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arXiv:2512.24142

Photon Echo in Uniaxially Stressed Germanium with Antimony Donors

R. Kh. Zhukavin, V. D. Kukotenko, P. A. Bushuykin, Yu. Yu. Choporova, N. D. Osintseva, K. A. Kovalevsky, V. V. Tsyplenkov, V. V. Gerasimov, N. Dessmann, N. V. Abrosimov, V. N. Shastin

physics.opticscond-mat.mes-hallquant-phSubmitted Dec 30, 2025• Announced Dec 31, 2025• 0 citations
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Abstract

Photon echo is observed in n-type Ge uniaxially stressed along the [111] crystallographic direction, with a coherence relaxation time of 300 ps. The nonlinear polarization responsible for the effect originates from antimony donors. Uniaxial stress induces valley splitting of the donor states, substantially enhancing the coherence time and enabling the observation of photon echo.

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7 pages, 3 figures

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Physical review. B, Condensed matter•Jan 15, 1998•13 citations
Photon echo is observed in n-type Ge uniaxially stressed along the [111] crystallographic direction, with a coherence relaxation time of 300 ps. The nonlinear polarization responsible for the effect originates from antimony donors. Uniaxial stress induces valley splitting of the donor states, substantially enhancing the coherence time and enabling the observation of photon echo.
A theoretical study was made of the conditions for observing the photon echo effect in a germanium crystal doped with shallow donors. A numerical calculation of the medium polarization excited by a sequence of two optical pulses at a frequency close to the impurity transition frequency has been made. The effect of excitation pulse parameters, such as the pulse duration, the inhomogeneous broadening of impurity transitions and the relaxation rate of population and coherence in the system on the echo is considered. The key aspect in the experimental implementation of the effect is the control of the crystal temperature under photoexcitation, since the rate of coherence relaxation in the system strongly depends on the temperature of the crystal lattice. Keywords: germanium, shallow donors, coherent effects, photon echo.
A theoretical study was made of the conditions for observing the photon echo effect in a germanium crystal doped with shallow donors. A numerical calculation of the medium polarization excited by a sequence of two optical pulses at a frequency close to the impurity transition frequency has been made. The effect of excitation pulse parameters, such as the pulse duration, the inhomogeneous broadening of impurity transitions and the relaxation rate of population and coherence in the system on the echo is considered. The key aspect in the experimental implementation of the effect is the control of the crystal temperature under photoexcitation, since the rate of coherence relaxation in the system strongly depends on the temperature of the crystal lattice.
The phase relaxation of optically excited electronic states can be studied in fourwave mixing experiments where three excitation pulses at t = 0, t =t21, and t = T, respectively, interact via the third-order polarization of the medium to generate a nonlinear signal whose intensity depends on the dephasing time T2. For inhomogeneously broadened optical transitions the signal will be emitted as a time delayed photon echo pulse at t = T + t21 provided the pulse duration is short compared with T2. The echo amplitude decays as exp(−4t21/T2).1
The nonlinear coherent emission of excitons in CuBr quantum dots was investigated using a phase-stabilized photon-echo technique. The echo signal was observed to be quite strong, with the emission efficiency being three orders of magnitude larger than that of II-VI semiconductor quantum wells. Time resolving of the echo signal confirmed that the strong nonlinear emission originates from the accumulation effect of the population grating due to the presence of the bottleneck state. Formation and decay kinetics of the population grating was analyzed by taking into account the light-induced deexcitation effect.