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ACS Photonics

2D Time-Domain Spectroscopy for Determination of Energy and Momentum Relaxation Rates of Hydrogen-Like Donor States in Germanium

T. B. Gill, Sergei G. Pavlov, C. Kidd, Paul Dean, Andrew D. Burnett, Aniela Dunn, Lianhe H. Li, Nikolay V. Abrosimov, Heinz‐Wilhelm Hübers, E. H. Linfield, Alexander Giles Davies, Joshua R. Freeman

Published Mar 27, 2024• 1 citation
Publisher

Abstract

High Resolution Image Download MS PowerPoint Slide We present measurements of the coherence times of excited states of hydrogen-like arsenic impurities in germanium (Ge:As) using a table-top two-dimensional time-domain spectroscopy (2D-TDS) system. We show that this laboratory system is capable of resolving the coherence lifetimes of atomic-like excited levels of impurity centers in semiconductors, such as those used in solid-state quantum information technologies, on a subpicosecond time scale. By fitting the coherent nonlinear response of the system with the known intracenter transition frequencies, we are able to monitor coherent population transfer and decay of the transitions from the 2p 0 and 2p ± states for different low excitation pulse fields. Furthermore, by examining the off-diagonal resonances in the 2D frequency-domain map, we are able to identify coherences between excited electronic states that are not visible via conventional single-frequency pump–probe or Hahn-echo measurements.

DOI
10.1021/acsphotonics.3c01522

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Two-Dimensional Time-Domain Spectroscopy for Determination of Energy and Momentum Relaxation Rates of Hydrogen-Like Donor States in Germanium

Th. B. Gill, Pavlov, Sergey, C. S. Kidd +9 more

We present measurements of coherence times of excited states of hydrogen-like arsenic impurities in germanium (Ge:As) using a table-top 2D-TDS system. We observe coherent population transfer and decay of transitions from the 2p0 and 2p± states by fitting the detected coherent nonlinear response with the known intracenter transition frequencies. Coherences between excited electronic states that are not visible via conventional single frequency pump-probe measurements are also observed in the off-diagonal resonances in the 2D frequency-domain map.

•Jan 1, 2024•0 citations

On the Intracenter Relaxation of Shallow Arsenic Donors in Stressed Germanium. Population Inversion under Optical Excitation

Veniamin V. Tsyplenkov, V. N. Shastin

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).

Semiconductors•Nov 7, 2018•12 citations

Quantum control in silicon using coherent THz pulses

Stephen A. Lynch, P. Thornton Greenland, Alexander F. G. van der Meer +5 more

It has long been known that shallow donors such as phosphorous and the other group-V elements, have a hydrogen-like optical spectrum. The main difference is that while the spectrum of atomic hydrogen lies in the visible band, the spectrum of shallow donors in silicon is downshifted to the THz frequency band. This is a direct consequence of the reduced Coulomb attraction seen by the loosely bound electron because the core electrons shield the positive donor atom nucleus, and because the electron is now moving in a dielectric material. While spectroscopy has already revealed much about the energy level structure, very little was known about the temporal dynamics of the system until now. We have used THz pulses from the FELIX free electron laser to probe these hydrogen-like levels. By exploiting the well-known pump-probe technique we have measured the characteristic lifetimes of the excited Rydberg states and found them to be of the order 200 ps. Then, by making subtle changes to the geometry of the pump-probe experimental setup we demonstrate the existence of a THz photon echo. The photon echo is a purely quantum phenomenon with no classical analogue, and it allows us to study the quantum state of the donor electron. We then show, using the photon echo, that it is possible to create a coherent superposition of the ground and excited state of the donor. Measuring the photon echo is important because it can also be used to measure a second important characteristic lifetime of the silicon-donor system, the phase decoherence time.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 15, 2012•0 citations

Silicon as a model ion trap: Time domain measurements of donor Rydberg states

N. Q. Vinh, P. Thornton Greenland, K. L. Litvinenko +9 more

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.

arXiv:0812.0148•Proceedings of the National Academy of Sciences•Jul 28, 2008•76 citations

Modern quantum optics of mid gap chalcogen donors in singlecrystal silicon

William S. Royle

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.

•Sep 29, 2018•0 citations

Electronic coupling and coherences in disordered polymers: Femtosecond 2D-photon echo correlation spectroscopy, signatures of an excitonic two-segmental site system: A theoretical study

Vojtech Szőcs, Tibor Pálszegi, Andreas Tortschanoff +1 more

The two-dimensional (2D) temporal shape of the (degenerate) three-pulse photon-echo (3-PPE) polarization P(3)(t′,τ12,τ23=0) has been theoretically analyzed for a weakly interacting two-site system (TSS) in the presence of site inhomogeneous broadening. The TSS has been modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site-representation (i.e., two S0 and S1 states forming a 4-level system). The 2D time-domain signal S(t′,τ12,τ23=0) has been derived in a closed-form solution which allowed to formulate the analytical Fourier transform analog under sequential δ-pulse excitation. The resulting 2D PE signal in frequency–frequency space S(ωt′,ωτ12) is formed in the region of the resonant, optical carrier frequency by, generally, four peaks, arranged at the edges of a square with distances determined by the excitonic coupling. The two diagonal peaks are of one-exciton origin, while the two off-diagonal (cross) peaks involve two-exciton effects, too. The relative heights of the four peaks are in distinct relation with the mutual orientation of the site-localized transition dipoles, thus these 2D line shapes serving as a structural probe for resonantly interacting molecules. The shapes of the peaks reflect the ratio between homogeneous and inhomogeneous dephasings and can be used for structural studies of statically disordered systems of TSS. The semiclassical two-site model is intended to provide a preparatory platform for mimicking electronically coupled segmental pairs dispersed in energy and space along the strongly disordered main chain contour. The results of the model calculation are taken to discuss the potential and the limitations of 2D line shape echo-spectroscopy in the study of short-range coherences and electronic coupling in π-conjugated polymers.

The Journal of Chemical Physics•May 8, 2002•12 citations
High Resolution Image Download MS PowerPoint Slide We present measurements of the coherence times of excited states of hydrogen-like arsenic impurities in germanium (Ge:As) using a table-top two-dimensional time-domain spectroscopy (2D-TDS) system. We show that this laboratory system is capable of resolving the coherence lifetimes of atomic-like excited levels of impurity centers in semiconductors, such as those used in solid-state quantum information technologies, on a subpicosecond time scale. By fitting the coherent nonlinear response of the system with the known intracenter transition frequencies, we are able to monitor coherent population transfer and decay of the transitions from the 2p 0 and 2p ± states for different low excitation pulse fields. Furthermore, by examining the off-diagonal resonances in the 2D frequency-domain map, we are able to identify coherences between excited electronic states that are not visible via conventional single-frequency pump–probe or Hahn-echo measurements.
We present measurements of coherence times of excited states of hydrogen-like arsenic impurities in germanium (Ge:As) using a table-top 2D-TDS system. We observe coherent population transfer and decay of transitions from the 2p0 and 2p± states by fitting the detected coherent nonlinear response with the known intracenter transition frequencies. Coherences between excited electronic states that are not visible via conventional single frequency pump-probe measurements are also observed in the off-diagonal resonances in the 2D frequency-domain map.
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).
It has long been known that shallow donors such as phosphorous and the other group-V elements, have a hydrogen-like optical spectrum. The main difference is that while the spectrum of atomic hydrogen lies in the visible band, the spectrum of shallow donors in silicon is downshifted to the THz frequency band. This is a direct consequence of the reduced Coulomb attraction seen by the loosely bound electron because the core electrons shield the positive donor atom nucleus, and because the electron is now moving in a dielectric material. While spectroscopy has already revealed much about the energy level structure, very little was known about the temporal dynamics of the system until now. We have used THz pulses from the FELIX free electron laser to probe these hydrogen-like levels. By exploiting the well-known pump-probe technique we have measured the characteristic lifetimes of the excited Rydberg states and found them to be of the order 200 ps. Then, by making subtle changes to the geometry of the pump-probe experimental setup we demonstrate the existence of a THz photon echo. The photon echo is a purely quantum phenomenon with no classical analogue, and it allows us to study the quantum state of the donor electron. We then show, using the photon echo, that it is possible to create a coherent superposition of the ground and excited state of the donor. Measuring the photon echo is important because it can also be used to measure a second important characteristic lifetime of the silicon-donor system, the phase decoherence time.
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.
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.
The two-dimensional (2D) temporal shape of the (degenerate) three-pulse photon-echo (3-PPE) polarization P(3)(t′,τ12,τ23=0) has been theoretically analyzed for a weakly interacting two-site system (TSS) in the presence of site inhomogeneous broadening. The TSS has been modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site-representation (i.e., two S0 and S1 states forming a 4-level system). The 2D time-domain signal S(t′,τ12,τ23=0) has been derived in a closed-form solution which allowed to formulate the analytical Fourier transform analog under sequential δ-pulse excitation. The resulting 2D PE signal in frequency–frequency space S(ωt′,ωτ12) is formed in the region of the resonant, optical carrier frequency by, generally, four peaks, arranged at the edges of a square with distances determined by the excitonic coupling. The two diagonal peaks are of one-exciton origin, while the two off-diagonal (cross) peaks involve two-exciton effects, too. The relative heights of the four peaks are in distinct relation with the mutual orientation of the site-localized transition dipoles, thus these 2D line shapes serving as a structural probe for resonantly interacting molecules. The shapes of the peaks reflect the ratio between homogeneous and inhomogeneous dephasings and can be used for structural studies of statically disordered systems of TSS. The semiclassical two-site model is intended to provide a preparatory platform for mimicking electronically coupled segmental pairs dispersed in energy and space along the strongly disordered main chain contour. The results of the model calculation are taken to discuss the potential and the limitations of 2D line shape echo-spectroscopy in the study of short-range coherences and electronic coupling in π-conjugated polymers.