Predicted ultrafast single-qubit operations in semiconductor quantum dots

Abstract

Several recently proposed implementations of scalable quantum computation rely on the ability to manipulate the spin polarization of individual electrons in semiconductors. The most rapid singlespin-manipulation technique to date relies on the generation of an effective magnetic field via a spin-sensitive optical Stark effect. This approach has been used to split spin states in colloidal CdSe quantum dots and to manipulate ensembles of spins in ZnMnSe quantum wells with femtosecond optical pulses. Here we report that the process will produce a coherent rotation of spin in quantum dots containing a single electron. The calculated magnitude of the effective magnetic field depends on the dot bandgap and the strain. We predict that in InAs/InP dots, for reasonable experimental parameters, the magnitude of the rotation is sufficient and the intrinsic error is low enough for them to serve as elements of a quantum dot based quantum computer.PACS numbers: 03.67. Lx, 73.63.Kv Scalable proposals for quantum computation[1] require well-defined individual qubits that can be manipulated individually (single-qubit gates) and also can controllably interact with each other (two-qubit gates) [2]. In solid-state systems often the two-qubit gates appear easier to realize, e.g. by the exchange interaction between electrons[3]. The manipulation of single qubits has been perceived as more difficult; this motivated the proposal of all-exchange-based quantum computation [4], which requires only two-qubit (exchange) gates. All-exchangebased computations require a large number of gate operations, although recent work indicates substantial reductions are possible [5]."Here we predict that a spin-AC Stark effect (1) produces coherent rotations of electron spin in quantum dots, (2) the rotation angle can exceed π for reasonable experimental parameters, and (3) the error rates are tolerable for quantum computation. The spin-splittings of states in CdSe quantum dots [6,7] and coherent manipulation of ensembles of spins in ZnMnSe quantum wells [8] has been demonstrated experimentally. Theoretical considerations of the AC Stark effect [9,10,11] have focused to date only on non-spin-selective shifts of energy levels. Here we consider a spin-selective AC Stark effect whereby a quantum dot is illuminated with a single intense pulse of circularly-polarized nonresonant light (Fig. 1a). Such a pulse shifts the energies of dot states, and due to differing transition matrix elements the two spin states are shifted differently. Hence this pulse produces a splitting of the two lowest energy conduction states. The splitting of these two states (spin-up and spin-down) can be viewed as an optically-induced pseudo-magnetic field ( B ef f ) acting on the state pair. Direct application of this approach to quantum computing is clear, for one well-known physical realization of a single qubit opera- * Electronic address: craig-pryor@uiowa.edu tion is a magnetic field applied to a spin for a definite period of time. We find that the size of the effective field...

Optically induced suppression of spin relaxation in two-dimensional electron systems with Rashba interaction

“…28 Physically, the optical Stark effect in semiconductors is related to optically induced modification ͑dressing͒ of quantum states, 28 including optically induced spin splitting. 27,29 Since a below-band-gap laser does not excite real excitons, the optically induced spin splitting lasts only as long as the pump pulse. The purpose of the current investigation is to study the effect of the pulse sequence on the electron spin relaxation time in 2D quantum structures with dominant D'yakonov-Perel' spin relaxation mechanism.…”

Strong hyperfine-induced modulation of an optically driven hole spin in an InAs quantum dot

“…After 30-50 ns delay, a short (13 ps, 150 μeV bandwidth), circularly-polarized pulse from a mode-locked laser is used to optically rotate the spin state by 2 π about the optical axis. The pulse is detuned below the lowest energy transition by 200-300 μeV to rotate the hole spin state through a virtual process [26,[29][30][31][32][33][34]. A second short pulse, with a variable delay τ from the first, again rotates the hole spin by π/2 about the optical axis, which brings the hole spin closer to ⇑ or ⇓ on the Bloch sphere, depending on the spin phase at the second pulse.…”

Quantum computing by optical control of electron spins

“…Thus the optical excitation is restricted by the angular momentum conservation along the z-axis. Now if the controlling optical pulses are applied normal to the sample surface, the conservation of the angular momentum about the growth direction makes it impossible to flip the electron spin along z-axis and thus impossible to complete an arbitrary quantum operation, unless the light beam is incident with an angle [311] or the symmetry is broken by a magnetic field with a non-zero in-plane component. Since in the near-field optics, the incident light is usually normal to the surface, we need a static in-plane magnetic field applied (whose direction is defined as x-axis).…”

“…This is equivalent to a magnetic field with strength |Ω(t)| 2 /(2gµ B ∆) precessing in the x-y plane with the angular frequency ω c (the time-dependent optical Stark shift [311] of the electron energy |Ω(t)| 2 /(2∆) contributes only a trivial global phase-shift and can be ignored). In cases that the optical pulse is much shorter than the spin precession period, the effective magnetic field becomes an instantaneous pulse which can be controlled in the femtosecond timescales (c.f.…”