Spin-based Quantum Information Processing Research Articles

Controlling the quantum dynamics of a mesoscopic spin bath in diamond.

Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.

Electrically tuned spin–orbit interaction in an InAs self-assembled quantum dot

Electrical control over electron spin is a prerequisite for spintronics spin-based quantum information processing. In particular, control over the interaction between the orbital motion and the spin state of electrons would be valuable, because this interaction influences spin relaxation and dephasing. Electric fields have been used to tune the strength of the spin-orbit interaction in two-dimensional electron gases, but not, so far, in quantum dots. Here, we demonstrate that electrical gating can be used to vary the energy of the spin-orbit interaction in the range 50-150 µeV while maintaining the electron occupation of a single self-assembled InAs quantum dot. We determine the spin-orbit interaction energy by observing the splitting of Kondo effect features at high magnetic fields.

Many-body singlets by dynamic spin polarization

We show that dynamic spin polarization by collective raising and lowering operators can drive a spin ensemble from arbitrary initial state to many-body singlets, the zero-collective-spin states with large scale entanglement. For an ensemble of $N$ arbitrary spins, both the variance of the collective spin and the number of unentangled spins can be reduced to O(1) (versus the typical value of O(N)), and many-body singlets can be occupied with a population of $\sim 20 %$ independent of the ensemble size. We implement this approach in a mesoscopic ensemble of nuclear spins through dynamic nuclear spin polarization by an electron. The result is of two-fold significance for spin quantum technology: (1) a resource of entanglement for nuclear spin based quantum information processing; (2) a cleaner surrounding and less quantum noise for the electron spin as the environmental spin moments are effectively annihilated.

Spin electric effects in molecular antiferromagnets

Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling in triangular molecules is governed by the modification of the exchange interaction, and is possible even in the absence of spin-orbit coupling. In pentagonal molecules the spin-electric coupling can exist only in the presence of spin-orbit interaction. This kind of coupling is allowed for both $s=1/2$ and $s=3/2$ spins at the magnetic centers. Within the Hubbard model, we find a relation between the spin-electric coupling and the properties of the chemical bonds in a molecule, suggesting that the best candidates for strong spin-electric coupling are molecules with nearly degenerate bond orbitals. We also investigate the possible experimental signatures of spin-electric coupling in nuclear magnetic resonance and electron spin resonance spectroscopy, as well as in the thermodynamic measurements of magnetization, electric polarization, and specific heat of the molecules.

Properties of the Shannon entropy of arrays of elastic scatterers

Recently, we used an effective spin concept to expound the analogy between spin-based quantum information processing and phase coherent charge transport through an array of elastic scatterers. Here, we extend that analogy by calculating an effective Shannon entropy for such an array and examining its various properties. For single-moded transport, the Shannon entropy is given by H bin ( | t | 2 ) = − | t | 2 log 2 | t | 2 − | r | 2 log 2 | r | 2 , where | t | 2 and | r | 2 are the transmission and reflection probabilities through the array of scatterers. A lower bound for H bin ( | t | 2 ) is found starting with the entropic quantum uncertainty principle. An important result is that although evanescent channels (modes) have | t | 2 = 1 − | r | 2 → 0 , so that their own contribution to H bin ( | t | 2 ) → 0 , they nevertheless have a profound influence on the total H bin ( | t | 2 ) of the array and its associated signal-to-noise ratio (SNR) since they renormalize the transmission probabilities of the propagating modes. This is reminiscent of the well-known fact that evanescent modes influence the conductance of a structure by renormalizing the transmission probabilities of the propagating modes. The numerical values of H bin ( | t | 2 ) and its SNR are strongly sensitive to the nature of the elastic scatterers, i.e., whether they are attractive (negative potential), repulsive (positive potential), or a combination of both. In samples with repulsive scatterers, the SNR can be tuned over a wide range by applying a potential through a gate to change the scattering potentials from repulsive to attractive by moving their energy levels with respect to the quasi-Fermi level in the sample. We also found that the mean free path of an electron traversing a random array of elastic scatterers is the length scale at which the sum of the cross-correlation coefficients of the effective spin components reaches a minimum. At that point, the sum of the effective Heisenberg and Zeeman Hamiltonians associated with effective spins describing the propagating channels, reaches a minimum. Hence the mean free path can be viewed as an order parameter for a phase transition.

Exact canonical decomposition of two-qubit operators in terms of CNOT

The canonical decomposition for two-qubit operators has proven very useful for applications in quantum computing. This decomposition generates equivalence classes up to local quantum gates. We provide a variety of complete, explicit decompositions of given two-qubit operators in terms of single, double, and triple controlled-NOT (CNOT) gates. By analytically addressing the needed pre- and post-tensor product factors, we demonstrate that exact results are possible, even when a parameter is included. The examples given are of interest to superconducting qubit, spin-based, dipolar molecule, and other quantum information processing systems.

An electron's spin---Part I

In Part I of this article, we introduced the notion of encoding binary bit information in the spin polarization of a single electron confined in a quantum dot and placed in a magnetic field. The spin polarization becomes bistable in a magnetic field and the spin can point either parallel to the field or antiparallel to it. These two polarizations encode the classical binary bits 0 and 1. We showed that since the bits can be switched by simply flipping the electron's spin without physically moving the electron in space and causing a current, the energy dissipated during the bit flip operation could be made very small. In Part II we discuss the notion of using a single electron's spin as a quantum bit (or qubit) that represents information in quantum computers. Just as spin is superior to charge as a vehicle to host classical bit information in classical computers it turns out that spin is superior to charge to host quantum information as well. That is why spin-based quantum information processing is gradually becoming the staple of scalable solid state versions of quantum computers.

Electron–nuclear interaction in 13C nanotube double quantum dots

Hyperfine coupling to nuclei can be detrimental to the coherence of electron spins, but properly harnessed it can provide a mechanism for manipulation and storage of quantum information. Spin-blockade measurements in 13C carbon nanotubes now show surprisingly strong effects of electron–nuclear interaction, with a hyperfine coupling two orders of magnitude larger than previously anticipated. For coherent electron spins, hyperfine coupling to nuclei in the host material can either be a dominant source of unwanted spin decoherence1,2,3 or, if controlled effectively, a resource enabling storage and retrieval of quantum information4,5,6,7. To investigate the effect of a controllable nuclear environment on the evolution of confined electron spins, we have fabricated and measured gate-defined double quantum dots with integrated charge sensors made from single-walled carbon nanotubes with a variable concentration of 13C (nuclear spin I=1/2) among the majority zero-nuclear-spin 12C atoms. We observe strong isotope effects in spin-blockaded transport, and from the magnetic field dependence estimate the hyperfine coupling in 13C nanotubes to be of the order of 100 μeV, two orders of magnitude larger than anticipated8,9. 13C-enhanced nanotubes are an interesting system for spin-based quantum information processing and memory: the 13C nuclei differ from those in the substrate, are naturally confined to one dimension, lack quadrupolar coupling and have a readily controllable concentration from less than one to 105 per electron.

Controlled measurement processes: Simple spin-chain model of controlled quantum-state amplification

Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of ``Schr\odinger cat'' states.

Spin polarization control via magnetic barriers and spin-orbit effects

We investigate the spin-dependent transport properties of two-dimensional electron gas (2DEG) systems formed in diluted magnetic semiconductors and in the presence of Rashba spin-orbit interaction in the framework of the scattering matrix approach. We focus on nanostructures consisting of realistic magnetic barriers produced by the deposition of ferromagnetic strips on heterostructures. We calculate spin-dependente conductance of such barrier systems and show that the magnetization pattern of the strips, the tunable spin-orbit coupling, and the enhanced Zeeman splitting have a strong effect on the conductance of the structure. We describe how these effects can be employed in the efficient control of spin polarization via the application of moderate fields. PACS numbers: 71.70.Ej, 73.23.Ad, 72.25.-b, 72.10.-d Spin-orbit coupling in semiconductors intrinsically connects the spin of an electron to its momentum, 1 providing a pathway for electrically initializing and manipulating electron spins for applications in spintronics 2,3 and spin-based quantum information processing. 4 This coupling can be regulated with quantum confinement in semiconductor heterostructures through band structure engineering, as well as by the application of external electric fields, as in the celebrated spin field-effect transistor proposed by Datta and Das. 5 Using diluted magnetic semiconductors (DMS) in such systems provides an additional degree of control of the transport properties. In particular, when an external magnetic field is applied, the magnetic dopant spins align, giving rise to a strong exchange field that acts on the electron spin. This sd exchange interaction between the electron spin in the conduction band and the localized magnetic ions induces a giant Zeeman splitting. In this communication we investigate the spindependent transport properties of two-dimensional electron gas (2DEG) systems formed in diluted magnetic semiconductors and take into account the electric-field– dependent Rashba spin-orbit (SOI) interaction. We focus our attention on nanostructures consisting of realistic magnetic barriers produced by the deposition of ferromagnetic strips near the heterostructures, 6 providing a relatively strong inhomogeneous magnetic field on the 2DEG. We show how the conductance of the 2DEG depends strongly on the magnetization pattern of the strips, as well as on geometry and externally applied electric fields. We demonstrate that significant spin polarization (exceeding 50%) can be obtained at low temperatures for ferromagnetic strips of typical dimensions and magnetization.

Measurement and noise performance of nano-superconducting-quantum-interference devices fabricated by focused ion beam

Science and industry demand ever more sensitive measurements on ever smaller systems, as exemplified by spintronics, nanoelectromechanical system, and spin-based quantum information processing, where single electronic spin detection poses a grand challenge. Superconducting quantum interference devices (SQUIDs) have yet to be effectively applied to nanoscale measurements. Here, we show that a simple bilayer deposition route, combining photolithography with focused ion beam patterning, produces high performance nanoscale SQUIDs. We present results of noise measurements on these nanoSQUIDs which correspond to a magnetic flux sensitivity of around 0.2μΦ0∕Hz1∕2. This represents one of the lowest noise values achieved for a SQUID device operating above 1K.

Pauli-spin-blockade transport through a silicon double quantum dot

We present measurements of resonant tunneling through discrete energy levels of a silicon double quantum dot formed in a thin silicon-on-insulator layer. In the absence of piezoelectric phonon coupling, spontaneous phonon emission with deformation-potential coupling accounts for inelastic tunneling through the ground states of the two dots. Such transport measurements enable us to observe a Pauli spin blockade due to effective two-electron spin-triplet correlations, evident in a distinct bias-polarity dependence of resonant tunneling through the ground states. The blockade is lifted by the excited-state resonance by virtue of efficient phonon emission between the ground states. Our experiment demonstrates considerable potential for investigating silicon-based spin dynamics and spin-based quantum information processing.

Spin qubits in antidot lattices

We suggest and study designed defects in an otherwise periodic potential modulation of a two-dimensional electron gas as an alternative approach to electron spin based quantum information processing in the solid-state using conventional gate-defined quantum dots. We calculate the band structure and density of states for a periodic potential modulation, referred to as an antidot lattice, and find that localized states appear, when designed defects are introduced in the lattice. Such defect states may form the building blocks for quantum computing in a large antidot lattice, allowing for coherent electron transport between distant defect states in the lattice, and for a tunnel coupling of neighboring defect states with corresponding electrostatically controllable exchange coupling between different electron spins.

GENERATING and MANIPULATING SPINS IN SEMICONDUCTORS

Spin-orbit coupling in semiconductors relates the spin of an electron to its momentum, and provides a pathway for electrically initializing and manipulating electron spins for applications in spintronics and spin-based quantum information processing. This coupling can be regulated with strain in bulk semiconductors and quantum confinement in semiconductor heterostructures. We will provide an overview of optical studies exploring spin dynamics in conventional and magnetic semiconductors, followed by recent experiments probing all-electrical generation and manipulation of spins. Using Faraday and Kerr rotation magneto-optical spectroscopies with temporal and spatial resolution, current-induced spin polarization1 and the spin Hall effect2 have been observed using both spatially-resolved and temporally-resolved techniques in bulk semiconductors. More recently, we have investigated the spin Hall effect and current-induced spin polarization in two-dimensional electron gases confined in (110) AlGaAs quantum wells using Kerr rotation microscopy.3 In marked contrast to previous measurements in three dimensional systems, the spin Hall profile in two dimensions shows a surprisingly complex structure and the current-induced spin polarization is out-of-plane. The experiments map the strong dependence of the current-induced spin polarization to the crystal axis along which the electric field is applied, reflecting the anisotropy of the spin-orbit interaction. The effect of reducing feature sizes in electrical spintronic devices is relevant for future technological applications. To this end, we discuss related measurements probing electron spin dynamics in narrow two-dimensional InGaAs quantum well wires with widths ranging from the micron to the submicron scale.4 The data reveal a surprising slowing of the electron spin relaxation in reduced geometries. These results reveal opportunities for tuning a spin source using quantum confinement, strain and device engineering in non-magnetic materials. This work was supported by the ARO, DARPA, NSF and ONR. Note from Publisher: This article contains the abstract only.

CONTROLLING SPIN COHERENCE WITH SEMICONDUCTOR NANOSTRUCTURES

We present two emerging opportunities for manipulating and communicating coherent spin states in semiconductors. First, we show that semiconductor microcavities offer unique means of controlling light-matter interactions in confined geometries, resulting in a wide range of applications in optical communications and inspiring proposals for quantum information processing and computational schemes. Studies of spin dynamics in microcavities — a new and promising research field — have revealed novel effects such as polarization beats, stimulated spin scattering, and giant Faraday rotation. Here, we study the electron spin dynamics in optically-pumped GaAs microdisk lasers with quantum wells and interface-fluctuation quantum dots in the active region. In particular, we examine how the electron spin dynamics are modified by the stimulated emission in the disks, and observe an enhancement of the spin coherence time when the optical excitation is in resonance with a high quality ( Q ~ 5000) lasing mode.1 This resonant enhancement, contrary to expectations from the observed trend in the carrier recombination time, is then manipulated by altering the cavity design and dimensions. In analogy to devices based on excitonic coherence, this ability to engineer coherent interactions between electron spins and photons may provide novel pathways towards spin dependent quantum optoelectronics. In a second example, the nitrogen-vacancy (N-V) center in diamond has garnered interest as a room-temperature solid-state system not only for exploring electronic and nuclear spin phenomena but also as a candidate for spin-based quantum information processing. Spin coherence times of up to 50 microseconds have been reported for ensembles of N-V centers and a two-qubit gate utilizing the electron spin of a N-V center and the nuclear spin of a nearby C-13 atom has been demonstrated. Here, we present experiments using angle-resolved magneto-photoluminescence microscopy to investigate anisotropic spin interactions of single N-V centers in diamond at room temperature.2 Negative peaks in the photoluminescence intensity are observed as a function of both magnetic field magnitude and angle, and can be explained by coherent spin precession and anisotropic relaxation at spin-level anticrossings. Additionally, precise field alignment with the symmetry axis of a single N-V center reveals the resonant magnetic dipolar coupling of a single "bright" electron spin of an N-V center to small numbers of "dark" spins of nitrogen defects in its immediate vicinity, which are otherwise undetected by photoluminescence. Most recently, we are exploring the possibility of utilizing this magnetic dipole coupling between bright and dark spins to couple two spatially separated single N-V center spins by means of intermediate nitrogen spins. Note from Publisher: This article contains the abstract only.

Coherent Control of a Single Electron Spin with Electric Fields

Manipulation of single spins is essential for spin-based quantum information processing. Electrical control instead of magnetic control is particularly appealing for this purpose, because electric fields are easy to generate locally on-chip. We experimentally realized coherent control of a single-electron spin in a quantum dot using an oscillating electric field generated by a local gate. The electric field induced coherent transitions (Rabi oscillations) between spin-up and spin-down with 90 degrees rotations as fast as approximately 55 nanoseconds. Our analysis indicated that the electrically induced spin transitions were mediated by the spin-orbit interaction. Taken together with the recently demonstrated coherent exchange of two neighboring spins, our results establish the feasibility of fully electrical manipulation of spin qubits.

Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.

Continuous Measurement of a Microwave-Driven Solid State Qubit

We analyze the dynamics of a continuously observed, damped, microwave-driven solid state charge qubit, consisting of a single electron in a double well potential. The microwave field induces transitions between the qubit eigenstates, which have a profound effect on the detector output current. Useful information about the qubit dynamics, such as dephasing and relaxation rates, and the Rabi frequency, can be extracted from the detector conductance and output noise power spectrum. We also propose a technique for single-shot electron spin readout, for spin based quantum information processing, which has a number of practical advantages over existing schemes.

Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases

Spin-orbit coupling in semiconductors relates the spin of an electron to its momentum and provides a pathway for electrically initializing and manipulating electron spins for applications in spintronics and spin-based quantum information processing. This coupling can be regulated with quantum confinement in semiconductor heterostructures through band structure engineering. Here we investigate the spin Hall effect and current-induced spin polarization in a two-dimensional electron gas confined in (110) AlGaAs quantum wells using Kerr rotation microscopy. In contrast to previous measurements, the spin Hall profile exhibits complex structure, and the current-induced spin polarization is out-of-plane. The experiments map the strong dependence of the current-induced spin polarization to the crystal axis along which the electric field is applied, reflecting the anisotropy of the spin-orbit interaction. These results reveal opportunities for tuning a spin source using quantum confinement and device engineering in non-magnetic materials.

Spin-Based Quantum Information Processing in Magnetic Quantum Dots

We define the qubit as a pair of singlet and triplet states of two electrons in a He-type quantum dot (QD) placed in a diluted magnetic semiconductor (DMS) medium. The molecular field is here essential as it removes the degeneracy of the triplet state and strongly enhances the Zeeman splitting. Methods of qubit rotation as well as two-qubit operations are suggested. The system of a QD in a DMS is described in a way which allows an analysis of the decoherence due to spin waves in the DMS subsystem.