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arXiv:1604.02884 · Physical review. B./Physical review. B

Quantum and tunneling capacitance in charge and spin qubits

Ryo Mizuta, R. M. Otxoa, Andreas C. Betz, M. Fernando González-Zalba

Published Jan 18, 2017• 87 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.045414

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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 ggg 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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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 RRR 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.
State readout is a key requirement for a quantum computer. For semiconductor-based qubit devices it is usually accomplished using a separate mesoscopic electrometer. Here we demonstrate a simple detection scheme in which a radio frequency resonant circuit coupled to a semiconductor double quantum dot is used to probe its charge and spin states. These results demonstrate a new noninvasive technique for measuring charge and spin states in quantum dot systems without requiring a separate mesoscopic detector.
We investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the ``double charge resonant'' regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well separated from the partially polarized (0211 and 1102) states. A rapid controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing $\ensuremath{\pi}$ pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise---charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction---and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate.
Spin qubits in gate-defined semiconductor quantum dots are a promising platform for realising a scalable quantum computer. This platform encodes quantum information into the intrinsic angular momentum (spin) of individual electrons or holes. In particular, hole spins in quantum dots enable the possibility of all-electrical spin control due to their intrinsic spin-orbit coupling. One important criterion of a quantum computer is the ability to reliably read out the state of the qubit. This is done by mapping spin information to the charge degree of freedom, combined with a method for charge detection. Charge detection can be facilitated by coupling a resonator directly to the quantum dot gate or to a charge sensor and measuring the resonator's phase or amplitude response. In this thesis, we describe a set of experiments relating to the implementation of hole spin qubit readout with superconducting resonators. First, we study gate-based charge sensing in a Si fin field-effect transistor (finFET) device using a superconducting NbN nanowire resonator. We find that the resonator amplifies capacitive crosstalk when electrical control pulses are applied to gate electrodes in this device. This occurs whenever a spectral component of qubit control pulses overlaps with the resonance frequency, which we show may occur for both baseband and radio-frequency (RF) drive signals. We quantify this crosstalk in a transport-based method, and attribute its source to the capacitance between the bondpads of neighbouring gate electrodes. In a second experiment, we use an RF charge sensor with the same nanowire technology to read out hole spin qubits formed in the quantum well of a Ge/SiGe heterostructure. A screening layer approach is used to facilitate RF matching due to large RF dissipation found in the heterostructure. We implement a double-latched readout scheme in this system to reduce errors arising from both spin and charge decay during readout. The spin-to-charge conversion process and its dependence on magnetic field orientation is studied. Spin and charge decay processes arising after spin-to-charge conversion are mitigated by choosing an optimal working point for the field orientation, field amplitude and readout pulse times. By doing so, we achieve an average single-shot state-preparation-and-measurement fidelity of 97%, primarily bounded by imperfect state preparation and limited signal-to-noise ratio. Finally, we study coplanar waveguide resonators fabricated from NbN. We investigate the feasibility of integrating this type of resonator onto the same chip as the Si finFET quantum dots. We then develop a novel resonator readout technique by the interference of two microwave sidebands. We demonstrate the insensitivity of this technique to common-mode phase and amplitude noise both theoretically and experimentally. This technique is then used to study resonator noise arising from two-level system defects. These results highlight both the practical constraints and the potential for achieving high readout fidelities using resonator-based hole spin qubit readout. This work establishes a blueprint for mitigating resonator-induced crosstalk and enabling high-fidelity readout in lossy materials by incorporating a screening layer.
We theoretically examine the capacitive coupling between two quantum dot hybrid qubits, each consisting of three electrons in a double quantum dot, as a function of the energy detuning of the double dot potentials. We show that a shaped detuning pulse can produce a two-qubit maximally entangling operation in $\ensuremath{\sim}50\phantom{\rule{0.28em}{0ex}}\mathrm{ns}$ without having to simultaneously change tunnel couplings. Simulations of the entangling operation in the presence of experimentally realistic charge noise yield two-qubit fidelities over 90%.