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arXiv:2204.04943 · Physical review. B./Physical review. B

Dynamical charge susceptibility in nonequilibrium double quantum dots

Adeline Crépieux C, M. Lavagna

Published Sep 30, 2022• 4 citations

Abstract

Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for $R$ depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.

DOI: 10.1103/physrevb.106.115439

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Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for

R

depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.

The coherent time evolution of electrons in double quantum dots (DQDs) induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven DQDs are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation, we obtain the energy- and time-resolved electron transfer through the device that resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots.

Abstract. The coherent time evolution of electrons in double quantum dots induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven double quantum dots are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation we obtain the energy- and time-resolved electron transfer through the device which resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the on initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots. PACS numbers: 73.63.Kv,73.23.Hk,72.10.-d

We present a theoretical analysis of the capacitance of a double quantum dot in the charge and spin qubit configurations probed at high frequencies. We find that, in general, the total capacitance of the system consists of two state-dependent terms: the quantum capacitance arising from adiabatic charge motion and the tunneling capacitance that appears when repopulation occurs at a rate comparable or faster than the probing frequency. The analysis of the capacitance lineshape as a function of externally controllable variables offers a way to characterize the qubits' charge and spin state as well as relevant system parameters such as charge and spin relaxation rates, tunnel coupling, electron temperature, and electron

g

factor. Overall, our analysis provides a formalism to understand dispersive qubit-resonator interactions which can be applied to high-sensitivity and noninvasive quantum-state readout.

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Quantum dot-based quantum computation employs extensively the exchange interaction between nearby electronic spins in order to manipulate and couple different qubits. The exchange interaction, however, couples the qubit states to charge noise, which reduces the fidelity of the quantum gates that employ it. The effect of charge noise can be mitigated by working at noise sweetspots in which the sensitivity to charge variations is reduced. In this work we study the response to charge noise of a double quantum dot based qubit in the presence of ac gates, with arbitrary driving amplitudes, applied either to the dot levels or to the tunneling barrier. Tuning with an ac driving allows to manipulate the sign and strength of the exchange interaction as well as its coupling to environmental electric noise. Moreover, we show the possibility of inducing a second-order sweetspot in the resonant spin-triplet qubit in which the dephasing time is significantly increased.

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