Session T29: Focus Session: Semiconductor Qubits - Coherent Control, Decoherence, and Relaxation

Electrical control of single spin dynamics

Over ten years ago, Daniel Loss and David DiVincenzo proposed using the spin of a single electron as a quantum bit. At the time of the proposal, it was not possible to trap a single electron in a device and measure its spin, let alone demonstrate control of quantum coherence. In this talk I will describe recent progress in the field, focusing on two new methods for single spin control that have been developed by my group at Princeton. The first method is based on quantum interference and implements spin-interferometry on a chip. The second method utilizes the strong spin-orbit coupling of InAs. By shifting the orbital position of the electronic wavefunction at gigahertz frequencies, we can control the orientation of a single electron spin and measure the full g-tensor, which exhibits a large anisotropy due to spin-orbit interactions. Both methods for single spin control are orders of magnitude faster than conventional electron spin resonance and allow investigations of single spin coherence in the presence of fluctuating nuclear and spin-orbit fields. I will also describe recent efforts to transfer these methods to silicon quantum dots, where the effects of fluctuating nuclear fields are much smaller.   

Harmonic Generation in InAs Nanowire Double Quantum Dots

InAs nanowires provide a useful platform for investigating the physics of confined electrons subjected to strong spin-orbit coupling. Using tunable, bottom-gated double quantum dots, we demonstrate electrical driving of single spin resonance.\footnote{S. Nadj-Perge {\it et al.}, Nature {\bf468}, 1084 (2010)}$^,$\footnote{M.D. Schroer {\it et al.}, Phys. Rev. Lett. {\bf107}, 176811 (2011)} We observe a standard spin response when the applied microwave frequency equals the Larmour frequency $f_{0}$. However, we also observe an anomalous signal at frequencies $f_n = f_0 / n$ for integer n up to n $\sim$5. This is equivalent to generation of harmonics of the spin resonance field. While a $f_0/2$ signal has observed,\footnote{E.A. Laird {\it et al.}, Phys. Rev. Lett. {\bf99}, 246601 (2007)} we believe this is the first observation of higher harmonics in spin resonance. Possible mechanisms will be discussed.\footnote{E.I. Rashba, arXiv:1110.6569 (2011)} Acknowledgements: Research supported by the Sloan and Packard Foundations, the NSF, and Army Research Office.   

Composite pulse sequences for Z-rotations robust against small magnetic field gradient in singlet-triplet qubits

We design piecewise composite pulse sequences of the exchange interaction in singlet-triplet qubits, suitable for achieving a Z-rotation along the Bloch sphere of arbitrary angle under the influence of a small stray magnetic field gradient. We explicitly show that upon appropriately choosing the pulse parameters, the error arising from the magnetic field gradient can be canceled at least to the third order. Examining the error as a function of the magnetic field gradient, we estimate the magnitude of fluctuation in the magnetic field gradient that can be tolerated under certain quantum error correction threshold.   

Composite pulse sequences for robust universal control of singlet-triplet qubits

We consider composite pulse sequences for the exchange interaction in singlet-triplet qubits, in the presence of a finite magnetic field gradient (producing a term in the Hamiltonian similar in magnitude to the exchange interaction). We find pulse sequences achieving arbitrary rotations on the Bloch sphere, for which there is no first-order term in the error arising from fluctuations of the magnetic field gradient. We quantify the range of experimental parameters where our composite sequences can outperform naive uncorrected sequences.   

Analytically solvable pulses for spin qubit rotations

The hyperbolic secant pulse is a well known pulse shape for which the time dependent Schrodinger equation of a two-level system is analytically solvable. It has in the past been proposed [1] for optical spin rotations in quantum dots, and used experimentally to that end [2]. In this talk, a family of pulses will be introduced which can be viewed as the generalization of the sech pulse. These pulses may have skewed temporal profiles and frequency modulation (``chirping''). I will present results for the fidelity of spin rotations using some of these pulses and show that in the case of ``Raman-type'' control, where an auxiliary excited state is used, it can be advantageous to replace the usual 2$\pi$ sech pulse. \\[4pt] [1] Economou et al., Phys. Rev. B \textbf{74}, 205415 (2006), Economou and Reinecke, Phys. Rev. Lett. \textbf{99}, 217401 (2007) \\[0pt] [2] Greilich et al., Nature Physics \textbf{5}, 262 (2009)   

Universal set of single-qubit gates based on geometric phase of electron spin in a quantum dot

The electron spin in a single quantum dot is one of the perspective realizations of a qubit for the implementation of a quantum computer. During last decade several control schemes to perform single gate operations on a single quantum dot spin have been reported. We propose a scheme that allows performing ultrafast arbitrary unitary operations on a single qubit. We demonstrate how to use the geometric phase, which the Bloch vector gains along the cyclic path, to prepare an arbitrary state of a single qubit. It is shown that, the geometrical phase is fully controllable by the relative phase between the external fields. Using the analytic expression of the evolution operator for the electron spin in a quantum dot, we propose a scheme to design a universal set of single-qubit gates based solely on the geometrical phase that the qubit state acquires after a cyclic evolution in the parameter space. The scheme is utilizing ultrafast linearly-chirped pulses providing adiabatic excitation of the qubit states and the geometric phase is fully controlled by the relative phase between pulses.   

A fast ``hybrid'' silicon double quantum dot qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers $S^2$ = 3/4 (S = 1/2) and $S_z$ = -1/2, with the two different states being singlet and triplet in the doubly occupied dot. The architecture is relatively simple to fabricate, a universal set of fast operations can be implemented electrically, and the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.   

Theory of Spin Relaxation in Two-Electron Lateral Coupled Quantum Dots

We present a global picture of the phonon-induced spin relaxation of two-electron lateral double quantum dots. The analysis covers a wide range of tuning parameters, such as the magnetic field, the exchange coupling, and the electric field (detuning). Our examples cover experimentally important scenarios. Quantitative results were obtained with a highly accurate numerical technique for the two most relevant host materials--GaAs and silicon. We find that in the presence of spin-orbit coupling, the rate becomes anisotropic and its maxima and minima are generated with an in-plane magnetic field parellel or perpendicular to the dots' alignment dependent on specifics, such as spectral (anti-)crossings (spin hot spots), or the detuning strength. For all regimes, we give qualitative explanations of our observations. By understanding the spin lifetimes ($T_1$), this work marks a crucial step to the realization of two-electron semiconductor qubits.   

Dephasing in lateral double quantum dot systems due to evanescent-wave Johnson noise

Lateral double quantum dots suffer decoherence due to coupling to the environment. Previous theoretical calculations of dephasing time based on the phonon bath model (Vorojtsov et al. PRB 71, 2005) and gate-voltage fluctuations (Valente et al. PRB 82, 2010) are insufficient to explain the short dephasing time observed in experiment with a charge-based double quantum dot system (Petta et al. PRL 93, 2004). Here we analyze the effect of fluctuating electromagnetic fields in the vicinity of conducting gates on the dephasing rate of charge-based double quantum dot systems.   

Spin relaxation times and spin-dependent transport of silicon 2DEG and donors in high magnetic fields

We measured the spin-lattice relaxation ($T_1$) and spin coherence ($T_2$) times of the two-dimensional electron gas (2DEG) and neutral donors in a silicon field-effect transistor by pulsed electrically detected magnetic resonance at $\approx3.4\:$T. The 2DEG $T_1$ varies between $\approx200-800\:$ns depending on the carrier density with an in-plane magnetic field configuration, but remains constant at $\approx400\:$ns with an out-of-plane field configuration. On the other hand, $T_2\approx50-150\:$ns for all carrier densities and both field orientations. The neutral donor $T_1$ and $T_2$ are found to be similar to that of the 2DEG. At even higher out-of-plane magnetic fields of $8-12\:$T, Landau levels are clearly resolved in transport measurements and both the 2DEG and donor EDMR signals show corresponding oscillatory behavior as the carrier density is varied. We attribute this behavior to the alignment of the Fermi level with spin-split and different indexed Landau levels.   

Two-electron dephasing in a single silicon quantum dot

We study the dephasing of two-electron states in a single silicon quantum dot. Specifically, we consider dephasing due to the electron-phonon coupling and charge noise, treating orbital, valley, and mixed valley-orbit excitations. For phonon-induced dephasing, the intervalley processes are most important and lead to a dephasing rate of about 1 MHz. In an ideal system, dephasing due to charge noise is strongly suppressed due to a vanishing dipole moment. However, introduction of disorder or anharmonicity leads to large effective dipole moments, and hence possibly strong dephasing.   

Long Spin Relaxation and Coherence Times of Electrons In Gated Si/SiGe Quantum Dots

Single electron spin states in semiconductor quantum dots are promising candidate qubits. We report the measurement of 250 $\mu $s relaxation (T$_{1})$ and coherence (T$_{2})$ times of electron spins in gated Si/SiGe quantum dots at 350 mK. The experiments used conventional X-band (10 GHz) pulsed electron spin resonance (pESR), on a large area (3.5 x 20 mm$^{2})$ dual-gate undoped high mobility Si/SiGe heterostructure sample, which was patterned with 2 x 10$^{8}$ quantum dots using e-beam lithography. Dots having 150 nm radii with a 700 nm period are induced in a natural Si quantum well by the gates. The measured T$_{1}$ and T$_{2}$ at 350 mK are much longer than those of free 2D electrons, for which we measured T$_{1}$ to be 10 $\mu $s and T$_{2 }$to be 6.5 $\mu $s in this gated sample. The results provide direct proof that the effects of a fluctuating Rashba field have been greatly suppressed by confining the electrons in quantum dots. From 0.35 K to 0.8 K, T$_{1}$ of the electron spins in the quantum dots shows little temperature dependence, while their T$_{2}$ decreased to about 150 $\mu $s at 0.8 K. The measured 350 mK spin coherence time is 10 times longer than previously reported for any silicon 2D electron-based structures, including electron spins confined in ``natural quantum dots'' formed by potential disorder at the Si/SiO$_{2}$\footnote{S. Shankar \textit{et al}., Phys. Rev. B 82, 195323 (2010)} or Si/SiGe interface, where the decoherence appears to be controlled by spin exchange.   

Creation of entangled exciton states in coupled quantum dots

Quantum state preparation through external control is fundamental to established methods in quantum information processing and in studies of dynamics. In this respect, systems such as excitons in semiconductor quantum dots (QDs) are of particular interest since they can be easily driven to a particular state through the coherent interaction with a tuned optical field such as an external laser pulse. Here we propose to use adiabatic rapid passage (ARP) to excite entangled states in an ensemble of coupled quantum systems. The ARP protocol makes use of optical pulses with both frequency and temporal modulation and it is an efficient method to achieve population inversion in quantum dot ensembles as it is robust with respect to fluctuations in coupling and detuning. We explore this problem using a generalized t-J Hamiltonian to model an interacting many-dot system described in terms of hard-core bosons. Our quantitative analysis shows that ARP can be successfully implemented to create entangled states in a realistic ensemble of inhomogeneously distributed QDs.