Long-lived state of a helium-like magnesium donor in silicon
R. Kh. Zhukavin, D. A. Postnov, P. A. Bushuikin, K. E. Kudryavtsev, K. A. Kovalevsky, V. V. Tsyplenkov, N. A. Bekin, A. N. Lodygin, L. M. Portsel, V. B. Shuman, Yu. A. Astrov, N. V. Abrosimov, V. N. Shastin
physics.opticscond-mat.mes-hallquant-phSubmitted Jan 8, 2026• Announced Jan 9, 2026
The relaxation of ortho states of a helium-like Mg donor in silicon is investigated by measuring the modulation of background radiation transmission through impurity centers under pulsed photoexcitation. Long-lived states of the spin-triplet 1s(3T2) group with a lifetime of about 20 ms are observed. The temperature dependence indicates that the relaxation is governed by the Orbach mechanism with an activation energy ~13 meV, which is close to the exchange splitting energy of the excited 1s states of the Mg donor.
The relaxation of ortho states of a helium-like Mg donor in silicon is investigated by measuring the modulation of background radiation transmission through impurity centers under pulsed photoexcitation. Long-lived states of the spin-triplet 1s(3T2) group with a lifetime of about 20 ms are observed. The temperature dependence indicates that the relaxation is governed by the Orbach mechanism with an activation energy ~13 meV, which is close to the exchange splitting energy of the excited 1s states of the Mg donor.
Abstract The results of experiments aimed at the observation of split 1s states in Mg-doped Si are reported. From the results, it is possible to determine the chemical shift and exchange interaction energy of a neutral Mg donor in Si. The position of the 1s(E), 1s(T2), and 2s(A1) parastates determines the possibility for attaining population inversion and the specific mechanism of stimulated Raman scattering. The energy of the 1s(T2) parastate is determined from the position of the Fano resonances in the photoconductivity spectrum of Si:Mg at T = 4 K, and the energies of the 1s(T2) and 1s(E) orthostates from the transmittance spectra at elevated temperatures. On the basis of the experimental data, the relaxation rates are estimated, and the possible mechanisms of stimulated emission are analyzed.
AbstractThe results of experiments aimed at the observation of split 1 s states in Mg-doped Si are reported. From the results, it is possible to determine the chemical shift and exchange interaction energy of a neutral Mg donor in Si. The position of the 1 s ( E ), 1 s ( T _2), and 2 s ( A _1) parastates determines the possibility for attaining population inversion and the specific mechanism of stimulated Raman scattering. The energy of the 1 s ( T _2) parastate is determined from the position of the Fano resonances in the photoconductivity spectrum of Si:Mg at T = 4 K, and the energies of the 1 s ( T _2) and 1 s ( E ) orthostates from the transmittance spectra at elevated temperatures. On the basis of the experimental data, the relaxation rates are estimated, and the possible mechanisms of stimulated emission are analyzed.
The negatively charged nitrogen vacancy ($\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$) defect in diamond serves as a popular platform for manipulating and exploiting long-lived coherent spin dynamics at room temperature combined with optical readout. The required spin polarization of the spin triplet 3A2 electronic ground state occurs through a cycle of repetitious optical photoexcitation events to the 3E electronic excited state that is accompanied by a series of electronic transitions to a 1A1 and a 1E electronic state, and back to the 3A2 state. The timescales of these transitions are largely known, yet for the relaxation time of the $^{1}A_{1}\ensuremath{\rightarrow}^{1}E$ infrared transition, which predominantly occurs via nonradiative recombination, only an upper limit of 1 ns could be determined so far. Here, we employ ultrafast transient absorption spectroscopy to probe the dynamics of the nonradiative relaxation from the 1A1 to the 1E state after photoexcitation of the 3E state and find a relaxation time of 100 ps at a temperature of 78 K.
Abstract The relaxation rates of lower excited states 1s(T), 2p0, 2s, 3p0, and 2p± of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between 2p states and the 1s triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO2 laser radiation in the medium at a donor concentration of 2 × 1015 cm–3 is ~0.35 cm–1 at a frequency of 1.98 THz if the laser transition is 2p± → 1s(T) and 1.25 THz if the laser transition is 2p0 → 1s(T).
In this thesis the reasons for pursuing an optically addressable quantum object
in silicon are outlined before introducing some possible technological applications.
Chalcogen donor electron systems in silicon are then discussed as a candidate for
these quantum technologies. The chalcogen donor complexes in silicon allow the
solid-state analogues of hydrogen and helium to be studied. The time-resolved
Fourier transform technique was employed to measure the photoluminescence from
a selenium doped silicon sample when pumped above band gap at the temperatures
10 K, 80 K and 300 K. The excited state lifetime of the 2p0 state was found to
be 28.2 ns for atomic centres and 66.4 ns for molecular centres at 10 K. The lifetimes
were seen to be similar across large emission bands indicating a rate limiting
step. A multi-colour pump-probe experiment, using time-resolved Fourier transform
spectroscopy, was performed at the FELIX institute to determine the excited state
lifetimes of the 2p0 and 1s(T2) to be <2.5 ns and 10.62 ns respectively. A system of 5
coupled rate equations was then implemented to verify the experimental results. The
lifetimes were theoretically determined from three sets of initial conditions. Carriers
were initially positioned in the conduction band, modelling the photoluminescence
experiment, the 2p and 1s states, imitating the FELIX experiment. The 2p state
was shown to have two decay lifetimes, one 15.1 ps and the second of 7.24 ns. The
first fast decay is due to the pure 2p state relaxation while the second long lifetime is
a result of the 1s(T2) state in
uencing the 2p excited state lifetime. The 1s(T2) excited
state lifetime that back-fills the 2p state elongates the 2p excited state lifetime,
causing the lifetime to appear longer than the true lifetime. This research implies
that silicon has the potential to be an accessible test bed for quantum experiments
by showing that it could be possible to create isolated non-interacting donor centres
that are individually optically addressable by mid-IR laser light.
One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr–Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus- and arsenic-doped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times—key to many well known schemes for quantum computing qubits—for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.