Photon Echo Signal Research Articles

Influence of Coulomb interaction on the photon echo in disordered semiconductors.

The photon-echo signal in disordered semiconductors is treated including the electron-hole Coulomb attraction. The amplitude of the spontaneous photon echo is calculated up to third order in the external-field amplitude using the semiconductor Bloch equations. Several idealized situations are analyzed showing the significance of a critical correlation of the polarization dynamics in the two time intervals preceding and following the second excitation pulse. Strong photon-echo decay is predicted for short-range disorder without Coulomb interaction. The inclusion of electron-hole attraction leads to a stabilization of the echo signal. For the case of long-range disorder with Coulomb interaction, we predict slow decay in the diffusive limit.

Photon-echo Varieties in Three-level Systems Formed by Non-rectangular Exciting Pulses of Arbitrary Area

Abstract A technique for the derivation of the electric field strength of varieties of photon-echo signals formed by exciting pulses with smooth envelopes is developed. This technique is based on joint solution of the d'Alembert and Schrödinger equations. The matrix of the evolution operator is constructed, which permits a description of the state of an individual atom (molecule) resulting from the action of an arbitrary exciting pulse sequence. The special form of exciting pulses with smooth envelope considered here is, together with the model of rectangular exciting pulses, one of the models that permits an analytical solution when the areas of the exciting pulses are not small. As an example, the technique is applied to the calculation of the electric field strength of signals of the modified three-level photon echo and the three-level photon echo formed by exciting pulses with smooth envelopes. The signal characteristics of photon-echo varieties formed by rectangular and non-rectangular exciting pulses are compared. It is shown that if the spectral lines of the resonant transitions are broad then the shapes and the peaks of the echo signals depend essentially on the shapes of the exciting pulses. The appearance of the fine structure of the modified three-level photon-echo and three-level photon-echo signal shapes is predicted. The necessity of setting up experiments aimed at observing the theoretically predicted special features of these photon-echo varieties is pointed out.

On the information storage time with stimulated photon echoes in gases on the [formula omitted] transition

The electric field strength of a stimulated photon echo generated in a gaseous medium on the transition with the electronic total angular momentum change J b= 1 2 →J a= 1 2 is calculated in the case when the spectral width of both exciting pulses greatly exceeds the hyperfine splitting frequencies Δ a and Δ a ( Δ a ⪢ Δ b ) of both the ground a and excited b atomic states. It is known that if the recording pulses have collinear polarization vectors and if the inequality | Δ b τ 1-2 πl| ⪡1 ( l=0,1,...) involving the time in terval τ 1 between them is satisfied the information storage time τ 2 depends on the information restoration time τ 1. The information storage time, instead, is much greater if | Δ a τ 1- π(2 n+1)| ⪡1, than in the case | Δ a τ 1-2 πm| ⪡1 ( n, m = 0, 1, 2,...). This property of a stimulated photon echo signal may be employed for the selection of even (or odd) elements from the pulse trains.

Theory of the phonon perturbed photon echo experiment: Direct determination of electronic excitation–phonon coupling

A theory is presented describing the proposed phonon perturbed photon echo experiment. This experiment is a combination of picosecond time scale stimulated Raman pumping and photon echo experiments. The theory demonstrates that the phonon perturbed photon echo can directly measure electronic excitation–phonon coupling matrix elements by observing the influence of a well defined coherent phonon wave on the photon echo signal. The theory predicts that the echo pulse area (integrated intensity) is reduced. The size of this change is related to the strength of the excitation phonon coupling. In addition, a realistic estimate is made of the size of the effect, and it is shown that the experiment is feasible with available laser equipment.

Optical dynamics of the reaction center of photosystem II. A hole-burning and photon-echo study

Photon-echo and transient hole-burning experiments on the P-band of the reaction center of photosystem II are reported which show that the P-band exhibits a large homogeneous width. A photon-echo signal with a decay time of 500 ps is also observed in the same spectral region and assigned to extraneous chlorophyll. These observations are discussed with reference to the bacterial reaction center and photosystem I.

On the possibility of determination of the orientation relaxation time of the thallium level by means of modified stimulated photon echo

The electric field strength of the modified stimulated photon echo signal formed on the hyperfine structure components of the thallium levels 6 2 P 1 2 (F=1), 6 2 P 3 2 (F=1) and 7 2 S 1 2 (F=0) is calculate. The possibility of determination of the orientation relaxation time of the metastable 2 P 3 2 thallium level with the use obatined theoretical relations is pointed out.

Influence of diffraction on formation of photon echo signals

A theoretical analysis is made of the formation of photon echo signals under one-photon resonance conditions when a medium is excited by light pulses with a finite transverse aperture. Basic equations are formulated and a method of solving these within the limits of perturbation theory using Green's functions is indicated. An analysis is made of some analytic solutions. An expression is derived to describe the spatial profile of the photon echo signal under diffraction conditions.

Photon echoes as a probe for long-range spatial correlations

A microscopic correlation-function expression for the photon-echo signal in systems with long-range spatial correlations is developed. In general, the signal is given by an eight-point correlation function of the dipole operator involving two particles. In the absence of long-range spatial correlations, this correlation function may be factorized into a product of two four-point, single-particle correlation functions. Only under these conditions is the signal proportional to the absolute square of the ensemble-averaged nonlinear polarization. We predict that photon echoes may be used to probe the long-range spatial correlations near critical points.

Study of relaxation processes in a gas with the aid of coherent transient processes

The paper is devoted to the study of two types of coherent transient processes, viz., coherent radiation in time-separated fields (CRSF) and photon echo (PE) in a traveling wave in SF6 gas. Study of CRSF signals produced at instants of time t = T + nT (T is the delay time between the exciting pulses and n is an integer) has made it possible to measure the relaxation rates of the polarization and of the populations in SF6 gas and draw qualitative conclusions concerning the character of the collisions. Damping of PE signals as a function of the delay time is nonlinear in the region of short T and permits measurement of the rates of rotationally inelastic processes, as well as of the contribution of other collisions with small velocity change.

Unified theory of photon echoes: The passage from inhomogeneous to homogeneous line broadening

We calculate the temporal profile of the photon echo signal from a collection of non-interacting two-level systems. whose frequencies undergo Gaussian random modulations. The model is exactly solvable and interpolates continuously between the inhomogeneous broadening limit in which a well-defined echo signal exists and the homogeneous broadening limit in which it is no longer present. The implications for the problem of concentration-dependent dephasing in mixed molecular crystals are discussed.

STUDY OF STIMULATED PHOTON ECHO IN DEGENERATE TWO-LEVEL SYSTEM GENERAL THEARY AND RELAXATION INDUCED STIMULATED PHOTON ECHO

The stimulated photon echo in degenerate two-level system has been studied. The stimulated photon echo signal for different polarization arrangement of incident lights was obtained basing on the third-order perturbation theory, where, the density matrix was expanded in an irreducible spherical-tensor operator. The characteristics of stimulated photon echo were discussed. Taking ja = jb = 1/2 system as example, we have also studied the relaxation induced stimulated photon echo, where, the polarization arrangement of the three incident pulses is σ+→σ+→σ-.

Erratum: “A Note on the Analytical Treatment of a Localized Electron-Phonon System Including the Change of Frequency”

The localized electron-phonon model, which was proposed by Takagahara, Hanamura and Kubo (THK), is extended by including the change of frequency and is treated analytically to obtain the response function and the photon echo signal. Our treatment also gives an analytical expression for the integrand of the transient emission spectrum of the second order optical processes in a localized electron-phonon system which was treated by THK in terms of the eigenvalue problem of the relaxation operator.

A Note on the Analytical Treatment of a Localized Electron-Phonon System Including the Change of Frequency

The localized electron-phonon model, which was proposed by Takagahara, Hanamura and Kubo (THK), is extended by including the change of frequency and is treated analytically to obtain the response function and the photon echo signal. Our treatment also gives an analytical expression for the integrand of the transient emission spectrum of the second order optical processes in a localized electron-phonon system which was treated by THK in terms of the eigenvalue problem of the relaxation operator.

Storage and phase conjugation of light pulses using stimulated photon echoes

We experimentally demonstrate that three-excitation-pulse (i.e., stimulated) photon echo signals can be backward-propagating, phase-conjugate replicas of the second echo-excitation pulse. Working on the 555.6-nm absorption line of atomic Yb vapor, echo signals, effectively 0.5% as intense as the second excitation pulse, are shown to reproduce image information carried by the second excitation pulse even when wave-front distorters are employed.

Storage and time reversal of light pulses using photon echoes

We have studied the temporal profile of photon-echo signals generated by combined gated cw and pulsed dye-laser excitation of the inhomogeneously broadened, 555.6-nm absorption line of (174)Yb vapor. We find that the echo profile is, after time reversal, essentially identical with that of the first excitation pulse. We give a new analysis of this effect. Since time-reversed pulse reproduction should also occur in inhomogeneously broadened solid samples, and since we observe time-reversed reproduced pulses up to 4% as intense as the input pulse, this effect may have important applications in optical signal-processing systems.

Stochastic Theory of Coherent Optical Transients

Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.

Tri-level Echo in the Case of Exciting Pulses with Arbitrary Shapes

In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.

Forced deformation of the reversed three-pulsed photon-echo signal on the ruby R1-line

Forced deformation of the reversed three-pulsed photon-echo signal on the ruby R1-line

Noble-gas broadening of the sodium D lines measured by photon echoes

Noble-gas-induced relaxation of photon echo signals is used to determine the broadening rates of the Na D lines. Since echo signals are 'Doppler free', precision measurements are possible at low perturber-gas pressures (<or=1 Torr), and are sensitive to the previously inaccessible central lineshape. Interestingly, the authors results disagree with other recently published broadening rates. The equivalence of linewidth measurements and echo measurements on transitions between states of low electronic angular momentum is discussed.

Spherical-tensor treatment of coherent transients

I present a spherical-tensor treatment of coherent transient effects induced in atoms by an optical pulse resonant with a dipole transition. The resonant pulse is shown to excite electronic multipole moments in the atom which can be higher than the dipole. The dependence of these moments on the length and intensity of the applied pulse is derived. It is shown that information about the damping of these moments due to thermal collisions is contained in photon-echo signals.