E.I. Nizamova*, L.A. Nefediev**, G.A. Gilmanova***
Kazan Federal University, Kazan, 420008 Russia
E-mail: *enizamova@yandex.ru, **nefediev@yandex.ru, ***gulfina.gilmanova2014@yandex.ru
Received October 5, 2017
Abstract
The increasing interest in the study of the interaction of several resonant fields with multilevel quantum systems is due to a wide range of possible applications of various effects observed in the multi-frequency excitation of quantum objects. Among them, we can note color echo holography, information compression in three-level environments, copying of quantum information, and multi-level quantum gates that perform logical operations. In addition, the recording and reproduction of echo holograms in multi-level systems leads to the possibility, along with logical operations, to perform a change in the real-time scale and the sequence of events in the echo-hologram response, the data on which were embedded into the temporal structure of the object laser pulse. The formation of optical transient processes in multilevel systems occurs when the short laser pulses separated in time and resonant of different frequency transitions at the substance have an effect on the system, so that their interaction with each other becomes possible only through the medium and only if the medium has a sufficiently long phase memory. In this situation, each laser pulse transmits information about its wave characteristics to the medium, and this information is retained here until the arrival of the next laser pulses. The formation of optical transient processes in a multilevel system in a solid depends essentially on the degree of correlation of the inhomogeneous broadening on different frequency transitions and different time intervals, in connection with the possible destruction of the reversible phase memory of the system due to a partial mutual fixation energies of transitions. The influence of external spatially inhomogeneous electric fields on the resonant medium can l ead to an additional artificially created inhomogeneous broadening. In this case, it is possible to control the phase memory of the system by changing the parameters of external spatially inhomogeneous electric fields, and the most pronounced effect on phase memory is the case of laser excitation of narrow frequency regions of inhomogeneously broadened lines of the resonance transitions. Moreover, the artificially created inhomogeneous broadening by external spatially inhomogeneous electric fields due to the Stark effect can be comparable with the spread of frequencies due to a partial mutual fixation of the transition energies, which leads to a partial restoration of the coherence of the multilevel system. This effect can lead to an increase in the intensity of the response of the stimulated photon echo (SPE) in the three-level system, which is the opposite effect of photon echo locking.
Keywords: stimulated photon echo, three-level system, inhomogeneous broadening, phase memory
Figure Captions
Fig. 1. The dependence of SPE response formed in the three-level system on the electric field gradient applied to the sample in the time interval between the third excitation pulse and the expected time of SPE response occurrence. σ' = 0.1 ns-1, Γ = 1.26, k = 0.1, sample size L = 0.1 m, inhomogeneously broadened line width at the 1–2 transition σ' = 5 ns-1, CS = 100 kHz/(V/cm), C'S = 100 kHz/(V/cm), |∇E1| = 0 V/cm2, τ12 = τ23 = 50 ns.
Fig. 2. The scheme showing the influence of external spatially inhomogeneous electric field on the system of three-level optical centers after the third scanning pulse.
Fig. 3. The scheme showing the interaction of two gradients of external spatially inhomogeneous electric field on the system of three-level optical centers.
Fig. 4. The dependence of the SPE response intensity formed in the three-level system on the gradients of electric fields applied to the sample in the time intervals between the first and second excitation pulse and the expected time of SPE response occurrence. σ' = 0.1 ns-1, Γ = 1.26, k = 0.1, sample size L = 0.1 m, inhomogeneously broadened line width at the 1–2 transition σ = 5 ns-1, CS = 100 kHz/(V/cm), C'S = 100 kHz/(V/cm), |∇E1| = 0 V/cm2, τ12 = τ23 = 50 ns.
References
1. Nefediev L.A., Samartsev V.V. Colored echo-holography. Opt. Spektrosk., 1987, vol. 62, no. 3, pp. 701–703. (In Russian)
2. Nefediev L.A., Samartsev V.V. The dynamic echo-hologram transformation in the three-level systems. Phys. Status Solidi A, 1985, vol. 88, pp. 631–635. doi: 10.1002/pssa.2210880229.
3. Nefed'ev L.A., Nizamova E.I., Taktaeva S.V. The effect of uncorrelatedness of inhomogeneous broadening on the formation of transient optical processes in multilevel systems. Opt. Spectrosc., 2012, vol. 113, no. 2, pp. 135–140. doi: 10.1134/S0030400X12080115.
4. Nefediev L.A., Sakhbieva A.R., Nizamova E.I. Determination of optimum conditions for reproducing information in optical echo processors. J. Russ. Laser Res., 2013, vol. 34, no. 4, pp. 331–335. doi: 10.1007/s10946-013-9358-3.
5. Nefediev L.A., Nizamova E.I. Formation of stimulated photon echo in three-level systems and recovery of phase memory by external spatially inhomogeneous electric fields. J. Appl. Spectrosc., 2014, vol. 81, no. 4, pp. 607–610. doi: 10.1007/s10812-014-9977-7.
6. Nefediev L.A., Nizamova E.I. Conditions for using stimulated photon echo to record and reproduce information in three-level systems. J. Appl. Spectrosc., 2016, vol. 82, no. 6, pp. 936–940. doi: 10.1007/s10812-016-0208-2.
7. Nefediev L.A., Garnaeva G.I., Nizamova E.I. Coherence restoring effect in the three-level system by spatially inhomogeneous electric field. Int. J. Adv. Res. Phys. Sci., 2016, vol. 3, no. 3, pp. 9–14.
8. Nizamova E.I., Nefediev L.A., Garnaeva G.I. The effect of coherence recovery in the three-level system by spatially inhomogeneous electric field. In: Salakhov M.Kh. (Ed.) Kogerentnaya optika i opticheskaya spektrosopiya: Sb. statei [Coherent Optics and Optical Spectroscopy: Collection of Papers]. Kazan, Izd. Kazan. Univ., 2016, pp. 122–126. (In Russian)
9. Chen Y.C., Chiang K.P., Hartmann S.R. Photon echo relaxation in LaF3:Pr3+. Opt. Commun., 1978, vol. 29, no. 2, pp. 181–185. doi: 10.1016/0030-4018(79)90012-9.
10. Chen Y.C., Chiang K.P., Hartmann S.R. Spectroscopic and relaxation character of the 3P0–3H4 transition in LaF3:Pr3+ by photon echoes. Phys. Rev. B, 1980, vol. 21, no. 1, pp. 40–47.
For citation: Nizamova E.I., Nefediev L.A., Gilmanova G.A. Phase memory of the three-level system in the presence of external spatially inhomogeneous electric fields. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 1, pp. 100–107. (In Russian)
The content is available under the license Creative Commons Attribution 4.0 License.