Fast and Robust Spin Manipulation in a Quantum Dot by Electric Fields

Abstract

We apply an invariant-based inverse engineering method to control by time-dependent electric fields electron spin dynamics in a quantum dot with spin-orbit coupling in a weak magnetic field. The designed electric fields provide a shortcut to adiabatic processes that flips the spin rapidly, thus avoiding decoherence effects. This approach, being robust with respect to the device-dependent noise, can open new possibilities for the spin-based quantum information processing.PACS numbers: 73.63. Kv, 72.25.Dc, 72.25.Pn Coherent spin manipulation in quantum dots (QDs) [1][2][3][4][5][6][7][8][9] is the key element in the state-of-the-art spintronics and solid-state quantum information [10,11]. Accurate spin manipulation can be achieved by several techniques. One of them is the conventional electron spin resonance induced by a magnetic field oscillating at the Zeeman transition frequency [1]. A more robust technique is the spin manipulation with geometric Berry phases during adiabatic motion [2,3]. Nowadays, there is also a growing interest in the electric control of spin using spin-orbit (SO) coupling [12]. It has been applied to high-fidelity spin manipulation on the 100 ns time scale [7][8][9]. This highly efficient all-electrical method has several advantages. For example, it is easy to generate time-dependent electric fields on the nanoscale by adding local electrodes and produce spin manipulation by making them Zeemanresonant [7]. As a result, Rabi spin oscillations appear at a frequency much smaller than the Zeeman frequency making the flip relatively slow and prone to decoherence. We shall propose here another all-electrical technique to flip spin with high fidelity via "shortcuts to adiabaticity", in a time that can be much shorter than any decoherence time.Recently, several shortcuts to adiabaticity have been put forward to speed up the adiabatic passage of quantum systems, and achieve a robust and fast adiabatic-like control [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The transitionless or counter-diabatic control algorithms proposed by Demirplak, Rice [13], and Berry [14], are designed to add supplementary timedependent interactions that cancel the diabatic couplings of a reference process. The system then follows exactly the adiabatic trajectory of the original unperturbed process, in principle in an arbitrarily short time. Transitionless quantum drivings have been implemented in two-level systems: spins in a magnetic field [14], atoms [15], and Bose-Einstein condensates in optical lattices [16]. A different shortcut is provided by inverse engineering the transient Hamiltonian [17,18] using LewisRiesenfeld invariants [27]. This method has been used for time-dependent traps [17-21], atomic transport [22], and other applications [23,24]. Although these two methods are potentially equivalent [25], their implementations and results can be quite different. Here we choose the invariant-based inverse engineering approach, since it is better suited than the transitionless driving to be produced by ...

Counter-diabatic driving for fast spin control in a two-electron double quantum dot

“…In reality, the electron spin is subject to the device-dependent noise, which could be the amplitude noise of the electric fields20. It can be quite important, especially when the electric fields are relatively weak.…”

“…This is different from the Hamiltonian in a single QD where there are only two controllable parameters, x and y components of the electric field, so that it is impossible to produce the required all-electrical interaction by counter-diabatic driving20.…”

“…In a single QD, we applied the inverse engineering method19 to design a fast and robust protocol of spin flip in the nanosecond timescale20, based on the Lewis-Riesenfeld invariant theory21. Furthermore, in a two-electron QD, more freedom in the applied electric fields provides the flexibility to control spin states by the invariant dynamics and controllable Lewis-Riesenfeld phases22.…”

High-fidelity non-adiabatic cutting and stitching of a spin chain via local control

“…Now we consider the influence of the 'apparatus' noise [34,35] in the control function g(t) on the fidelity of cutting. The noise is simulated as a set of rectangular pulses with a fixed lengthΔt and the random strengthD…”

Electric-field-induced interferometric resonance of a one-dimensional spin-orbit-coupled electron

“…Being an intrinsic property of condensed-matter materials, spin-orbit coupling (SOC) mixes the orbital and spin degrees of particles, and opens the possibility of electric control of the electron spin via its orbit, apart from the well-known magnetic responses1234567891011121314151617. A notable example exploiting SOC in semiconductor nanostructures is called the electric-dipole spin resonance technique6789 (EDSR), in which a spin-orbit qubit is encoded into a SOC-hybridized spin doublet and an oscillating electric field is further applied to manipulate this qubit on its Bloch sphere.…”