Thermodynamic effects of single-qubit operations in silicon-based quantum computing

Silicon-based quantum logic is a promising technology to implement universal quantum computing. It is widely believed that a millikelvin cryogenic environment will be necessary to accommodate silicon-based qubits. This prompts a question of the ultimate scalability of the technology due to finite cooling capacity of refrigeration systems. In this work, we answer this question by studying energy dissipation due to interactions between nuclear spin impurities and qubit control pulses. We demonstrate that this interaction constrains the sustainable number of single-qubit operations per second for a given cooling capacity.     

Hierarchy of equations for reduced density matrices in the case of thermodynamic equilibrium

A hierarchy of equations for s-particle density matrices at thermodynamic equilibrium is obtained, with the equation for the nonequilibrium density matrix as the starting point. When deducing the hierarchy the hypothesis of maximum statistical independence for the density matrices is used. The hierarchy obtained is an analogue of the classical equilibrium BBGKY hierarchy and goes over into it when . It is shown that thermodynamic quantities can be expressed in terms of functions that enter only into the first hierarchy equations. The hierarchy is analysed in detail in the case of a uniform fluid. As an example in which the equations can be solved easily enough, a hard-sphere system wherein triplet correlations are neglected is considered. Different approximations that can be used when solving the equations derived are discussed. Comparisons are made with the results of other theoretical treatments.     

Quantum Groups GLp,q(2)- and $\mathit{SU}_{q_{1}/q_{2}}(2)$ -Invariant Bosonic Gases: A Comparative Study

We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries: GL _p,q (2) and . We establish the nature of the basic numbers which follow from these GL _p,q (2)- and -invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic and high-temperature thermo-statistical properties.     

Reaction kinetic model of height selection in heteroepitaxial growth of quantum dots

A reaction kinetic model is proposed for height selection of heteroepitaxially growing nanometer-thick quantum dots. The model describes the growth by a set of rate equations for the combined size and height distributions of the dots. In addition to nucleation and growth, the model includes a coarse-grained conversion rate incorporating kinetics of height changes. With suitably chosen rate coefficients the model reproduces qualitatively the experimentally observed height-selected size distributions and their evolution. The results support the view that the height selection and the form of the size distribution both result from the oscillating energy barrier for the transformation of dots of different heights, and this transformation barrier is considerably larger in magnitude than oscillations in the electronic energy due to quantum well states in the dot.     

Extensivity and the thermodynamic limit: Why size really does matter

The thermodynamic limit and extensivity are central concepts in thermodynamics. In this paper, these are critically examined in light of systems for which they appear inadequate. It is found that their limitations lead to counterintuitive thermodynamic results involving heat flow, phase separations, thermostatistics of gravitating systems and the conversion efficiency of heat into work. Ultimately, these limitations are shown to bear on the utility of entropy and the universality of the second law of thermodynamics.     

The carrier “antibinding” in quantum dots: a charge separation effect

We show that the carrier “antibinding” observed recently in semiconductor quantum dots, i.e., the fact that the ground state energy of two electron-hole pairs goes above twice the ground-state energy of one pair, can entirely be assigned to a charge separation effect, whatever its origin. In the absence of external electric field, this charge separation comes from different “spreading-out” of the electron and hole wavefunctions linked to the finite height of the barriers. When the dot size shrinks, the two-pair energy always stays below when the barriers are infinite. On the opposite, because barriers are less efficient for small dots, the energy of two-pairs in a dot with finite barriers, ends by behaving like the one in bulk, i.e., by going above twice the one-pair energy when the pairs get too close. For a full understanding of this “antibinding” effect, we have also reconsidered the case of one pair plus one carrier. We find that, while the carriers just have to spread out of the dot differently for the “antibinding” of two-pairs to appear, this “antibinding” for one pair plus one carrier only appears if this carrier is the one which spreads out the less. In addition a remarkable sum rule exists between the “binding energies” of two pairs and of one pair plus one carrier.     

Current in a quantum driven thermostatted system with off-diagonal disorder

We analyze a one dimensional quantum model with off-diagonal disorder, consisting of a sequence of potential energy barriers whose width is a random variable either uniformly or “half-normally” distributed, subjected to an external electric field. We shed light on how the microscopic disorder affects the value of the transmission coefficient and on the structure of the fluctuations around the solutions corresponding to the regular lattice configuration. We also characterize the asymptotic limit obtained by letting the number of barriers diverge. Thus, we explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature and also evidence the onset of a large deviation principle for the transmission coefficient.     

Size selected growth of nanodots: effects of growth kinetics and energetics on the formation of stationary size distributions

The size selection of nanodots during the growth is studied by using a reaction kinetic model, where reaction rates depend on the dot size. The characteristic feature of the reaction rates is the energetics, where the free energy of dots has a minimum at the certain dot size. The model equations are solved by using a particle coalescence simulation method. We find phenomenologically three distinct stages of growth. First, during the initial deposition stage, distributions with high density of small dots occur. Second, there is an intermediate and short-lived stationary state, which is controlled by kinetics of growth. Third, a long-lived stationary state is obtained, with nearly Gaussian size distributions, mostly determined by the energetics of the growth but also significantly affected by the kinetics. In the final stage, size selection and narrowing of the distributions occur. It is also shown that in the final stage of growth the Fokker-Planck type continuum model describes well the evolution of the distributions and the size selection.     

The exact solutions of Kane equations which have position-dependence band gap in an external non-uniform electric field

The energy spectrum of electrons in narrow band gap semiconductor nanocrystals which have position dependence band gap in an external non-uniform electric field which compensate the position dependence of the band edge of the valence band potential are studied theoretically taking into account the non-parabolicity of electrons in dispersion laws. The exact solutions of the Kane equations with strong spin–orbital interaction are determined with and without magnetic field via the band gap changes as a function of the position. The position dependence of the band gap is taken parabolically.     

Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires

The energy spectrum and corresponding wave functions of a flat quantum dot with elliptic symmetry are obtained exactly. A detailed study is made of the effect of ellipticity on the energy levels and the corresponding wave functions. The analytical behavior of the energy levels in certain limiting cases is obtained.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

Nanophotonic waveguidance in quantum networks - A simulation approach for quantum state transfer

A cavity-assisted Raman process can initialize the inter-conversion of stationary spin qubits and flying photon qubits in quantum channels. The qubit transmission essentially requires the implementation of special laser fields to excite atoms at the transmitting node of the quantum cavity. The flying qubit is ultimately absorbed at the receiving node of the channel to regenerate the original spin state of the nanodot. The present paper deals with the phenomena involved in such nanophotonic waveguidance by the process of rigorous simulation, and it is reported that the results obtained by implementing suitable transmission protocol reflect well the reliable transfer/entanglement of the quantum states of the nanodot qubit.     

Selecting wave function states in open quantum dots

We study how wave function scarring in an open quantum dot is influenced as the strength of its environmental coupling is varied and show evidence for groups of wave function scars that recur periodically with gate voltage. The precise form of these scars is found to evolve with gate voltage, which we discuss in terms of the properties of the semi-classical orbits that give rise to the scars. We also provide convincing experimental evidence for a correlation between the scars and the oscillations observed in the conductance when the gate voltage is varied.     

Control of the entanglement between triple quantum dot molecule and its spontaneous emission fields via quantum entropy

The time evolution of the quantum entropy in a coherently driven triple quantum dot molecule is investigated. The entanglement of the quantum dot molecule and its spontaneous emission field is coherently controlled by the gate voltage and the rate of an incoherent pump field. The degree of entanglement between a triple quantum dot molecule and its spontaneous emission fields is decreased by increasing the tunneling parameter.     

Quantum-Gravity Thermodynamics, Incorporating the?Theory of Exactly Soluble Active Stochastic Processes, with Applications

A re-visitation of QFT is first cited, deriving the Feynman integral from the theory of active stochastic processes (Glueck and Hueffler, Phys. Lett. B. 659(1–2):447–451, 2008; Hueffel and Kelnhofer, Phys. Lett. B 588(1–2):145–150, 2004). We factor the lie group “generator” of the inverse wavefunction over an entropy-maximizing basis. Performing term-by-term Ito-integration leads us to an analytical, evaluable trajectory for a charged particle in an arbitrary field given a Maximum-Entropy distribution. We generalize this formula to many-body electrodynamics. In theory, it is capable of predicting plasma’s thermodynamic properties from ionic spectral data and thermodynamic and optical distributions. Blessed with the absence of certain limitations (e.g., renormalization) strongly present in competing formalisms and the incorporation of research related to many different phenomena, we outline a candidate quantum gravity theory based on these developments.     

Temperature-induced broadening of the emission lines from a quantum-dot nanostructure

We report on the effect of temperature fluctuations on the midinfrared electroluminescence from a cascade of coupled AlInAs quantum dots and GaAs quantum wells. The observed line width is significantly broadened with increasing temperature. We then present our theoretical results on homogeneous line broadening due to temperature fluctuations for our experimental system. Our numerical simulations clearly indicate that, temperature fluctuations can account for the observed finite width of the emission lines at high-temperatures.     

Cluster State Entanglement of Semiconductor Quantum Dots Based on Faraday Rotation

We propose a scheme for a large-scale cluster state preparation of single-charged semiconductor quantum dots utilizing Faraday rotation. Without interaction between quantum dots, the exciton induced Faraday rotation could distribute the spatially separate quantum dots into a quantum network assisted by cavity QED. We obtain the corresponding parameters from the numerical simulation based on the input-output process for the required Faraday rotation and some discussion is made in view of experimental feasibility.     

Far-infrared spectroscopy of quantum wires and dots, breaking Kohn’s theorem

We review far-infrared experiments on quantum wires and dots. In particular, we show that with tailored deviations from a parabolic external lateral confinement potential one can break Kohn’s theorem. This allows a detailed investigation of the internal relative motion in quantum dots and wires and the study of electron–electron interaction effects, for example, the formation of compressible and incompressible states in quantum dots and antidots.     

The effect of confinement on the electron thermal conductance of a nanocrystal

Coulomb blockade oscillations are found in the electron thermal conductance of a quantum dot (nanocrystal) in the regime of weak coupling with two electrode leads that is calculated within a linear response theory. An analytical expression is obtained in the quantum limit where electron level spacing is non-negligible. The effect of confinement on the electron thermal conductance is thereby explicitly shown. It is shown that in the quantum limit the periodicity of the Coulomb-blockade oscillations of the electron thermal conductance is the same as of the conductance. The shape and the magnitude of the electron thermal conductance depend explicitly on the temperature and the energy level spacing. It is found that the electron thermal conductance decreases nearly exponentially with increasing confinement and decreasing temperature.