Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known results of the interplay of them are reproduced naturally. The prescription for separating the non-perturbative contribution from the perturbative is given in terms of the analytic continuation of the valley parameter. Our method is illustrated on a new series of examples with the asymmetric double-well potential. We obtain the non-perturbative part explicitly, which leads to the prediction of the large order behavior of the perturbative series. We calculate the first 200 perturbative coefficients for a wide range of parameters and confirm the agreement with the prediction of the valley method.
In this paper, we studied the inter-valley interactions between the orbital functions associated with multi-valley of silicon (Si) quantum dots. Numerical calculations show that the inter-valley coupling between orbital functions increases rapidly with an applied electric field. We also considered the potential applications to the quantum bit operation utilizing controlled inter-valley interactions. Quantum bits are the multi-valley symmetric and anti-symmetric orbitals. Evolution of these orbitals would be controlled by an external electric field which turns on and off the inter-valley intera…
In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a n…
The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small an…
Quantum dots in silicon are promising candidates for implementation of solid-state quantum information processing. It is important to understand the effects of the multiple conduction band valleys of silicon on the properties of these devices. Here we introduce a novel, systematic effective mass theory of valley-orbit coupling in disordered silicon systems. This theory reveals valley-orbit hybridization effects that are detrimental for storing quantum information in the valley degree of freedom, including non-vanishing dipole matrix elements between valley states and altered intervalley tunnel…
At the center of quantum computing1 realization is the physical implementation of qubits - two-state quantum information units. The rise of graphene2 has opened a new door to the implementation. Because graphene electrons simulate two-dimensional relativistic particles with two degenerate and independent energy valleys,3 a novel degree of freedom (d.o.f.), namely, the valley state of an electron, emerges as a new information carrier.4 Here, we expand the Loss-DiVincenzo quantum dot (QD) approach in electron spin qubits,5,6 and investigate the feasibility of double QD (DQD) structures in gapful…
We discuss the valley-orbit interaction (VOI) and the concept of VOI based valleytronics. Potential of such valleytronics is illustrated, with graphene as an example material, in several frontier applications comprising FETs, quantum computing, and quantum communications. Two important devices are discussed as examples, namely, 1) valley pair qubits in coupled graphene quantum dots, to build quantum networks consisting of graphene and photons, and 2) valleybased FETs consisting of graphene quantum wires (channels) and armchair graphene nanoribbons (sources and drains), to build graphene-based,…
Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted in silicon quantum wells due to strain and electronic confinement, but the "valley splitting" of the two lowest lying valleys is known to be sensitive to atomic-scale disorder. Large valley splittings are desirable to have a well-defined spin qubit. In addition, an understanding of the inter-valley tunnel coupling that couples different valleys in …
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 rotation…
The electron-photon interaction in 2D materials obeys the rule of electron valley-photon polarization correspondence. At the quantum level, such correspondence can be utilized to entangle valleys and polarizations and attain the transfer of quantum states (or information) between valley and photon qubits. Our work presents a theoretical study of the interaction between the two types of qubits and the resultant quantum state transfer. A generic setup is introduced, which involves optical cavities enhancing the electron-photon interaction as well as facilitating both the entanglement and un-enta…
We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field $B$ and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with $B$ and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density $eB/h$ across q…
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 temperature or applying a finite source-drain bias across the DQD, resulting in an increased signal. Using cavity input-output theory and a four-level model of the DQD, it is possible to efficiently extract valley splittings and the inter- and intra-valley tunnel coup…
Valley-orbit coupling is a key parameter for a silicon quantum dot in determining its suitability for applications in quantum information processing. In this paper we study the effect of interface steps on the magnitude and phase of valley-orbit coupling for an electron in a silicon quantum dot. Within the effective mass approximation, we find that the location of a step on the interface is important in determining both the magnitude and the phase of the valley-orbit coupling in a Si/SiGe quantum dot. Specifically, our numerical results show that the magnitude of valley orbit coupling can be s…
Multi-valley effective mass theory for silicon quantum well structure is studied taking into account the external fields and the quantum interfaces. It is found that the phenomenological delta function potential, employed to explain the valley splitting caused by the quantum well interface in the previous work [Ref. 10], can be derived self-consistently from the multi-valley effective mass theory. Finite element method is used to solve the multi-valley effective equations. Theoretical predictions are in a reasonably good agreement with the recent experimental observation of valley splitting in…
We study the relaxation of an electron spin qubit in a Si quantum dot due to electrical noise. In particular, we clarify how the presence of conduction-band valleys influences 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 the additional spin relaxation channel, via spin-valley mixing and electrical noise, is indeed important for an electron spin in a Si quantum dot. By considering bot…
Topological photonics has been introduced as a powerful platform for integrated optics, since it can deal with robust light transport, and be further extended to the quantum world. Strikingly, valley-contrasting physics in topological photonic structures contributes to valley-related edge states, their unidirectional coupling, and even valley-dependent wave-division in topological junctions. Here, we design and fabricate nanophotonic topological harpoon-shaped beam splitters (HSBSs) based on $120$-deg-bending interfaces and demonstrate the first on-chip valley-dependent quantum information pro…
The energies of valley-orbit states in silicon quantum dots are determined by an as yet poorly understood interplay between interface roughness, orbital confinement, and electron interactions. Here, we report measurements of one- and two-electron valley-orbit state energies as the dot potential is modified by changing gate voltages, and we calculate these same energies using full configuration interaction calculations. The results enable an understanding of the interplay between the physical contributions and enable a new probe of the quantum well interface.
We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes, or silicon, and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of the valley degeneracy in the electronic band structure alters the form of the exchange coupling and in general leads to spin-valley entanglement. Here, we show t…
Electron spins in silicon quantum dots are excellent qubits because they have long coherence times, high gate fidelities, and are compatible with advanced semiconductor manufacturing techniques. The valley degree of freedom, which results from the specific character of the Si band structure, is a unique feature of electrons in Si spin qubits. However, the small difference in energy between different valley levels often poses a challenge for quantum computing in Si. Here, we show that the spin-valley coupling in Si, which enables transitions between states with different spin and valley quantum…
Silicon quantum dot qubits must contend with low-lying valley excited states which are sensitive functions of the quantum well heterostructure and disorder; quantifying and maximizing the energies of these states are critical to improving device performance. We describe a spectroscopic method for probing excited states in isolated Si/SiGe double quantum dots using standard baseband pulsing techniques, easing the extraction of energy spectra in multiple-dot devices. We use this method to measure dozens of valley excited state energies spanning multiple wafers, quantum dots, and orbital states, …
Giant-atom-enabled quantum optics with valley-polarized photons
Quantum Advanced Research Center (QuARC), CSIC（量子先进研究中心 (QuARC)，西班牙国家科学研究委员会）；Institute of Fundamental Physics (IFF), CSIC（基础物理研究所 (IFF)，西班牙国家科学研究委员会）；National Institute of Optics (CNR-INO)（意大利国家光学研究所 (CNR-INO)）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室 (LENS)）
Recent experiments on silicon nanostructures have seen breakthroughs toward scalable, long-lived quantum information processing. The valley degree of freedom plays a fundamental role in these devices, and the two lowest-energy electronic states of a silicon quantum dot can form a valley qubit. In this work, we show that a single-atom high step at the silicon/barrier interface induces a strong interaction of the qubit and in-plane electric fields, and analyze the consequences of this enhanced interaction on the dynamics of the qubit. The charge densities of the qubit states are deformed differe…
The presence of non-degenerate valley states in silicon can drastically affect electron dynamics in silicon-based heterostructures, leading to electron spin relaxation and spin-valley coupling. In the context of solid-state spin qubits, it is important to understand the interplay between spin and valley degrees of freedom to avoid or alleviate these decoherence mechanisms. Here we report the observation of relaxation from the excited valley state to the ground state in a Si/SiGe quantum dot, at zero magnetic field. Valley state read-out is aided by a valley-dependent tunneling effect, which we…
Silicon-based metal-oxide-semiconductor quantum dots are prominent candidates for high-fidelity, manufacturable qubits. Due to silicon's band structure, additional low-energy states persist in these devices, presenting both challenges and opportunities. Although the physics governing these valley states has been the subject of intense study, quantitative agreement between experiment and theory remains elusive. Here, we present data from a new experiment probing the valley states of quantum dot devices and develop a theory that is in quantitative agreement with both the new experiment and a rec…
Confinement drives valley splitting above 4K in buried silicon quantum wells
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克研究所与卡弗里纳米科学研究所）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）
The topological valley Hall effect was predicted as a consequence of the bulk topology of electronic systems. Now it has been observed in photonic crystals, showing that both topology and valley are innate to classical as well as quantum systems. The discovery of counterflow in opposite valleys not only demonstrates that the valley can be a novel carrier of information and energy --- particularly valuable for systems without charge and spin --- but also exemplifies that symmetry-protected band topology can be universal to both quantum and classical systems.
