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The spin degrees of freedom is crucial for the understanding of any condensed matter system. Knowledge of spin-mixing mechanisms is not only essential for successful control and manipulation of spin qubits, but also uncovers fundamental properties of investigated devices and material. For electrostatically defined bilayer graphene quantum dots, in which recent studies report spin-relaxation times T_{1} up to 50 ms with strong magnetic field dependence, we study spin-blockade phenomena at charge configuration (1,2)↔(0,3). We examine the dependence of the spin-blockade leakage current on interdot tunnel coupling and on the magnitude and orientation of externally applied magnetic field. In out-of-plane magnetic field, the observed zero-field current peak could arise from finite-temperature cotunneling with the leads; though involvement of additional spin- and valley-mixing mechanisms are necessary for explaining the persistent sharp side peaks observed. In in-plane magnetic field, we observe a zero-field current dip, attributed to the competition between the spin Zeeman effect and the Kane-Mele spin-orbit interaction. Details of the line shape of this current dip, however, suggest additional underlying mechanisms are at play.

Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and 1/f^{α} noise in more detail. Additionally, we propose a way of extracting the noise power spectral density in a frequency band only bounded by the range of the qubit-cavity detuning and with an exponentially decaying error due to finite measurement times. Our results suggest that measurements of the time-dependent transmission probability represent a novel way of extracting noise characteristics.

The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by coherent-field driving in a thin nonlinear crystal with second-order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. They can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides results in spin-valley coupled band structures. Such a band structure leads to novel applications in the fields of electronics and optoelectronics. Density functional theory calculations as well as optical experiments have focused on spin-valley coupling in the valence band. Here we present magnetotransport experiments on high-quality n-type monolayer molybdenum disulphide (MoS_{2}) samples, displaying highly resolved Shubnikov-de Haas oscillations at magnetic fields as low as 2 T. We find the effective mass 0.7m_{e}, about twice as large as theoretically predicted and almost independent of magnetic field and carrier density. We further detect the occupation of the second spin-orbit split band at an energy of about 15 meV, i.e., about a factor of 5 larger than predicted. In addition, we demonstrate an intricate Landau level spectrum arising from a complex interplay between a density-dependent Zeeman splitting and spin- and valley-split Landau levels. These observations, enabled by the high electronic quality of our samples, testify to the importance of interaction effects in the conduction band of monolayer MoS_{2}.

We propose a quadrupolar exchange-only spin qubit that is highly robust against charge noise and nuclear spin dephasing, the dominant decoherence mechanisms in quantum dots. The qubit consists of four electrons trapped in three quantum dots, and operates in a decoherence-free subspace to mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise, the qubit can be completely operated at an extended charge noise sweet spot that is first-order insensitive to electrical fluctuations. Because of on-site exchange mediated by the Coulomb interaction, the qubit energy splitting is electrically controllable and can amount to several GHz even in the "off" configuration, making it compatible with conventional microwave cavities.

We study an accumulation mode Si/SiGe double quantum dot (DQD) containing a single electron that is dipole coupled to microwave photons in a superconducting cavity. Measurements of the cavity transmission reveal dispersive features due to the DQD valley states in Si. The occupation of the valley states can be increased by raising the temperature or applying a finite source-drain bias across the DQD, resulting in an increased signal. Using the cavity input-output theory and a four-level model of the DQD, it is possible to efficiently extract valley splittings and the inter- and intravalley tunnel couplings.

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

The valley degree of freedom in the electronic band structure of silicon, graphene, and other materials is often considered to be an obstacle for quantum computing (QC) based on electron spins in quantum dots. Here we show that control over the valley state opens new possibilities for quantum information processing. Combining qubits encoded in the singlet-triplet subspace of spin and valley states allows for universal QC using a universal two-qubit gate directly provided by the exchange interaction. We show how spin and valley qubits can be separated in order to allow for single-qubit rotations.

We study finite-time Landau-Zener transitions at a singlet-triplet level crossing in a GaAs double quantum dot, both experimentally and theoretically. Sweeps across the anticrossing in the high driving speed limit result in oscillations with a small visibility. Here we demonstrate how to increase the oscillation visibility while keeping sweep times shorter than T(2)(*) using a tailored pulse with a detuning dependent level velocity. Our results show an improvement of a factor of ~2.9 for the oscillation visibility. In particular, we were able to obtain a visibility of ~0.5 for Stückelberg oscillations, which demonstrates the creation of an equally weighted superposition of the qubit states.

We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spin-mechanical coupling allows for detection, as well as manipulation of the spin qubit, and may yield enhanced performance of nanotubes in sensing applications.

We propose a scheme for coherent rotation of the valley isospin of a single electron confined in a carbon nanotube quantum dot. The scheme exploits the ubiquitous atomic disorder of the nanotube crystal lattice, which induces time-dependent valley mixing as the confined electron is pushed back and forth along the nanotube axis by an applied ac electric field. Using experimentally determined values for the disorder strength we estimate that valley Rabi oscillations with a period on the nanosecond time scale are feasible. The valley resonance effect can be detected in the electric current through a double quantum dot in the single-electron transport regime., (© 2011 American Physical Society)

We propose and analyze a technique for producing a beam-splitting quantum gate between two modes of a ring-resonator superconducting cavity. The cavity has two integrated superconducting quantum interference devices (SQUIDs) that are modulated by applying an external magnetic field. The gate is accomplished by applying a radio frequency pulse to one of the SQUIDs at the difference of the two mode frequencies. Departures from perfect beam splitting only arise from corrections to the rotating wave approximation; an exact calculation gives a fidelity of >0.9992. Our construction completes the toolkit for linear-optics quantum computing in circuit quantum electrodynamics.

We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level anticrossing with alternating slow and rapid sweeps of an external bias voltage. Using a Landau-Zener-Stückelberg model, we find that in addition to a small nuclear polarization that weakly affects the electron spin coherence, the slow sweeps are only partially adiabatic and lead to a weak nuclear spin measurement and a nuclear-state narrowing which prolongs the electron spin coherence. This resolves some open problems brought up by a recent experiment [D. J. Reilly, Science 321, 817 (2008).10.1126/science.1159221]. Based on our description of the weak measurement, we simulate a system with up to n=200 nuclear spins per dot. Scaling in n indicates a stronger effect for larger n.

We study dc charge and spin transport through a weakly coupled quantum dot, driven by a nonadiabatic periodic change of system parameters. We generalize the model of Tien and Gordon to simultaneously oscillating voltages and tunnel couplings. When applying our general result to the two-parameter charge pumping in quantum dots, we find interference effects between the oscillations of the voltage and tunnel couplings. We show that these interference effects may explain recent measurements in metallic islands. Furthermore, we discuss the possibility to electrically pump a spin current in presence of a static magnetic field.

We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.

We determine a lower bound for the entanglement of formation of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross correlators) after transmission through an electronic beam splitter and can be used to gain information about the entanglement from experiment. Spin relaxation (T1 processes) and decoherence (T2) during the ballistic coherent transmission of carriers are taken into account within Bloch theory. A variable inhomogeneous magnetic field gives rise to a useful lower bound for the entanglement of arbitrary states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and T(1,2) can be determined from current correlators.

We study shot noise for spin-polarized currents and entangled electron pairs in a four-probe (beam-splitter) geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. Within the scattering formalism we find that shot noise exhibits Rashba-induced oscillations with continuous bunching and antibunching. We show that entangled states and triplet states can be identified via their Rashba phase in noise measurements. For two-channel leads, we find an additional spin rotation due to s-o induced interband coupling which enhances spin control. We show that the s-o interaction deter-mines the Fano factor, which provides a direct way to measure the Rashba coupling constant via noise.

We study the effect of the spin-orbit interaction on quantum gate operations based on the spin exchange coupling where the qubit is represented by the electron spin in a quantum dot or a similar nanostructure. Our main result is the exact cancellation of the spin-orbit effects in the sequence producing the quantum XOR gate for the ideal case where the pulse shapes of the exchange and spin-orbit interactions are identical. For the nonideal case, the two pulse shapes can be made almost identical and the gate error is strongly suppressed by two small parameters, the spin-orbit constant and the deviation of the two pulse shapes. We show that the dipole-dipole interaction leads only to very small errors in the XOR gate.