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Zero-phonon line shape in single InAs/GaAs quantum dots

Guillaume Cassabois

Published Apr 12, 2010• 0 citations
OpenAlex

Abstract

In this paper, I will discuss the extrinsic dephasing mechanism of spectral diffusion that dominates the decoherence in semiconductor quantum dots at cryogenic temperature. I will first present the existence of two fluctuation regimes: the slow modulation one where the zero-phonon line in the quantum dot optical spectrum directly reflects the statistical distribution of the quantum dot emission energy, and the fast modulation one, also called motional narrowing regime, where the zero-phonon line is a Lorentzian with a width smaller than the standard deviation of the quantum dot energy. I will then emphasize the unconventional phenomenology of motional narrowing in standard semiconductor quantum dots at low incident power and temperature, that makes the quantum dot emission line a sensitive probe of the extrinsic reservoir fluctuation dynamics [1,2]. I will further show that the text book phenomenology of motional narrowing in nuclear magnetic resonance is recovered in quantum dots embedded in field-effect heterostructure. In that case, the electrical control of the mesoscopic environment of the quantum dot leads to conventional motional narrowing where the motion consists in carrier tunneling out of the defects around the quantum dot [3]. References [1] A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, Nature Phys. 2, 759 (2006). [2] I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, Phys. Rev. B 75, 073308 (2007). [3] A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, R. Ferreira, Ph. Roussignol, J. Skiba-Szymanska, R. Kolodka, A. I. Tartakovskii, M. Hopkinson, and M. S. Skolnick, NewJ. Phys. 11, 093032 (2009).

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Solid-state single photon source is one of the most important applications of single quantum dot-based devices. However, the photo-induced spectral diffusion phenomenon broadens the quantum dot optical spectrum in photoluminescence spectroscopy. This effect originates from the fluctuating electric fields created by carriers in defects or traps in the quantum dot environment. Indeed, a single photon source with a life-time limited line still remains an experimental challenge for quantum cryptography applications. In a previous work, we had shown that the observation of a Lorentzian line broader than the natural linewidth in single quantum dot spectroscopy comes from a non-standard form of motional narrowing for spectral diffusion [1]. In fact the fluctuation dynamics of the quantum dot electrostatic environment is governed by the capture and escape times of carriers in traps or defects located around the quantum dot. Motional narrowing occurs at low temperature and low excitation power in contrast to Nuclear Magnetic Resonance (NMR), because the escape process is much less efficient than the capture one. \vspace{0.5cm} In this paper, we demonstrate the electrical control of the spectral diffusion dynamics for single quantum dots embedded in a Schottky diode structure. Our goal is to reach the standard phenomenology of motional narrowing described in NMR by hastening carrier escape from the traps around the QD through tunnelling under reverse bias voltage. We show that, under increasing reverse bias, the spectral diffusion dynamics changes for the neutral exciton line, and that the lineshape variations are governed by the modifications of the escape time. At 30K, we observe that the linewidth decreases on increasing the reverse bias, thus demonstrating a tunnel-assisted motional narrowing effect. At lower temperatures, we observe a more complex emission spectrum with a doublet structure attributed to an isolated strongly-perturbating trap. The coalescence of the doublet structure when varying gate voltage (or temperature) reveals a motional narrowing phenomenology specific to the Poissonian occupation law of this isolated trap. These data pave the way to a protection of zero-dimensional electronic states from outside coupling through a voltage-controlled motional narrowing effect. [1] A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gerard, Nature Phys. 2, 759 (2006).

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A single spin confined to a semiconductor quantum dot is a system of significant interest for quantum information science, as a potential optically-addressable qubit. In many respects, a quantum dot behaves like a single atom with high quality single photon emission. By controlling the light-matter coupling in such a system, it is possible to generate highly non-classical states of light and coherently control a single spin confined to the quantum dot. A departure from the ideal atomic picture appears once we consider the mesoscopic environment with which the quantum dot interacts. Charge fluctuations in the surroundings of the quantum dot affect the photon emission frequency leading to inhomogeneous broadening. Further broadening of the emission is caused by coupling to phonon modes of the host semiconductor material. Finally, coupling between the spin of a confined electron and a large bath of nuclear spins residing in the quantum dot leads to fast dephasing of the electron spin. All of these effects are typically considered detrimental to the potential use of quantum dots for quantum technologies. In this thesis, we develop the environmental coupling of a negatively charged quantum dot as a resource for quantum optics and spin control. First, the phonon-assisted fluorescence is shown to be a useful independent channel for feedback stabilisation of the quantum dot emission frequency, without requiring a measurement of the indistinguishable zero-phonon line. With stabilisation, the corresponding frequency broadening is drastically improved, and the sub-Hz frequency fluctuations are no longer resolved. Next, we show low-power resonance fluorescence emission spectra of the negatively charged trion transition. In the low power regime of resonance fluorescence, the excited state is not populated and most of the emission is coherent. In addition to elastic Rayleigh scattering, we observe coherent Raman sidebands, linked to an effective magnetic field created by the hyperfine interaction, the Overhauser field. This fluctuating effective field lifts the electron spin degeneracy in the absence of a magnetic field, and dictates the optical selection rules of the trion system. These spectra therefore allow for a measurement of the time-averaged distributions of in-plane and out-of-plane Overhauser field components. In the final part of the thesis, we use this hyperfine-generated Λ -scheme to optically create electron spin superpositions through two-colour excitation and coherent population trapping. We then show that rapid shifts in the relative phase of the lasers lead to initialisation of the electron spin into a rotated dark state.

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In this paper, I will discuss the extrinsic dephasing mechanism of spectral diffusion that dominates the decoherence in semiconductor quantum dots at cryogenic temperature. I will first present the existence of two fluctuation regimes: the slow modulation one where the zero-phonon line in the quantum dot optical spectrum directly reflects the statistical distribution of the quantum dot emission energy, and the fast modulation one, also called motional narrowing regime, where the zero-phonon line is a Lorentzian with a width smaller than the standard deviation of the quantum dot energy. I will then emphasize the unconventional phenomenology of motional narrowing in standard semiconductor quantum dots at low incident power and temperature, that makes the quantum dot emission line a sensitive probe of the extrinsic reservoir fluctuation dynamics [1,2]. I will further show that the text book phenomenology of motional narrowing in nuclear magnetic resonance is recovered in quantum dots embedded in field-effect heterostructure. In that case, the electrical control of the mesoscopic environment of the quantum dot leads to conventional motional narrowing where the motion consists in carrier tunneling out of the defects around the quantum dot [3]. References [1] A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, Nature Phys. 2, 759 (2006). [2] I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, Phys. Rev. B 75, 073308 (2007). [3] A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, R. Ferreira, Ph. Roussignol, J. Skiba-Szymanska, R. Kolodka, A. I. Tartakovskii, M. Hopkinson, and M. S. Skolnick, NewJ. Phys. 11, 093032 (2009).
Solid-state single photon source is one of the most important applications of single quantum dot-based devices. However, the photo-induced spectral diffusion phenomenon broadens the quantum dot optical spectrum in photoluminescence spectroscopy. This effect originates from the fluctuating electric fields created by carriers in defects or traps in the quantum dot environment. Indeed, a single photon source with a life-time limited line still remains an experimental challenge for quantum cryptography applications. In a previous work, we had shown that the observation of a Lorentzian line broader than the natural linewidth in single quantum dot spectroscopy comes from a non-standard form of motional narrowing for spectral diffusion [1]. In fact the fluctuation dynamics of the quantum dot electrostatic environment is governed by the capture and escape times of carriers in traps or defects located around the quantum dot. Motional narrowing occurs at low temperature and low excitation power in contrast to Nuclear Magnetic Resonance (NMR), because the escape process is much less efficient than the capture one. \vspace{0.5cm} In this paper, we demonstrate the electrical control of the spectral diffusion dynamics for single quantum dots embedded in a Schottky diode structure. Our goal is to reach the standard phenomenology of motional narrowing described in NMR by hastening carrier escape from the traps around the QD through tunnelling under reverse bias voltage. We show that, under increasing reverse bias, the spectral diffusion dynamics changes for the neutral exciton line, and that the lineshape variations are governed by the modifications of the escape time. At 30K, we observe that the linewidth decreases on increasing the reverse bias, thus demonstrating a tunnel-assisted motional narrowing effect. At lower temperatures, we observe a more complex emission spectrum with a doublet structure attributed to an isolated strongly-perturbating trap. The coalescence of the doublet structure when varying gate voltage (or temperature) reveals a motional narrowing phenomenology specific to the Poissonian occupation law of this isolated trap. These data pave the way to a protection of zero-dimensional electronic states from outside coupling through a voltage-controlled motional narrowing effect. [1] A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gerard, Nature Phys. 2, 759 (2006).
Single quantum dot optical spectroscopy has routinely been implemented in photoluminescence experiments for the last ten years. More recently photocurrent[1] and transmission [2] experiments have shown that the resonant excitation of a single quantum dot (QD) strongly decreases the broadening due to photo-induced spectral diffusion in photoluminescence spectra. However in the context of quantum cryptography applications, a single photon source with a life-time limited line still remains an experimental challenge under non-resonant excitation.In a previous work, we had shown that the observation of a Lorentzian line broader than the natural linewidth comes from a non-standard form of motional narrowing for spectral diffusion[3]. In fact the fluctuation dynamics of the quantum dot electrostatic environment is governed by the capture and escape times of carriers in traps or defects located around the QD.Motional narrowing occurs at low temperature and low excitation power in contrast to Nuclear Magetic Resonance (NMR), because the escape process is much less efficient than the capture one.In this paper, we demonstrate the electrical control of the spectral diffusion dynamics for single QDs embedded in a Schottky diode structure. Our goal is to reach the standard phenomenology of motional narrowing described in NMR by hastening carrier escape from the traps around the QD through tunneling under reverse bias voltage. We show for the neutral exciton line that, under increasing reverse bias, a Lorentzian to Gaussian lineshape transition takes place together with a linewidth increase as in Ref.[3]. Then, for higher bias voltages, the reverse transition from Gaussian to Lorentzian lineshapes occurs with a line-narrowing due to the shortening of the escape time.These data pave the way to a protection for zero-dimensional electronic states from outside coupling through a voltage-controlled motional narrowing effect. [1]A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler and G. Abstreiter, Nature 418, 612-614 (2002). [2]A. Hogele, S. Seidl, M. Kroner, K. Karrai, R. J. Warburton, B. D. Gerardot and P. M. Petroff, Phys. Rev. Lett. 93, 217401 (2004). [3]A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R.Ferreira, and J. M. Gerard, Nature Phys. 2, 759 (2006).
We report a study on temperature-dependent resonant fluorescence from InAs/GaAs quantum dots. We combined spectral and temporal measurements in order to identify sources of dephasing. In the spectral domain, we observed temperature-dependent broadening of the zero-phonon line as $0.3\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{eV}/\mathrm{K}$, and a temperature-dependent phonon broadband. Time-resolved autocorrelation measurements revealed temperature-dependent spin pumping times between T1,s=6{T}_{1,s}=6T1,s​=6 ns (4 K) and 0.50.50.5 ns (15 K). These results are compared against theoretical modeling with a master equation for a four-level system coupled to phonon and spin baths. We explained the results by phonon-mediated hole-spin scattering between two excited states, with the piezophonons as a dominant mechanism.
We investigate the temperature dependence of photon coherence properties through two-photon interference (TPI) measurements from a single quantum dot (QD) under resonant excitation. We show that the loss of indistinguishability is related only to the electron-phonon coupling and is not affected by spectral diffusion. Through these measurements and a complementary microscopic theory, we identify two independent separate decoherence processes, both of which are associated with phonons. Below 10 K, we find that the relaxation of the vibrational lattice is the dominant contribution to the loss of TPI visibility. This process is non-Markovian in nature and corresponds to real phonon transitions resulting in a broad phonon sideband in the QD emission spectra. Above 10 K, virtual phonon transitions to higher lying excited states in the QD become the dominant dephasing mechanism, this leads to a broadening of the zero phonon line, and a corresponding rapid decay in the visibility. The microscopic theory we develop provides analytic expressions for the dephasing rates for both virtual phonon scattering and non-Markovian lattice relaxation.
We present temperature-dependent measurements of the dephasing time in the ground-state transition of strongly-confined InGaAs quantum dots, using a highly sensitive four-wave mixing technique. At low temperature we measure a dephasing time of several hundred picoseconds. Between 7 and 100 K the polarization decay has two distinct components resulting in a non-Lorentzian lineshape with a sharp zero-phonon line and a broad band from elastic exciton-acoustic phonon interactions. We also explore the dephasing time beyond the one exciton occupation, by electrically injecting carriers. Electrical injection into the barrier region results in a dominantly pure dephasing of the excitonic ground-state transition. Once the injected carriers have filled the electronic ground state, additional filling of the excited states creates multiexcitons that show a fast dephasing due to population relaxation.
A single spin confined to a semiconductor quantum dot is a system of significant interest for quantum information science, as a potential optically-addressable qubit. In many respects, a quantum dot behaves like a single atom with high quality single photon emission. By controlling the light-matter coupling in such a system, it is possible to generate highly non-classical states of light and coherently control a single spin confined to the quantum dot. A departure from the ideal atomic picture appears once we consider the mesoscopic environment with which the quantum dot interacts. Charge fluctuations in the surroundings of the quantum dot affect the photon emission frequency leading to inhomogeneous broadening. Further broadening of the emission is caused by coupling to phonon modes of the host semiconductor material. Finally, coupling between the spin of a confined electron and a large bath of nuclear spins residing in the quantum dot leads to fast dephasing of the electron spin. All of these effects are typically considered detrimental to the potential use of quantum dots for quantum technologies. In this thesis, we develop the environmental coupling of a negatively charged quantum dot as a resource for quantum optics and spin control. First, the phonon-assisted fluorescence is shown to be a useful independent channel for feedback stabilisation of the quantum dot emission frequency, without requiring a measurement of the indistinguishable zero-phonon line. With stabilisation, the corresponding frequency broadening is drastically improved, and the sub-Hz frequency fluctuations are no longer resolved. Next, we show low-power resonance fluorescence emission spectra of the negatively charged trion transition. In the low power regime of resonance fluorescence, the excited state is not populated and most of the emission is coherent. In addition to elastic Rayleigh scattering, we observe coherent Raman sidebands, linked to an effective magnetic field created by the hyperfine interaction, the Overhauser field. This fluctuating effective field lifts the electron spin degeneracy in the absence of a magnetic field, and dictates the optical selection rules of the trion system. These spectra therefore allow for a measurement of the time-averaged distributions of in-plane and out-of-plane Overhauser field components. In the final part of the thesis, we use this hyperfine-generated Λ -scheme to optically create electron spin superpositions through two-colour excitation and coherent population trapping. We then show that rapid shifts in the relative phase of the lasers lead to initialisation of the electron spin into a rotated dark state.