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arXiv:0904.2754 · Physical Review B

Phase readout of a charge qubit capacitively coupled to an open double quantum dot

Christoph Kreisbeck, Franz J. Kaiser, Sigmund Kohler

Published Mar 3, 2010• 10 citations
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Abstract

We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit with sufficient resolution.

DOI
10.1103/physrevb.81.125404

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We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit with sufficient resolution.
Abstract.- We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit. Quantum algorithms usually terminate with qubit readout, i.e., a measurement of the quantum register’s state. Generally, the laws of quantum mechanics inhibit one to directly and fully determine the wave function of the qubit from a single measurement. With repeated projective measurements, it is only possible to sample the probability that the qubit is in the one or the other of two orthogonal states. Such destructive measurements can nevertheless be used to demonstrate coherent oscillations by repeating
We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady-state currents through the system, the entanglement between the transport double quantum dots, and the back-action on the charge qubit. We use a Born-Markov secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds, it is also possible to stabilize pure entangled states of the transport double quantum dots.
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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.
Understanding the interactions that couple gate-defined quantum-dot qubits is an important step to using such devices in quantum computing. For double-quantum-dot qubits with an effective charge dipole moment, a capacitive dipole-dipole interaction can yield coherent coupling between neighboring qubits. Here researchers reveal the tunability of this capacitive-coupling energy with applied gate voltages in a quadruple-quantum-dot array, tuning the coupling energy from 15 to 32 GHz. Modeling the system as a network of charge nodes joined by capacitors, the authors demonstrate how the capacitive-coupling energy between pairs of double dots depends on the various capacitances in the network.
We study the short time dynamics of a charge qubit encoded in two coherently coupled quantum dots connected to external electrodes.In the regime of sequential tunneling the waiting time distribution is used to investigate in details statistics of the tunneling events and their correlations.We show that the coherent rotation of the qubit state on the Bloch sphere can be seen in tunneling events when an electron is injected and leave the system.Decoherence, relaxation of the qubit state as well as leakage processes are studied by means of transient currents.