallow, smooth profiles. We give numerical results for a profile synthesis and a reconstruction problem. We discuss the question of nonuniqueness.     

Open-system theory of photodetection

The transfer of the statistical properties of the electromagnetic field to the detector signal is reinvesti?ated in terms of the Dicke model with coupling of the photosensitive atoms to a reservoir. The interrelated dynamics of the atomic moments and the field moments as well as the photocounting rate for any initial field state are given in terms of not only the field-atom, but also the atom-reservoir, coupling constants.