Session Z19: Focus Session: Spin Dynamics in Quantum Dots

Single electron Transport in diluted magnetic semiconductor quantum dots

We consider a single electron transistor based upon a II-VI semiconductor quantum dot doped with a few Mn atoms.Our proposal is motivated by the recent fabrication and optical probing of single CdTe quantum dots doped with a single Mn [1]. The numerical diagonalization of the quantum dot Hamiltonian is possible in the case of small number of both carriers and Mn [2],[3],[4]. Our calculations [5] reveal that the magnetic ions behave like a quantum nanomagnet whose the total spin and magnetic anisotropy depend dramatically both on the number of carriers and their orbital nature. We show that single electron transport spectroscopy permits a complete characterization of electronic excitations of the dot. A protocol of gate voltage pulses that permits the preparation and detection of the quantum state of a single Mn spin is presented. \newline \newline (1) L. Besombes, et al. Phys. Rev. Lett. {\bf 93}, 207403 (2004) \newline (2) J. Fern\'{a}ndez-Rossier, . PRB, Jan 2006 \newline (3) A. O. Govorov, Phys. Rev. B{\bf 72 }, 075359(2005). \newline (4) F. Qu, P. Hawrylak, Phys. Rev. Lett. {\bf 95}, 217206 (2005) \newline (5) J. Fern\'{a}ndez-Rossier, R. Aguado, in prep.   

Optimizing g-factor tuning with electric fields in self-assembled InAs/GaAs quantum dots

Single-spin manipulation in quantum dots can be achieved without a time-dependent magnetic field by modulating the electron g tensor in the dots with an electric field. Using a recently-developed envelope-function formalism for quantum dot g factor calculations[1], we have studied the dependence of the electron g tensor tuning range on quantum dot size and shape. The electric field is applied in the growth direction of the dot, assumed to be along [001]. We find that larger percentage changes in the g factors along the principal axes can be achieved in taller dots (more extended along the growth direction) and also, surprisingly, in more elliptical dots. The [110] and [1$\overline{1}$0] g factors change sign as a function of dot height and lateral extent. Tuning ranges are of the order of $\Delta$ g 0.02 for electric fields changing from 0 to $\pm$100 kV/cm. By choosing a dot with a g factor near 0 we identify dots whose g factors should change sign along one principal axis as a function of electric field. This should generate very rapid spin manipulation using g tensor modulation resonance[2]. This work supported by DARPA/ARO DAAD19-01-1-0490. [1] C. E. Pryor and M. E. Flatt\'e, \textit{Phys. Rev. Lett.} in press. [2] Y. Kato \textit{et al.}, \textit{Science} \textbf{299}, 1201 (2003).   

Calculations of Land\'e g-factors in III-V nanowhisker quantum dots

We present detailed numerical calculations of Land\'e g-factors in semiconductor nanowire based quantum dots. We consider 111 oriented InAs nanowires with InP double barriers forming the dot, for which transport properties have recently been investigated[1]. We find that compared to recent calculations of self-assembled InAs/GaAs quantum dots[2], typical nanowire dots have larger, and negative, g-factors. We attribute this to the nanowire dots being larger than self-assembled dots, resulting in less angular momentum quenching. For nanowire sizes typical of those that have been fabricated to date, we find $g \approx -3$.\\ 1. M. T. Bj{\"o}rk et~al., Nano Letters, {\bf 4}, 1621 (2004).\\ 2. C. E. Pryor, M. E. Flatte, Phys. Rev. Lett., in press, www.arxiv.org/abs/cond-mat/0410678   

Control and manipulation of charge and spin in single and coupled quantum dots

I will discuss measurements of the spin lifetime in self-assembled InGaAs dots in GaAs. The spin relaxation time (T$_{1})$ is found to be extremely long (e.g. $>$25ms at T=1K, B=4T) decreasing with magnetic field according roughly to a clear B$^{-4}$ power law [1]. Furthermore, T$_{1}$ is found to reduce linearly with lattice temperature and be very strongly sensitive to the motional quantisation (s-p shell splitting). Another topic is the the coherent quantum coupling of a vertically stacked pair of quantum dots. The interaction can be tuned in such quantum dot molecule devices using an applied voltage as external parameter [2]. At the resonance the electron component of the exciton wave function hybridizes, giving rise to a quantum coupling energy in the excitonic spectrum. This work is supported financially by Deutsche Forschungsgemeinschaft via collaborative research center 631 and by German Federal Ministry of Research via NanoQuit. [1] M. Kroutvar, Y. Ducommun, D. Heiss, D. Schuh, M. Bichler, G. Abstreiter and J. J. Finley. Nature\textbf{ 432}, 81 (2004) [2] H. J. Krenner, E. C. Clark, A. Kress, D. Schuh, M. Bichler, G. Abstreiter and J.J. Finley. PRL \textbf{94}, 057402 (2005)   

Anisotropic phonon-assisted spin relaxation in elliptical quantum dots

We study theoretically phonon-assisted spin relaxation of an electron confined in elliptical quantum dot subjected to a tilted magnetic field. We show that in the presence of both Rashba and Dresselhaus spin-orbit terms the relaxation rate exhibits anisotropy with respect to the in-plane field orientation. This anisotropy originates from the interference, at non-zero tilt angle, between the two spin-orbit terms that couple adjacent spin-split energy levels. The variation of the relaxation rate for different azimuthal angles is determined by the quantum dot geometry and by the relative strengths of the Rashba and Dresselhaus coupling constants. The effect is strongest when adjacent spin-split levels are brought into resonance by tuning the total field magnitude and tilt angle. In this case, for certain values of tilt angle, the relaxation rate can be drastically reduced by varying the in-plane field orientation. Calculations were performed for InSb quantum dots.   

Spin Relaxation in Spherical CdS Quantum Dots

We present results of the time-resolved spin-sensitive differential transmission experiments and the quantitative theoretical analysis of the spin relaxation mechanism in quasi-spherical CdS quantum dots (QD) in a glass matrix. The measured decay of the degree of circular polarization (DCP) on ns timescale can be explained well by intralevel exciton transitions with electron spin flip, driven by the electron-hole exchange interaction and assisted by two LO phonons. The predicted spin relaxation rates for different QD sizes and temperatures are in line with experimentally determined values. The developed theoretical model provides also a qualitative understanding of the observed behavior of DCP as a function of central energy of pump and probe pulses. This work was supported by the Ministry of Education of the Czech Republic in the framework of research plan MSM 0021620834 and the research centre LC510, as well as by the GOA BOF UA 2000, IUAP, FWO-V projects G.0274.01N, G.0435.03, WOG WO.035.04N (Belgium) and the European Commission SANDiE Network of Excellence, contract No. NMP4-CT-2004-500101.   

Theory of spin-orbit effects and spin relaxation in single and coupled quantum dots.

Spin-orbit effects and phonon-induced spin relaxation in laterally coupled quantum dots in the presence of magnetic field are investigated by exact numerical diagonalization. Both Bychkov-Rashba and Dresselhaus spin-orbit couplings are included. Several new phenomena are predicted. In particular, we shown that coherent tunneling between the dots depend on the spin, enabling a scheme for spin-to-charge conversion by spin separation in a {\it homogeneous} magnetic field. Furthermore, we show that spin relaxation is highly anisotropic, both in terms of the direction of the double-dot axis as well as the direction of the magnetic field. The anisotropy comes from spin-orbit coupling. Calculated spin relaxation rates of GaAs single dots agree with a recent experiment.   

Asymmetric electron-electron exchange in a single quantum dot

Recent photoluminescence experiments on negative trions in a self-assembled quantum dot [1] reveal a high dephasing rate inconsistent with the electron-hole exchange mechanism. We find, however, that this rate can be explained by the asymmetric electron-electron exchange due to electron spin-orbit coupling in the excited singlet and triplet states. The necessary and sufficient condition for the existence of asymmetric exchange is the lack of inversion symmetry in the plane transverse to the growth direction. We develop a model that describes the two relevant cases of this asymmetry: when the system has a single reflection plane along the growth axis, and when the system has no reflection plane along the growth axis. These asymmetries are characteristic for shapes of self-assembled quantum dots. We find typical values for the dephasing part of the asymmetric exchange that are $\sim $10$^{-1}$ of the symmetric exchange. We also find that the asymmetric exchange is important for electron spin relaxation when the triplet states with non-zero projection of spin are brought into resonance with the singlet. [1] Ware M.E. et al -- Phys. Rev. Lett. 95(17), 177403 (2005)   

Spin Dynamics in InAs Quantum Dots

Spin coherence in InAs Self-Assemble Quantum Dots (SAQD's) could be useful for optical delay lines and quantum information technology. Very uniform dots and a very accurate measurement of dephasing processes are required to realize these possibilities. To this effect we report decoherence times in InAs SAQD. Here we describe measurements of spin dynamics from a 17 layered nominally undoped wafer of InAs SAQDs with a varying dot-size. We used Time Resolved Kerr Rotation (TRKR) for a wavelength resonant with the 3D InAs Stranski-Krastanow strain mediated quantum dots. Response is observed from 0 to 5 T that corresponds to a freely precessing spin with g = 0.45, a 1.2 ns lifetime at B=0 that decreases with B, and a sine-like phase. We attribute this spin to an electron from either the ground state of a negative trion or the excited state of a positive trion. The dots are dots unintentionally doped from background doping in the MBE chamber. Work supported in part by ONR, NSA/ARO, and DARPA/QUIST. JW is an NRC/NRL Postdoctoral Research Associate.   

Optical Control of Spin Coherence in Singly Charged Quantum Dots

In singly charged dots, resonant light couples an electron in the ground state with a trion consisting of the electron and an excited electron-hole pair. We show that a polarized laser pulse, driving the electron/trion transition, coherently changes the spin state of the ground state electron. The controlled spin dynamics provide a mechanism for the optical orientation of an electron spin in a quantum dot. The theory is supported by experimental evidence of the electron spin coherence induced and controlled by optical pulses in (In,Ga)As/GaAs quantum dots.   

Dynamics of Coupled Qubits Interacting with an Off-Resonant Cavity

We study a model for a pair of qubits which interact with a single off-resonant cavity mode and, in addition, exhibit a direct inter-qubit coupling\footnote{O. Gywat, F. Meier, D. Loss, and D. D. Awschalom, cond-mat/0511592}. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the inter-qubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct inter-qubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct inter-qubit coupling can be controlled optically via the ac Stark effect.   

Cavity Enhanced Faraday Rotation in Semiconductor Quantum Dots

The promise of quantum computation is helping fuel the development of single spin manipulation and measurement techniques. Photonic cavities provide an intriguing platform to increase the sensitivity of optical measurements, as well as the possibility to explore emergent light-matter interactions. The flexibility of a dielectric vertical cavity is exploited to study the spin dynamics within molecularly self-assembled CdSe quantum dots (QDs). Through the integration of QDs in microcavities, a twenty-fold enhancement of Faraday rotation is observed, which scales with the quality factor of the cavity. In this weak coupling regime, the amplified rotation is attributed to optically generated excited spins and multiple passes of the probe photons in the cavity. By applying this general planar cavity motif to Faraday rotation, dynamical measurements are accessible at extremely low powers on relatively small numbers of quantum confined states. In CdSe QDs, low power measurements reveal that contributions from both exciton and electron spin precession are largely dependent upon the power of excitation. This scheme is amenable to both soft and hard systems as a means to increase detection sensitivity.   

Optical manipulation of electron spin in quantum dot systems

Self-assembled quantum dots (QDs) are of particular interest for fundamental physics because of their similarity with atoms. Coupling two of such dots and addressing them with polarized laser light pulses is perhaps even more interesting. In this paper we use a multi-exciton density matrix formalism to model the spin dynamics of a system with single or double layers of QDs. Our model includes the anisotropic electron-hole exchange in the dots, the presence of wetting layer states, and interdot tunneling [1]. Our results show that it is possible to {\em switch} the spin polarization of a single self-assembled quantum dot under elliptically polarized light by increasing the laser intensity. In the nonlinear mechanism described here, intense elliptically polarized light creates an effective exchange channel between the exciton spin states through biexciton states, as we demonstrate by numerical and analytical methods. We further show that the effect persists in realistic ensembles of dots, and we propose alternative ways to detect it. We also extend our study to a double layer of quantum dots, where we find a competition between Rabi frequency and tunneling oscillations. [1] J. M. Villas-Boas, S. E. Ulloa, and A. O. Govorov, Phys. Rev. Lett. 94, 057404 (2005); Phys. Rev. B 69, 125342 (2004).