Oscillations of the photon echo intensity in a pulsed magnetic field: Zeeman splitting in LiLuF<Subscript>4</Subscript>:Er<Superscript>3+</Superscript>

A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF₄:Er³⁺ and LiYF₄:Er³⁺. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ～2 G at a duration of 30 ns. The Zeeman splitting in this field is ～10 MHz, which is much less than the laser spectral width (0.15 Å ～ 9 GHz). The g factor of the ⁴ F _9/2(I) excited state of the Er³⁺ ion in the LiLuF₄ matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.     

Resonant excitation of single-pulse nuclear spin echo in magnetically ordered media

An analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of the spectroscopic transition and non-uniform distribution of the enhancement factor. The signal has been shown to result from superimposing the nuclear magnetic moment oscillations of the same amplitude and phase that arise upon termination of a radio-frequency pulse. The cause for the effective suppression of oscillations of nuclear magnetic moments in the initial phase of the free precession signal has been determined analytically. The single-pulse echo signal amplitude has been found as a function of the external variable magnetic field strength, the exciting pulse duration, the inhomogeneous NMR line broadening, and the distribution width of the enhancement factor. The results have been compared with experimental data observed in a Co₂MnSi ferromagnetic polycrystalline sample. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 387–394, May–June, 2009.     

Single-pulse nuclear echo signals in magnetically ordered media

An analytical expression for the amplitude of a single-pulse nuclear echo signal generated in magnetically ordered materials is obtained taking into account the inhomogeneous broadening of the spectroscopic transition and the inhomogeneous distribution of the gain with an average value of greater than unity. It is shown that, in this signal, summation of the oscillations of nuclear magnetic moments with equal amplitudes and phases occurs at each instant of time. The cause of the effective suppression of the nuclear magnetic moment oscillations in the initial portion of the free precession signal is revealed analytically. The dependence of the amplitude of the one-pulse echo signal on the strength of an external alternating magnetic field, the pulse duration, and the width of the gain distribution is determined. The results obtained are compared with the experimental data for a Co₂MnSi ferromagnetic polycrystalline sample.     

Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF4:Er3+ and YLiF4:Er3+

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF₄:Er³⁺ and YLiF₄:Er³⁺. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment ?? and makes it possible to determine the difference of the g factors of the ground and excited ⁴ F _9/2(I) states of the Er³⁺ ion in the LuLiF₄ the YLiF₄ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.     

Zero-field splittings of NQR spectra for bismuth(III) oxy compounds revealed by quadrupole spin echo envelopes

Local magnetic fields up to 250 G were earlier found by measuring the NQI parameters in bismuth(III) oxy compounds conventionally considered as diamagnets, a strong increase in the ²⁰⁹Bi line intensities being observed in external magnetic fields. An approach based on registration of the quadrupole spin-echo envelopes enabled to reveal small (within an inhomogeneous line broadening) splittings in some other compounds of this type. The modeling of time dependence of the quadrupole spin echo amplitude indicated that modulations of the spin echo envelope in BaBiO₂Cl and Bi₃B₅O₁₂ resulted from weak (≤5 G) local magnetic fields. By using this approach, it was found that an increase in the ²⁰⁹Bi resonance intensity in external magnetic fields is related to an influence of the fields on the nuclear spin-spin relaxation rate for the appropriate compounds.     

Weak magnetic field behavior of photon echo in a LuLiF4:Er3+ crystal

We report the first observation and study of the photon echo in Er³⁺:LuLiF₄. The energy transition is ⁴ I _15/2 → ⁴ F _9/2 (λ = 6536 Å). The density of ErF₃ is 0.025 wt %. The operation temperature is 1.9 K. Measurements were made at low (up to 1200 Oe) and even zero external magnetic fields. We studied the behavior of the photon echo intensity vs. the magnetic field magnitude and direction about the crystal axis C and vs. the laser pulse separation t ₁₂ and observed an exponential growth and then, after a certain plateau, an exponential decrease in the photon echo intensity as a function of magnetic field upon increasing the magnetic field from zero. The parameters describing the exponential growth and decrease are independent of the direction of magnetic field. The value of the magnetic field (～20–200 Oe) at which the echo intensity is maximal and the value of the maximum itself decrease with increasing pulse separation t ₁₂ and the angle Θ between the magnetic field and crystal axis. The echo intensity decreases exponentially with increasing Θ. The parameter describing the exponential decrease is independent of the magnitude of the field. The echo intensity as a function of pulse separation shows exponential decay. The phase relaxation time depends on the magnitude and direction of the magnetic field. T ₂ is equal to 202 ± 16 ns at zero magnetic field. A phenomenological formula is suggested, which qualitatively presents the mentioned dependences, and the polarization properties of the backward photon echo in this crystal are studied. Because the ion of trivalent erbium is an optimum data carrier, the above results show that fine control of the multichannel transfer of processed optical information may be achieved by weak magnetic fields.     

Photon echo in the presence of a magnetic field: New prospects for data accumulation and processing

The possibility for echo signal switching-off and the switching of echo polarization between the ±45° positions is demonstrated for the photon echo (PE) and stimulated photon echo (SPE) generated in Yb vapor at the (6s6p)³ P ₁ ? (6s ²)¹ S ₀ transition by two pulses of the resonant linearly polarized radiation at appropriate experimental parameters in the weak magnetic field limit. The experimental data are in qualitative agreement with the theoretical analysis and the calculations made for the 1 ? 0 transition. The strong magnetic field limit leads to unpolarized PE and SPE signals generated by linearly polarized radiation pulses. The possibility of the generation of a long-lived echo in ytterbium vapor due to the magnetic field induced mixing of the upper working level with the metastable level is discussed. The results can be employed for the optical data storage and processing.     

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl₂. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the ²⁷Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from ¹⁵⁵Gd and ¹⁵⁷Gd nuclei.     

Optical bistability via coherent and incoherent fields in an Er-doped yttrium-aluminum-garnet crystal

We investigated the optical bistability in an Er³⁺-doped yttrium-aluminum-garnet (YAG) crystal inside a unidirectional ring cavity. We find that the intensity and the frequency detuning of the coherent field as well as the rate of incoherent field can affect the optical bistability dramatically, which can be used to manipulate efficiently the threshold intensity and the hysteresis loop. The effect of the cooperation parameter on the OB is also studied.     

Optimum conditions for correlation of the temporal shape of an object pulse with a stimulated photon echo response in inhomogeneous external electric fields

We have studied the information locking effect and the effect of correlation of the shape of an object laser pulse with the shape of a stimulated photon echo response in the presence of external spatially inhomogeneous electric fields. We have shown that, for the transition ³H₄-³P₀ in a LaF₃:Pr³⁺ crystal, one can observe the effect of the correlation of the shape of an object laser pulse with the shape of a stimulated photon echo response and, depending on the scheme of the action of external spatially inhomogeneous electric fields, either the information locking effect or the information destroying effect.     

Ultrasound and vortex oscillations in high-temperature superconductors

An HTSC powder sample with grain (particle) diameter of 20–50 μm placed in a dc magnetic field B ₀ and cooled to a temperature below the superconducting transition temperature was exposed to the radiofrequency (rf) pulsed magnetic field B _∼ (B _∼ ⊥ B ₀) at a carrier frequency of 30.7 MHz. Stable echo signals were recorded which followed different rf-pulse trains. This phenomenon has the following mechanism. The rf magnetic field stimulates fluxoid oscillations on the HTSC grain surface, which are transformed into lattice oscillations through the pinning centers and induce a propagating sound wave. The second-order nonlinearity with respect to the gradient of the crystal lattice deviation from the equilibrium position taken into account in the sound wave equation yields the dependence of the crystal lattice natural frequency on the amplitude and length of the pulses which excite these oscillations. This dependence is responsible for the emergence of echo signals.     

Laser frequency stabilization at 1.5 microns using ultranarrow inhomogeneous absorption profiles in Er:LiYF4

Single-frequency diode lasers have been frequency stabilized to 1.5 kHz Allan deviation over 0.05-50 s integration times, with laser frequency drift reduced to less than 1.4 kHz/min, using the frequency reference provided by an ultranarrow inhomogeneously broadened Er³⁺:⁴I_15/2→⁴I_13/2 optical absorption transition at a vacuum wavelength of 1530.40 nm in a low-strain LiYF₄ crystal. The 130 MHz full-width at half-maximum (FWHM) inhomogeneous line width of this reference transition is the narrowest reported for a solid at 1.5 μm. Strain-induced inhomogeneous broadening was reduced by using the single isotope ⁷Li and by the very similar radii of Er³⁺ and the Y³⁺ ions for which it substitutes. To show the practicability of cryogen-free cooling, this laser stability was obtained with the reference crystal at 5 K; moreover, this performance did not require vibrational isolation of either the laser or crystal frequency reference. Stabilization is feasible up to T=25 K where the Er³⁺ absorption thermally broadens to ∼500 MHz. This stabilized laser system provides a tool for interferometry, high-resolution spectroscopy, real-time optical signal processing based on spatial spectral holography and accumulated photon echoes, secondary frequency standards, and other applications such as quantum information science requiring narrow-band light sources or coherent detection.     

Large refractive index with vanishing absorption in optical fibers

We propose and demonstrate a novel scheme for realizing large refractive index with vanishing absorption in a three-level quantum system consisting of the energy levels of Er³⁺-doped ZrF₄–BaF₂–LaF₃–AlF₃–NaF (ZBLAN) optical fiber. It is found that the refractive index of the probe field can be controlled via the coherent coupling field and incoherent pumping field. The switching from negative refractive index to positive refractive index and manipulation of the value of the index of refraction while maintaining vanishing absorption of the probe field can be achieved via tuning the detuning of the coherent coupling field. Our scheme may provide some new possibility for technological applications in fiber communication.     

De Haas-van Alphen effect in unconventional superconductors

A theory of the de Haas-van Alphen effect in type-II p-wave and D-wave superconductors (the latter corresponds to the B _1g one-dimensional representation of group D _4h ) has been developed. Solutions for the order parameter and density of quasiparticle states near the upper critical field have been calculated. If the curve enclosing the extremal cross section of the Fermi surface in the plane perpendicular to the external magnetic field coincides with the line of nodes of the superconducting order parameter, the effect of the transition to the superconducting state on the amplitude of magnetization oscillations is negligible. If the line of nodes is oriented differently with respect to the applied magnetic field, the de Haas-van Alphen oscillations are suppressed in a manner qualitatively similar to the case of conventional superconductors. Zh. éksp. Teor. Fiz. 113, 2174–2192 (June 1998)     

Coherent transients at dressed levels

Possibilities for the control of the parameters of free-polarization decay (FPD), optical nutation, and photon echo (PE) using the dressing field are studied. Coherent transients are generated with the Stark switching technique and are detected in the radiation of the probe field polarized orthogonally to the dressing field. The evolution-operator technique is employed in the calculations. The experiments are performed at the R(4, 3) transition of the 0 ? 1 v₃ ¹³CH₃F vibrational band with the radiation of a cw CO₂ laser. It is theoretically and experimentally demonstrated that FPD and PE are suppressed upon an increase in the intensity of the dressing field. The observed shapes of the transient FPD and PE signals and their variations with the dressing field intensity are in qualitative agreement with the results of the calculations.     

Optical decoherence times and spectral diffusion in an Er-doped optical fiber measured by two-pulse echoes, stimulated photon echoes, and spectral hole burning

Two-pulse and stimulated photon echoes and spectral hole burning were measured on the transition from the lowest component of the ⁴I_15/2 manifold to the lowest component of ⁴I_13/2 of Er³⁺ in a silicate optical fiber at 1.6 K. The two-pulse echo decays gave decoherence times as long as 230 ns for magnetic fields above 2 T. A large field dependent contribution to the homogeneous line width of >2 MHz was found and interpreted in terms of coupling to magnetic tunneling modes (TLS) in the glass. The stimulated echoes measured at 2 T showed spectral diffusion of 0.8 MHz/decade of time between 0.4 and 500 μs. Spectral diffusion in this high field region is attributed to coupling to elastic TLS modes which have a distribution of flip rates in glasses. Time-resolved spectral hole burning at very low field showed stronger spectral diffusion of 5.7 MHz/decade of time, attributed to coupling to magnetic spin-elastic TLS modes.     

Infrared absorption on impurity excitations near the upper edge of spin-wave band of the antiferromagnet

The dependence of infrared (IR) light absorption on external magnetic field is considered when the impurity level approaches the upper edge of spin-wave band of antiferromagnet. It is explained a strongly nonlinear field dependence and rapid decrease of corresponding line intensity been observed experimentally in Fe_1?cCo_cF₂. Such behaviour is due to existence of some subthreshold range near the band edge and corresponds to the incoherent collective rearrangement (ICR) of the system spectrum.     

Chaotization of the virtual cathode oscillations in the external magnetic field created by a ring magnet

The physical mechanisms leading to the chaotization of the virtual cathode oscillations in a low-voltage vircator system at an increase in the amplitude of the external inhomogeneous magnetic field created by a ring magnet have been studied within a two-dimensional numerical model. It has been established that the chaotization of the virtual cathode oscillations in a strongly inhomogeneous external magnetic field is due to the formation of the secondary electronic structure (electron beam) in the electron flow resulting from the magnetic trap in the outer layers of the electron beam.     

Photon Echo from Localized Excitons in Semiconductor Nanostructures

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.     

Collective rearrangement of spin excitation spectrum of antiferromagnet with magnetic impurities in external magnetic field

Antiferromagnetic resonance (AFMR) in Co_1?cMn_cF₂ (c ～ 10^-4) in the external magnetic field is investigated. It was established that coherent and incoherent rearrangements (CR and ICR) of spectrum in the region of AFMR and impurity lines crossing are possible in the same sample depending on field orientation. Topology of the phase diagram of spin excitation (SE) spectrum in variables c-H is obtained.