Probability Of Double Occupancy Research Articles

Double-occupancy probability and entanglement of two holes in double Ge/Si quantum dots

We have calculated the exchange energy, double occupation probability of the lowest singlet state, and degree of entanglement of two holes in vertically coupled double Ge/Si quantum dots. We determined the conditions on which the exchange coupling is large enough for a fast swap operation in quantum computation and the double-occupancy probability is still low, thus maximizing the entanglement for a small computation error. We found that both the degree of entanglement and double-occupancy probability for quantum dots with different dot size collapse onto universal, size independent curves when plotted as a function of singlet-triplet splitting.

10.1007/s11490-008-3019-1

The effects of elastic collisions in optical-lattice atomic clocks are analyzed. Calculations are presented using a separated oscillatory fields clock arrangement. The interactions of atoms in multiply occupied lattice sites cause a linear frequency shift, and also generate asymmetric Ramsey fringe patterns, both complicate the determination of the resonance frequency and reduce the fringe visibility due to interparticle entanglement. A method of reducing these collisional effects in an optical lattice clock containing bosonic atoms by introducing a phase difference of π between the Ramsey driving fields in adjacent sites is developed. This configuration suppresses site-to-site hopping due to the interference of two tunneling pathways, without degrading the fringe visibility. The probability of double occupancy is, thereby, reduced and collisional shifts are, thus, ameliorated.

Trapped Ultracold Fermions in Double-Well Optical Lattices

We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.

Ground-state properties of the two-site Hubbard–Holstein model: an exact solution

We study the two-site Hubbard–Holstein model by using an extended phonon coherentstate. For the nontrivial singlet bipolarons, the double occupancy probability, the fidelityand the entanglement entropy are calculated to characterize the ground-state properties inboth two-site and single-site bipolaron-dominated regimes. We use the localized minimumof the fidelity to define a crossover and plot the bipolaron phase diagram, which separatesthe large and small entanglement region. Furthermore, the relation between the bipolaronentanglement and the correlation functions demonstrates that the large entanglementcorresponds to the large magnitude of lattice deformations induced by electrons.

Collisional shifts in an optical-lattice atomic clock

The effects of elastic collisions in optical-lattice atomic clocks are analyzed. Calculations are presented using a separated oscillatory fields clock arrangement. The interactions of atoms in multiply occupied lattice sites cause a linear frequency shift, and also generate asymmetric Ramsey fringe patterns, both complicate the determination of the resonance frequency and reduce the fringe visibility due to interparticle entanglement. A method of reducing these collisional effects in an optical lattice clock containing bosonic atoms by introducing a phase difference of π between the Ramsey driving fields in adjacent sites is developed. This configuration suppresses site-to-site hopping due to the interference of two tunneling pathways, without degrading the fringe visibility. The probability of double occupancy is, thereby, reduced and collisional shifts are, thus, ameliorated.

Collisional shifts in optical-lattice atom clocks

We theoretically study the effects of elastic collisions on the determination of frequency standards via Ramsey-fringe spectroscopy in optical-lattice atom clocks. Interparticle interactions of bosonic atoms in multiply occupied lattice sites can cause a linear frequency shift, as well as generate asymmetric Ramsey-fringe patterns and reduce fringe visibility due to interparticle entanglement. We propose a method of reducing these collisional effects in an optical lattice by introducing a phase difference of $\ensuremath{\pi}$ between the Ramsey driving fields in adjacent sites. This configuration suppresses site-to-site hopping due to interference of two tunneling pathways, without degrading fringe visibility. Consequently, the probability of double occupancy is reduced, leading to cancellation of collisional shifts.

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighbouring P donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position and inter donor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, whilst the magnitude of the double occupancy probability can affect the error rate.

Spin swap versus double occupancy in quantum gates

We propose an approach to realize quantum gates with electron spins localized in a semiconductor that uses double occupancy to advantage. With a fast (non-adiabatic) time control of the tunnelling, the probability of double occupancy is first increased and then brought back exactly to zero. The quantum phase built in this process can be exploited to realize fast quantum operations. We illustrate the idea focusing on the half-swap operation, which is the key two-qubit operation needed to build a CNOT gate.

Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots

Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schr\"odinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasiadiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement that explicitly takes into account the possibilty of double occupancies and provides a necessary and sufficient criterion for entangled states.

QUANTUM MONTE CARLO SIMULATION STUDY OF ONE-DIMENSIONAL PERIODIC ANDERSON MODEL

Many rare earth and actinide intermetallics, known as Heavy Fermion Systems, have recently been successfully described by the Periodic Anderson Model. We investigate, in this work, various electronic and magnetic properties of the one-dimensional Periodic Anderson model using path integral formulation along with the quantum Monte Carlo simulation technique. We have studied the singlet and triplet pairing correlation functions, nearest neighbor charge-density correlations, spin density correlations, local squared magnetic moment and probability of double occupancy of f-electrons, as a function of intra-atomic Coulomb interaction for various values of hybridization parameter and the temperatures.

Numerical Study of One‐Dimensional Strongly Correlated Systems

AbstractThe path‐integral formulation along with the quantum Monte Carlo method is used to study the physical properties of the one‐dimensional Hubbard model for various band fillings and values of interaction strength U. Results for singlet and triplet pairing correlations, local square magnetic moment, total energy, probability of double occupancy, and nearest‐neighbour charge‐density correlations are presented. These results are explored at β (inverse temperature) = 2.0, 1.0, and 0.5 for the linear chain N = 16. These results show that the effect of correlation on the physical quantities is small for low band‐filling and it becomes most evident for the half‐filled band at finite temperatures.

Permeation properties of a Ca(2+)-blockable monovalent cation channel in the ectoderm of the chick embryo: pore size and multioccupancy probed with organic cations and Ca2+.

A Ca(2+)-blockable monovalent cation channel is present in the apical membrane of the ectoderm of the gastrulating chick embryo. We used the patch clamp technique to study several single-channel permeation properties of this channel. In symmetrical conditions without Ca2+, the Na+ current carried by the channel rectifies inwardly. The channel has an apparent dissociation constant for extracellular Na+ of 115 mM at 0 mV and a low density of negative surface charge (-0.03 e/nm2) at its extracellular entrance. The minimal pore diameter is approximately 5.8 A, as calculated from the relative permeabilities of 10 small organic cations. Extracellular application of six large organic cations decreased the inward Na+ current in a voltage-dependent manner, which strongly suggests an intrachannel block. The presence of at least two ion binding sites inside the pore is inferred from the Na+ dependence of the block by the organic cations. This hypothesis is strengthened by the fact that the extracellular Ca2+ block is also modified by the Na+ concentration. In particular, the rise of the unblocking rate with increased Na+ concentrations clearly suggests the presence of an interaction between Ca2+ and Na+ inside the channel. A low probability of double occupancy at physiological ionic conditions is implied from the absence of an anomalous mole fraction effect with mixtures of extracellular Li+ and K+. Finally, the absence of inward current at very strong hyperpolarizations and in the presence of 10 mM extracellular Ca2+ demonstrates the absence of significant Ca2+ current through this channel. It is argued that this embryonic epithelial Ca(2+)-blockable monovalent cation channel is related to both L-type Ca2+ channel and cyclic nucleotide-gated channels.

Quantum Monte Carlo simulation study of one-dimensional strongly correlated systems

The physical properties of strongly correlated fermionic systems, described by the Hubbard model, have been studied using the path integral formulation. In this study, we have used the quantum Monte Carlo simulation technique. The partition function of the fermionic system is evaluated within the usual path integral formulation, treating β, the inverse temperature, as imaginary time and dividing it into small discrete intervals. The single and triplet pairing correlation functions, nearest-neighbour charge density correlations, local squared magnetic moment, energy and the probability of double occupancy are studied as a function of interaction strength U for different band fillings and different temperatures.

Analysis of static and dynamic electron and spin properties within the interaction space of the one-dimensional Hubbard chain; a path-integral quantum Monte Carlo approach

Feynman path-integral quantum Monte Carlo (QMC) simulations have been performed to investigate electronic structure properties of the one-dimensional (1D) Hubbard chain. On the basis of the calculated on-site densities 〈 n i 〉 the following electronic configurations can be discriminated: (i) symmetry nonbroken 〈 n i 〉 distributions, (ii) on-site charge density waves (CDWs), (iii) clusters, (iv) statistical 〈 n i 〉 distributions resulting from chaotic QMC trajectories. The stability region for the different configurations is discussed as a function of the average electron density 〈 n〉 and the parameters of the extended Hubbard Hamiltonian, the two-electron elements U, V and the kinetic hopping t. It is suggested that the formation of cluster structures is a position-space concomitant of superconducting configurations in the 1D chain. The role of attractive on-site elements U and attractive intersite couplings V are analyzed in detail. The conditions stabilizing on-site CDWs are compared with the conditions favouring cluster formation. The static and dynamic electronic properties are discussed in terms of the on-site densities 〈 n i 〉 of the monoatomic 1D chain, electronic charge and spin fluctuations 〈Δ n 2)〉, 〈(Δ s 2)〉 and the probability of double occupancy P(2). Prerequisites leading to simultaneous and nonsimultaneous occurrence of charge and spin degrees of freedom are formulated. The possible violation of particle—hole (ph) symmetry in the presence of attractive on-site elements U is discussed. Consequences emerging from ph violation in charge transfer salts are also considered. It is suggested that low-temperature superconductivity in these materials is supported by attractive intersite interactions.

On-site charge-density wave formation in one-dimensional chains investigated by Feynman path-integral quantum Monte Carlo calculations

The formation of on-site charge-density waves (CDWs) in the one-dimensional (1D) Hubbard chain is studied by path-integral quantum Monte Carlo (QMC) simulations as a function of the band filling, the ratio between on-site and nearest-neighbor intersite interaction as well as the net Coulomb interaction and kinetic hopping. The dynamics of the electrons of the 1D system are quantified by the charge fluctuations 〈(Δ n 2 i )〉 and the probability of double occupancy P(2) averaged over all lattice sites i. Electronic conditions favouring CDWs are summarized. It is shown that one quarter, one half and three quarter filled bands are optimum conditions for on-site CDWs.

FIRST ORDER METAL-INSULATOR TRANSITION IN AN ALLOY ANALOGY APPROACH TO THE HUBBARD MODEL

The self-consistent coherent potential approximation introduced in Ref. 3 is extended to the hopping part of the Hubbard Hamiltonian in an alloy analogy scheme. There results the renormalization of the unperturbed bandwidth w by the appearance of a spin and potential strength dependent factor Φσ(u), the latter leads — in the magnetically disordered case, at electron densities n not far from 1, for small values of the temperature k B T with respect to w and values of u smaller than those needed to cause the Hubbard splitting — to a first order metal-insulator transition: Φ and the double occupancy probability D undergo a sudden drop. It is also shown that in the approximation proposed the system becomes strongly ferromagnetic in the thermodynamic limit at n = 1 and T = 0 if u is sufficiently large.

THE SELF CONSISTENT COHERENT POTENTIAL APPROXIMATION TO THE HUBBARD MODEL

We introduce, by an exact formula for the double occupancy probability δ in the Hubbard model, a self consistent version of the CPA which is aimed at taking into better account correlations of the electrons motion. We show that CPA breaks down at large values of the interaction strength, and we suggest a way of overcoming this limitation along the lines of the model proposed here.