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Physical Review B

Three-spin coherent oscillations and interference

Gabriel Poulin-Lamarre, J. Thorgrimson, Sergei Studenikin, G. C. Aers, A. Kam, P. Zawadzki, Z. R. Wasilewski, Andy S. Sachrajda

Published Mar 12, 2015• 8 citations
Publisher

Abstract

We utilize magnetic field dependencies to identify two hitherto unobserved quantum interference processes in a triple quantum dot circuit. The first observation involves the interplay of Landau-Zener-St\"uckelberg behavior from two separate anticrossings between two energy levels that anticross twice as a function of a detuning parameter. The second process involves quantum interference between all-exchange and hyperfine qubits activated in a three-spin system.

DOI
10.1103/physrevb.91.125417

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We utilize magnetic field dependencies to identify two hitherto unobserved quantum interference processes in a triple quantum dot circuit. The first observation involves the interplay of Landau-Zener-St"uckelberg behavior from two separate anticrossings between two energy levels that anticross twice as a function of a detuning parameter. The second process involves quantum interference between all-exchange and hyperfine qubits activated in a three-spin system.
The triple quantum dot energy level spectrum is far more complex than its double quantum dot counterpart. As a result it is a challenge to cleanly manipulate only the two required qubit states without invoking more complex multistate coherent evolution. In this talk I will describe experiments and modeling of lateral triple quantum dot devices where by suitable device gate (i.e. energy level spectrum) tuning and pulse characteristics we were able to characterize and manipulate various three spin qubit species. In particular I will describe measurements where the Landau-Zener –Stuckelberg approach previously demonstrated in double dots is extended to threeinteracting spin states permitting us to demonstrate phenomena such as pairwise exchange control. I will also demonstrate how by tuning the experimental parameters one can controllably switch to coherent oscillations originating from alternative potentially useful qubit states and how to distinguish them.
Single-spin state evolution induced by the Landau-Zener-St\"uckelberg-Majorana (LZSM) interference in a Zeeman-spit four-level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the electric dipole spin resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A number of special points in the parameter space are identified, out of which all three features are merged. Under this triple-crossing resonance condition, the interdot tunneling is combined with a fast spin evolution in each dot at the EDSR frequency. Harmonics of the EDSR are revealed in the spin-dependent tunneling maps versus variable magnetic field and MW frequency. The results are applicable for both electron and hole systems with strong spin-orbit interaction and may be useful for developing new time-efficient schemes of the spin control and readout in qubit devices.
We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system, a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau–Zener transitions. In the triangular case, both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others, one can observe Rabi oscillations that can be used for coherent manipulation of the qubit states. The linear system is easier to fabricate; however, then the qubit states are not equivalent, making qubit operations more difficult to control.
Asymmetry in a three-electron double quantum dot (DQD) allows spin blockade, when spin-3/2 (quadruplet) states and spin-1/2 (doublet) states have different charge configurations. We have observed this DQD spin blockade near the (1,2)-(2,1) charge transition using a pulsed-gate technique and a charge sensor. We, then, use this spin blockade to detect Landau-Zener-St\"uckelberg interference and coherent oscillations between the spin quadruplet and doublet states. Such studies add to our understandings of coherence and control properties of three-spin states in a double dot, which, in turn, would benefit explorations into various qubit encoding schemes in semiconductor nanostructures.
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau–Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau–Zener probabilities reveal two different patterns: “step”- and “beats”-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by the change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between a pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.