Session L36: Focus Session: Semiconductor Qubits: Relaxation, Decoherence, and Realistic Devices

Long spin coherence in a strong spin-orbit qubit

We measure long spin coherence and strong spin-orbit coupling in Ge/Si nanowire quantum dots. Spin coherence is measured by examining the dephasing of singlet-correlated spins separated between two quantum dots, with each quantum dot occupied by several holes. Spin-orbit coupling is measured by examining the statistical properties of Coulomb blockade peak heights. The measured spin dephasing and spin-orbit coupling suggest that a spin-orbit qubit formed in a Ge/Si nanowire may have an unprecedentedly high manipulation fidelity.   

Electron Spin Coherence Times in Si/SiGe Quantum Dots

Single electron spin states in silicon have shown a great deal of promise as qubits due to their long spin relaxation (T1) and coherence (T2) times. Recent results exhibit a T2 of 250 us for electrons confined in Si/SiGe quantum dots at 350 mK. These experiments used conventional X-band (10 GHz) pulsed Electron Spin Resonance on a large area (3.5 mm x 20 mm), dual-gated, undoped Si/SiGe heterostructure quantum dots. These dots are induced in a natural Si quantum well by e-beam defined gates having a lithographic radius of 150 nm and pitch of 700 nm. The relatively large size of these dots led to closely spaced energy levels and long T2's could only be measured at sub-Kelvin temperatures. At 2K confined electrons displayed a 3 us T2, which is comparable to that of 2D electrons at that temperature. Decreasing the quantum dot size increases the electron confinement and reduces the effects of valley-splitting and spin-orbit coupling on the electron spin coherence times. We will report results on dots with 80 nm lithographic radii and a 375 nm pitch. This device displays an extended electron coherence time of 30 us at 2K, suggesting tighter confinement of electrons. Further measurements at lower temperatures are in progress.   

Electron spins at metal-oxide-silicon (MOS) interfaces

Single electron spins confined in lithographically defined quantum dots in silicon demonstrate long coherence times and are an attractive candidate for qubits and quantum computing applications. Confining electrons at the interface of a metal-oxide-silicon (MOS) structure, as opposed to other Si-based heterostructures, allows for smaller quantum dots by bringing the 2-dimensional electron gas closer to the confining gates. In order to use these electrons as qubits they must be individually confined in quantum dots, but defects at the oxide-silicon interface can lead to unintended electron trapping. The density and depth of these states are functions of the oxide quality and device processing conditions. As such, we have tailored our fabrication process to avoid any high energy processes after the final high temperature anneal. In this work we will characterize the density of trap states in a large area MOS device using electron spin resonance techniques and will present work towards the fabrication of MOS quantum dots.   

Spin Relaxation due to Charge Noise in Si Quantum Dot with Valley Splitting

We study the relaxation of an electron spin qubit in a Si quantum dot due to charge noise. In particular, we clarify how the presence of the conduction band valleys influences the spin relaxation. In single-valley semiconductor quantum dots, spin relaxation is through the mixing of spin and envelope orbital states via spin-orbit interaction. In Si, the relaxation could also be through the mixing of spin and valley states. We find that this additional spin relaxation channel, via spin-valley mixing and charge noise, is indeed important for an electron spin in a Si quantum dot. By considering both spin-valley and intra-valley spin-orbit mixings and the charge noise in a Si device, we find that spin relaxation rate peaks at the hot spot, where the Zeeman splitting matches the valley splitting. Furthermore, because of a weaker field-dependence, the spin relaxation rate due to charge noise could dominate over phonon noise at low magnetic fields, which fits well with recent experiments.   

Prediction of Dephasing Rates of Si/SiO$_2$ Singlet-Triplet Qubits due to Charge and Spin Defects

Previous theoretical studies of dephasing rates due to time-dependent fluctuations of defects in Si have mostly used ``model'' defects, without reference to the body of knowledge concerning such defects. In this talk, we will present theoretical predictions of the dephasing rates of singlet-triplet qubits in quantum dots at the Si/SiO$_2$ interface, using properties of the known classes of defects in this material system; these defects have been studied intensively for many years in the microelectronics industry, and thus there is a fair amount of knowledge known about them. We set up a theoretical framework aimed at enabling experiment to efficiently identify the most deleterious defects, and complement it with the knowledge of defects. We relate the dephasing rates $\Gamma_\phi$ due to various classes of defects to experimentally measurable parameters such as charge dipole moment, spin dipole moment and fluctuator switching times. Perhaps surprisingly, we find that for spin qubits charge fluctuators are more efficient in causing dephasing than spin fluctuators.   

Atomistic analysis of valley-orbit hybrid states and inter-dot tunnel rates in a Si double quantum dot

Silicon quantum dots are promising candidates for solid-state quantum computing due to the long spin coherence times in silicon, arising from small spin-orbit interaction and a nearly spin free host lattice. However, the conduction band valley degeneracy adds an additional degree of freedom to the electronic structure, complicating the encoding and operation of qubits. Although the valley and the orbital indices can be uniquely identified in an ideal silicon quantum dot, atomic-scale disorder mixes valley and orbital states in realistic dots. Such valley-orbit hybridization, strongly influences the inter-dot tunnel rates.Using a full-band atomistic tight-binding method, we analyze the effect of atomic-scale interface disorder in a silicon double quantum dot. Fourier transform of the tight-binding wavefunctions helps to analyze the effect of disorder on valley-orbit hybridization. We also calculate and compare inter-dot inter-valley and intra-valley tunneling, in the presence of realistic disorder, such as interface tilt, surface roughness, alloy disorder, and interface charges. The method provides a useful way to compute electronic states in realistically disordered systems without any posteriori fitting parameters.   

Spin-valley physics in realistic silicon quantum dots

Silicon quantum dots are leading approach for solid-state quantum bits. However, one must contend with new physics due to the multi-valley nature of silicon. At a Si heterostructure interface the valley degeneracy is lifted and the different valley subspaces of the confined electron spin configurations do not interact. When, however, the valley states are brought at resonance in the presence of a non-ideal interface, spin-valley mixing can occur via spin-orbit coupling. Within the same theoretical framework, we can successfully describe the spin relaxation processes in non-ideal quantum dots [e.g., relaxation ``hot spots'' in C. H. Yang, A. Rossi, R. Ruskov, N. S. Lai, F. A. Mohiyaddin, S. Lee, C. Tahan, G. Klimeck, A. Morello, and A. S. Dzurak, Nature Comm. 4, 2069, (2013)] and a new electron spin resonance (ESR) anticrossing splitting in a double quantum dot transport experiment [X. Hao, R. Ruskov, M. Xiao, C. Tahan, and H. W. Jiang, work in preparation]. Understanding the spin-valley physics of inelastic tunneling is critical to a proper understanding of the transport through double quantum dots, with or without an ESR drive field.   

Anisotropic spin-echo dynamics: Maximizing purity for hole spins in quantum dots

We theoretically study spin-echo dynamics for a central spin qubit coupled anisotropically to a spin bath. Our main focus is on hole spins in quantum dots, with an anisotropic hyperfine coupling to nuclear spins. Through direct application of a systematic Magnus expansion, we analyze the purity of the spin qubit. The purity can characterize non-classical correlations between the spin qubit and bath and provides a figure-of-merit for preserving an ancilla qubit in some initial state. Interestingly, we show that the purity can be preserved to a greater degree by `parking' the spin qubit in a superposition of Zeeman eigenstates, rather than allowing it to align along an applied magnetic field. The procedure reported here provides a general strategy for preserving ancilla qubits in the presence of anisotropic interactions.   

The decoherence of exchange-only qubits in triple quantum dots

We study decoherence of a three-electron-spin qubit in a linear triple quantum dot (TQD) by hyperfine interaction. The qubit is encoded in the ($S=1/2$, $S_{z}=1/2$) subspace, and can be fully controlled electrically via exchange interactions $J_{12}$ and $J_{23}$ between the electron spins. We clarify how hyperfine interaction dephases the qubit by constructing effective Hamiltonians and presenting estimates of free evolution and Hahn echo decay for such qubit in a GaAs TQD. When the three electron spins are uniformly coupled, i.e., $J_{12}=J_{23}$, the two states of our qubit are the eigenstates. We find that the qubit decoherence is of order of single-spin decoherence ($T^{*}_{2}\sim 10$ ns, $T_{2}$ on the scale of $\mu$s). On the other hand, a difference between $J_{12}$ and $J_{23}$ requires one to diagonalize the qubit space to obtain an appropriate eigenbasis. Alternatively, the qubit can be viewed as undergoing a rotation. We find that the decoherence rates in the new basis are not significantly modified when comparing them with those in the $J_{12}=J_{23}$ case.   

Microscopic models for charge dephasing in semiconductor qubits

Charge noise is a ubiquitous source of dephasing in solid-state qubits. In typical models seeking to explain this decoherence mechanism, the charge qubit is dipole-coupled to two-level charge fluctuators distributed in the host material, at interfaces or in oxide layers. Here, we consider various microscopic mechanisms causing fluctuations in the environmental two-level systems, and study the charge qubit's coherence properties in each scenario. In light of recent experimental results reported with semiconductor qubits, we identify which noise mechanism reasonably dominates, and make testable predictions for future experiments.   

Effect of Nuclear Quadrupole Moments on Electron Spin Coherence in Semiconductor Quantum Dots

We theoretically investigate the influence of the fluctuating Overhauser field on the spin of an electron confined to a quantum dot. The fluctuations arise from nuclear spin being exchanged between different nuclei via the nuclear magnetic dipole coupling. We focus on the role of the nuclear interaction from electric quadrupole moments (QPM), which generally cause a reduction in internuclear spin transfer efficiency. By dividing the nuclear problem into subcells we are able to describe $10^4 - 10^5$ nuclei, which are realistic numbers for a quantum dot. The effects on the electron spin coherence time are studied by modeling an electron spin echo experiment. We find that the QPM cause an increase in the electron spin coherence time and that an inhomogeneous distribution, where different nuclei have different QPM, causes an even larger increase than a homogeneous distribution.   

Slow Exciton Spin Relaxation in Single Self-Assembled In$_{1-x}$Ga$_x$As/GaAs Quantum Dots

We calculate the acoustic phonon-assisted exciton spin relaxation in single self-assembled In$_{1-x}$Ga$_x$As/GaAs quantum dots using an atomic empirical pseudopotential method. We show that the transition from bright to dark exciton states is induced by Coulomb correlation effects. The exciton spin relaxation time obtained from sophisticated configuration interaction calculations is approximately 15--55 $\mu$s in pure InAs/GaAs QDs and even longer in alloy dots. These results is more than three orders of magnitudes longer than previous theoretical and experimental results (a few ns), but agree with more recent experiments that suggest that excitons have long spin relaxation times ($>$ 1 $\mu$s).   

Decoherence of a Driven Qubit

We study the relaxation of a field-driven qubit. In particular, we find that driving, whether on resonance or off resonance, alters the qubit relaxation rate, allowing both a blue and a red sideband contribution. Depending on the reservoir spectral density and its frequency dependence, the qubit relaxation rate could either be accelerated or reduced. We apply our general theory to the example of an electron spin qubit that is driven by an electric field via electrically driven spin resonance (EDSR), and analyze how spin relaxation induced by charge noise during EDSR varies as a function of driving frequency, driving magnitude, spin-orbit coupling strengths, noise spectrum, and the applied field.