Robust manipulation of electron spin coherence in an ensemble of singly charged quantum dots

Abstract

Using the recently reported mode locking effect [1] we demonstrate a highly robust control of electron spin coherence in an ensemble of (In,Ga)As quantum dots during the single spin coherence time. The spin precession in a transverse magnetic field can be fully controlled up to 25 K by the parameters of the exciting pulsed laser protocol such as the pulse train sequence, leading to adjustable quantum beat bursts in Faraday rotation. Flipping of the electron spin precession phase was demonstrated by inverting the polarization within a pulse doublet sequence. PACS numbers: 72.25.Dc, 72.25.Rb, 78.47.+p, 78.55.Cr The spin of an electron in a quantum dot (QD) is an attractive quantum bit candidate [2,3,4,5] due to its favorable coherence properties [1,6,7,8]. As the interaction strength is rather small for direct spin manipulation, the idea to swap spin into charge has been furbished [6,9,10]. For example, the electron may be converted into a charged exciton by optical injection of an electronhole pair [10], depending on the residual electron's spin orientation, leading to distinctive polarization selection rules.The fundamental quantity regarding spin coherence is the transverse relaxation time T 2 . In a QD ensemble, this time is masked by dephasing, mostly caused by dotto-dot variations of the spin dynamics. The dephasing time does not exceed 10 ns, much shorter than T 2 . This leads to the general believe that manipulations ought to -1 0 1 2 3 4 5 -1 0 1 2 3 4 5 T D = 1.86 ns 3.26 ns 3.66 ns 3.76 ns 3.86 ns T D = 4.26 ns FR amplitude (arb. units) B = 6 T, T = 6 K 4.92 ns 5.22 ns 5.42 ns 5.62 ns 5.92 ns Time (ns) FIG. 1: Faraday rotation traces measured as function of delay between probe and first pump pulse at time zero. A second pump pulse was applied, delayed relative to the first one by TD , indicated at each trace. The top left trace gives the FR without second pump.be performed on a single spin. Measurement of a single electron spin polarization, however, also results in dephasing due to temporal sampling of varying nuclear spin configurations [11,12], as statistically significant measurements on a single QD may require multiple repetition of the experiment. The dephasing can be overcome by spin-echo techniques, which give a single electron spin coherence time on the scale of micro-seconds [8]. This long coherence time derived by spin-echo is result of a refocusing of the electron spin and possibly the nuclear spin configuration [11], and it is viewed as an upper bound on the free-induction decay of spin coherence [11,13].Recently, however, we have shown that mode locking of electron spin coherence allows one to overcome the ensemble dephasing [14] and to measure the single electron spin relaxation time T 2 without applying spin-echo refocusing [1]. For monitoring the coherence, pump-probe Faraday rotation (FR) measurements [15] on a QD ensemble were used: after optical alignment of the spins normal to an external magnetic field the electron spins precess about this field. Due to precession frequency varia...

Pump-probe Faraday rotation and ellipticity in an ensemble of singly charged quantum dots

“…One can check that, for a periodic train of pulses of arbitrary intensity and shape, the electron spin polarization reaches the highest value at the magnetic field satisfying the PSC condition Ω = 2πN/T R , where N is an integer 3,11,12,43 . For such electrons cos (ΩT R ) = 1 and the z -component of their spin polarization at the moment of pulse arrival can be written as…”

“…They are (i) inhomogeneity of a QD ensemble expressed in dispersion of the QD resonant transition energies and electron g -factors, and (ii) dispersion of electron precession frequencies connected with fluctuations of the nuclear contribution to these frequency. Here we conduct calculations for the QD ensemble assuming that the broadening of trion resonance frequency, dispersion of electron g -factors and fluctuations of the nuclear contributions to the electron spin precession frequency are similar to those in the samples studied in a series of works 11,12,13,28 . Those samples contained 20 layers of InGaAs QDs self-organized during the molecular-beam epitaxy growth.…”

“…The discovery of a very long spin coherence time in bulk GaAs 3 and II-VI compound quantum wells 4 using these highly sensitive techniques was one of the cornerstones for the initiation of spintronics, and today pump-probe spin-dependent spectroscopy has become a common way to study carrier spin coherence in bulk crystals 5,6 , quantum wells (QWs) 7,8 and quantum dot (QD) samples 9,10,11,12,13 . At the same time Kerr rotation measurements have become the most visual and impressive method to study electron spin transport 14,15 , spin accumulation and injection 16,17 , and the spin-Hall effect 18,19 .…”

Generation and detection of mode-locked spin coherence in (In,Ga)As/GaAs quantum dots by laser pulses of long duration

“…3,4 Due to the combined action of a periodic train of pump pulses and the hyperfine electron-nuclear interaction, a mode locking of electron spin precession may occur. [5][6][7] As a result, an ensemble of approximately one million QD electron spins is pushed into a regime given by a limited number of precession modes with commensurable frequencies. This may pave a road toward large-scale spintronic applications.…”

Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: Resonant spin amplification versus spin mode locking

“…They have been demonstrated to be among the most reliable tools for investigating coherent spin dynamics [1,[4][5][6][7][8][9][10][11][12][13][14][15][16]. The principle of these magneto-optical techniques is the following: an intense laser pulse of circularly polarized light (the pump) is used to orient spins and, therefore, to create a macroscopic spin polarization [17].…”