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arXiv:cond-mat/0703334 · Physical Review B

Decoherence of Rabi oscillations of electronic spin states in a double quantum dot

Alessandro Romito, Yuval Gefen

Published Nov 16, 2007• 6 citations
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Abstract

We study the role of charge fluctuations in the decoherence of Rabi oscillations between spin states \ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩, \ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\uparrow}⟩ of two electrons in a double dot structure. We consider the effects of fluctuations in energy and in the quantum state of the system, both in the classical and quantum limits. The role of state fluctuations is shown to be of leading order at sufficiently high temperature, applicable to actual experiments. At low temperature, the low frequency energy fluctuations are the only dominant contribution.

DOI
10.1103/physrevb.76.195318

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We study the role of charge fluctuations in the decoherence of Rabi oscillations between spin states \ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩, \ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\uparrow}⟩ of two electrons in a double dot structure. We consider the effects of fluctuations in energy and in the quantum state of the system, both in the classical and quantum limits. The role of state fluctuations is shown to be of leading order at sufficiently high temperature, applicable to actual experiments. At low temperature, the low frequency energy fluctuations are the only dominant contribution.
Lateral semiconductor quantum dot structures have been proposed as an effective quantum bit (qubit) for quantum computation. A single excess electron with the freedom to move between two capacitively coupled quantum dots creates a `pseudo'-spin system with the same qubit behavior as the more natural two level system of a single electron spin. The excess electron in the double dot system is restricted to one of the two dots, thereby creating two separate and distinct states (usually referred to as |L> and |R>). The benefit of these charge qubits lie in the relative ease with which they can be manipulated and created. Experiments have been performed in this area and have shown controllable coherent oscillations and thus efficient single-qubit operations. However, the decoherence rates observed in the experiments is still quite high, making double dot charge qubits not very appealing for large-scale implementations. The following work describes the effect of the electromagnetic (EM) environment of the double quantum dot system on the decoherence of the charge state. Sources of decoherence in similar systems have been extensively investigated before and this paper follows a close theoretical framework to previous work done in the area. The effect of the EM environment can been seen in the calculations discussed below, although it is clear that the decoherence seen in experiments cannot be fully explained by the voltage fluctuations as they are investigated here. The limitations of the calculations are discussed and improvements are suggested.
We discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use effective circuit model to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1)({T}_{1})(T1​) and phase (T2)({T}_{2})(T2​) relaxation times of the qubit system. Our theoretical estimate of the quality factor due to dephasing by electromagnetic fluctuations yields values much higher than those found in recent experiments, indicating that other sources of decoherence play a dominant role.
We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩$ state and the $\ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\uparrow}⟩$ state of the two-electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩$ state and to perform a SWAP\sqrt{\mathrm{SWAP}}SWAP​ operation with unit fidelity.
In this dissertation we discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes and electromagnetic environmental fluctuations. In the case of decoherence caused by phonon coupling, two distinct quantum dot configurations are studied and proposed as setups that mitigate its nocive effects : (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have Q factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit. We also discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use effective circuit models to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. We also discuss the dependence the quality factor Q shows with respect to parameters of the setup, such as temperature and capacitive coupling between the electrodes.
Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here we present a detailed theory for electron-spin dynamics in two-electron double-dot systems that was used to guide those experiments and analyze the results. Specifically, we analyze both spin- and charge-relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron systems. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits.
We study the pumping of spin-polarized electrons in a double quantum dot system with up to two electrons per dot, via an applied AC field and a constant magnetic field. The behaviour of the current through the double-dot system is studied as a function of the AC field and coupling to the leads, using a Markov master equation approach for the time evolution of the reduced density matrix. For up to two electrons in the system, we find that the formation of a spin-triplet state blocks the current through the device, and analyse possible solutions. When we incorporate three-and four-particle states, with up to two opposite spin electrons per dot, we find a regime where the pumping of spin-polarized electrons is realized through double occupancy states in each dot. This property is robust against spin-relaxation and decoherence processes which are taken into account phenomenologically. Finally we study the effects of applying a pulsed AC field and the possibility of the resolution of Rabi oscillations.