Characterization of Qubit Dephasing by Landau-Zener-Stückelberg-Majorana Interferometry

Abstract

Controlling coherent interaction at avoided crossings is at the heart of quantum information processing. The regime between sudden switches and adiabatic transitions is characterized by quantum superpositions that enable interference experiments. Here, we implement periodic passages at intermediate speed in a GaAs-based two-electron charge qubit and observe Landau-Zener-Stückelberg-Majorana (LZSM) quantum interference of the resulting superposition state. We demonstrate that LZSM interferometry is a viable and very general tool to not only study qubit properties but beyond to decipher decoherence caused by complex environmental influences. Our scheme is based on straightforward steady state experiments. The coherence time of our two-electron charge qubit is limited by electron-phonon interaction. It is much longer than previously reported for similar structures.LZSM interferometry is a double-slit kind experiment which, in principle, can be realized with any qubit, while the specific measurement protocol might vary. Our system is a charge qubit based on two-electron states in a lateral double quantum dot (DQD) embedded in a twodimensional electron system (2DES) (Fig. 1). Source and drain leads at chemical potentials µ S,D , each tunnel coupled to one dot, allow current flow by single-electron tunneling. Applying the voltage V = (µ S − µ D )/e = 1 mV across the DQD (Fig. 1B) we use this current to detect the steady-state properties of the driven system. We interprete the singlets, S 11 (one electron in each dot) and S 20 (two electrons in the left dot), as qubit states. They form an avoided crossing (Fig. 1C), described by the Hamiltonianwhere we consider a variable energy detuning (t) and a constant inter-dot tunnel coupling tuned to ∆ 13 µeV, corresponding to a clock speed of ∆/h 3.1 GHz, where h is the Planck constant. Let us first discuss a single sweep through the avoided crossing at = 0: as shown back in 1932 independently by Landau, Zener, Stckelberg, and Majorana it brings the qubit into a superposition state [1][2][3][4], the electronic analog to the optical beam splitter. The probability to remain in the initial qubit state, P LZ = exp(−π∆ 2 /2 v), thereby grows with the velocity v = d /dt, here assumed to be constant [1][2][3][4]. Because the relative phase between the split wavepackets depends on their energy evolutions, repeated passages by a periodic modulation (t) =¯ +A cos(Ωt), give rise to so-called LZSM quantum interference [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We present a breakthrough which * These authors contributed equally to this work.makes LZSM interferometry a powerful tool: it is based on systematic measurements together with a realistic model, which explicitly includes the noisy environment. We demonstrate how to decipher the detailed qubit dynamics and directly determine its decoherence time T 2 based on straightforward steady state measurements. Keeping the experiment simple we detect the dccurrent I through the DQD. It involves electron tunneling giving rise to the confi...

Electric-dipole-induced spin resonance in a lateral double quantum dot incorporating two single-domain nanomagnets

“…Such a behavior can be explained in terms of higher order harmonics generation and has also been observed to such a high order in comparable EDSR experiments in an InAs nanowire based double QD [27] and to second order in another GaAs based double QD [28]. A related example of higher order harmonics generation are Landau-ZenerStückelberg-Majorana interference oscillations [29,30]. The multiple resonances here (with variable slopes) are fundamentally different from the two resonances (with identical slopes) observed in our previous sample with two nanomagnets.…”

Transport, shot noise, and topology in AC-driven dimer arrays

“…At least for double dots with an AC gating of a few GHz and amplitudes  w A 10 , intra-dot excitations turned out to play a minor role [16]. While the nearest neighbor interaction of such systems is typically much larger than the inter-dot tunneling [2,16], the magnitude of the long-range Coulomb repulsion is still to be determined.…”

“…At least for double dots with an AC gating of a few GHz and amplitudes  w A 10 , intra-dot excitations turned out to play a minor role [16]. While the nearest neighbor interaction of such systems is typically much larger than the inter-dot tunneling [2,16], the magnitude of the long-range Coulomb repulsion is still to be determined. A promising alternative are conducting polymers which are tunable by atomic force microscopy techniques [39] and, owing to their small size, possess a huge charging energy so that the one-electron regime should be easier to reach.…”

“…For both trivial and non-trivial topology, dissipation reduces the Fano factor which soon assumes values close to the Poissonian F = 1. This means that measuring the topological phase diagram via the Fano factor (see figure 4) will require samples with very good coherence properties such that  g t -10 3 0 , a value that seems feasible with present quantum dot technology [16].…”

“…Then for not too small frequencies, the driving essentially renormalizes the inter-dot tunnel coupling [9][10][11][12] and, thus, allows the emulation of a dimer chain with highly tunable tunneling. In the corresponding transport setting, i.e., in the presence of electron source and drain, one expects a corresponding current suppression [13,14] which has been measured in double quantum dots [15,16]. Moreover, the driving may have significant impact on the shot noise [17].…”