Coherent manipulation of quantum bits (qubits) on timescales much shorter than the coherence time 1,2 is a key prerequisite for quantum information processing. Electron spins in quantum dots are particularly attractive for implementations of qubits, and efficient optical methods for initialization and readout of spins have been developed in recent years 3,4 . Spin coherence times in the microsecond range have been demonstrated 5 . Therefore, spin control by picosecond optical pulses would be highly desirable so that a large number of spin rotations could be carried out while coherence is maintained. A major remaining challenge is demonstration of such rotations with high fidelity. Here, we use an ensemble of quantum-dot electron spins focused into a small number of precession modes about a magnetic field by periodic optical pumping. We demonstrate ultrafast optical rotations of spins about arbitrary axes on a picosecond timescale using laser pulses as control fields.Spin rotations have been obtained for gated GaAs transport quantum dots using radiofrequency fields. But such manipulations are slow, with times comparable to the spin coherence time 6 . Fast optical rotation operations on spins in quantum dots are being sought actively, but progress so far has been limited. In an all-optical experiment on shallow interface-fluctuation quantum dots, weak confinement precluded full unitary spin rotations 7 . Evidence for spin rotations was reported for a single GaAs interface-fluctuation quantum dot using very intense optical excitation needed for spins to be rotated by precession about the effective laser magnetic field 8 . Very recently, convincing rotations in a single InAs self-organized quantum dot were reported 9 . This work on single quantum dots 8,9 used pulses far from resonance, which could lead to excitation of other spins. This could inhibit the use of spins with separations less than the laser spot size for two-quantum-bit entanglement. In general, optical coupling to a spin in a single quantum dot is weak, and thus spin rotations on single quantum dots give weak responses. This generally necessitates many optical pulses in time to obtain sufficient fidelity, and it can lead to extra dephasing.An ensemble of quantum dots has the advantage of increasing the optical coupling and can decrease the loss of information from the loss of a few spins. However, ensemble approaches typically are hampered by the inhomogeneities in quantum dot properties, particularly in the spin-splitting g -factor, and lead to dephasing of the spin precession about a magnetic field 10,11 . Recently we have demonstrated techniques for eliminating part of the inhomogeneity in the electron spin precession in ensembles of singly charged quantum dots 12 . We have found that at low magnetic fields the spin ensemble can be put into a Zeeman spectrum 13 that is very close to a single precession mode. This is the system that we study S about the magnetic field. b, Spin polarization is generated by laser pulses resonant with the trion (two e...

We have studied the Faraday rotation and ellipticity signals in ensembles of singly-charged (In,Ga)As/GaAs quantum dots by pump-probe spectroscopy. For degenerate pump and probe we observe that the Faraday rotation signal amplitude first grows with increasing the time separation between pump and probe before a decay is observed for large temporal separations. The temporal behavior of the ellipticity signal, on the other hand, is regular: its amplitude decays with the separation. By contrast, for detuned pump and probe the Faraday rotation and ellipticty signals both exhibit similar and conventional behavior. The experimental results are well described in the frame of a recently developed microscopic theory [Phys. Rev. B 80, 104436 (2009)]. The comparison between calculations and experimental data allows us to provide insight into the spectral dependence of the electron spin precession frequencies and extract the electron g factor dependence on energy.

We show that the spins of all electrons, each confined in a quantum dot of an (In,Ga)As/GaAs dot ensemble, can be driven into a single mode of precession about a magnetic field. This regime is achieved by allowing only a single mode within the electron spin precession spectrum of the ensemble to be synchronized with a train of periodic optical excitation pulses. Under this condition a nuclei induced frequency focusing leads to a shift of all spin precession frequencies into the synchronized mode. The macroscopic magnetic moment of the electron spins that is created in this regime precesses without dephasing.PACS numbers: 78.67. Hc, 78.55.Cr Solid state implementations of quantum information processing promise scalability towards large numbers of qubits [1,2]. However, they are typically impeded by the non-ideal crystal environment leading to a wide dispersion of the properties of elementary excitations envisaged as qubits. This gives rise to a number of complications: a single excitation needs to be isolated, which often requires high resolution in space, energy, etc. The readout signal of such an excitation is typically weak, so that measurements may require times comparable to the decoherence time [3]. These problems may be overcome, if one had access to an ensemble of identical quantum bits, all prepared in the same quantum state, which is, however, complicated by the unavoidable inhomogeneities.A qubit candidate with promising features is an electron spin confined in a quantum dot (QD) [1,2,3,4,5,6,7,8]. Its decoherence time T 2 at cryogenic temperatures, for example, is in the microseconds range, as determined by a spin-echo measurement on a single GaAs/AlGaAs gated QD [9]. This property, which should allow one to perform many operations coherently, is, however, obscured in a QD ensemble by fast dephasing of electron spin polarization due to frequency dispersion for precession about a transverse magnetic field [10, 11]. The dephasing could be suppressed for particular electron spin subsets by synchronizing their precession with the repetition rate of the periodically pulsed laser used for generation of spin polarization [12]. The precession frequencies in these subsets satisfy the mode-locking condition: ω K = 2πK/T R , where T R is the pulse repetition period and K is an integer. Fulfillment of this condition gives rise to bursts in the Faraday rotation (FR) signal measured from a (In,Ga)As/GaAs QD ensemble right before excitation pulse arrival. The FR signal decay allowed us to measure T 2 = 3 µs [12].The majority of electrons in the ensemble would not satisfy the mode-locking condition, if the electron spin precession frequency in an individual dot was determined just by the external magnetic field B and the electron gfactor g e . In most III-V compound QDs, however, an electron is also exposed to the collective hyperfine field of the dot nuclei. As a result, the electron spin precession frequency, ω = µ B g e B/ +ω N,x , contains the nuclear contribution, ω N,x , which is proportional to the projecti...

Coherent interactions between spins in quantum dots are a key requirement for quantum gates. We have performed pump-probe experiments in which pulsed lasers emitting at different photon energies manipulate two distinct subsets of electron spins within an inhomogeneous InGaAs quantum dot ensemble. The spin dynamics are monitored through their precession about an external magnetic field. These measurements demonstrate spin precession phase shifts and modulations of the magnitude of one subset of oriented spins after optical orientation of the second subset. The observations are consistent with results from a model using a Heisenberg-like interaction with µeV-strength.PACS numbers: 78.67. Hc, 78.47.jh Considerable progress has been made recently in establishing optical control of spins confined in semiconductor quantum dots (QDs), a system of interest for quantum bits (qubits) in implementations of quantum information [1]. Single spin decoherence times on the order of microseconds have been demonstrated [2], and methods for spin initialization and readout have been developed [3,4]. Recently, progress in demonstrating optical rotations of single spins has been made [5][6][7][8]. To be useful in quantum information, spin manipulation times must be orders of magnitude faster than decoherence times [1], which is possible using fast optical methods. Interactions between spins in QD systems can provide the mechanism for coherent control in quantum logic but can also complicate their coherent dynamics. The case of coupling between spins in QD molecules has been well studied [9][10][11][12], but long ranged interactions are not yet understood.An ensemble of QDs has the advantage of having strong optical coupling, but ensemble approaches typically have been hampered by inhomogeneities in their properties, particularly spin splittings, which lead to fast spin dephasing. In previous work we have demonstrated nuclear assisted optical techniques for removing some of the effects of these inhomogeneities [2,13]. In these techniques, periodic pulse trains orient spins normal to an external magnetic field, and particular subsets of spins precess in phase with the pulse trains. At rather low magnetic fields, around B = 1 T, a spin ensemble can be put into a state in which only few spin precession modes contribute [14]. This is the system that we study here.In the present work two subsets of spins are selected by spectrally narrow, circularly polarized laser pulse trains of different photon energies. The subsets are oriented by the two laser pulses (pump 1 and pump 2), and precess around a perpendicular magnetic field. The relative phase of the two precessions is controlled by the time difference between the two pulses. We find that after the second pump pulse, the precession associated with the first spin subset acquires a phase shift that depends on the relative orientation of the spins. It emerges smoothly in time after pump 2. In addition, the precession amplitude shows modulations and decreases with time. The major experiment...

The electron spin precession about an external magnetic field was studied by Faraday rotation on an inhomogeneous ensemble of singly charged, self-assembled (In,Ga)As/GaAs quantum dots. From the data the dependence of electron g-factor on optical transition energy was derived. A comparison with literature reports shows that the electron g-factors are quite similar for quantum dots with very different geometrical parameters, and their change with transition energy is almost identical.