On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair-states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter thereby increasing the conversion efficiency; ``the collision rate'' is the pair decorrelation rate.Comment: 4 pages, 3 figures, final version accepted to Phys. Rev. Let

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $\Gamma \propto \alpha^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.Comment: 5 pages, 4 figure

Calculation of pure dephasing for excitons in quantum dots

Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shapes. We show that the dephasing from LO phonon scattering, occurs on a much larger time scale than that of dephasing due to acoustic phonons which for low temperatures are also a more efficient dephasing mechanism. The typical dephasing time is shown to strongly depend on the quantum dot size whereas the electron phonon ``coupling strength'' and external electric fields tend mostly to effect the residual coherence. The relevance of the dephasing times for current quantum information processing implementation schemes in quantum dots is discussed

Entanglement distribution for a practical quantum-dot-based quantum processor architecture

We propose a quantum dot (QD) architecture for enabling universal quantum information processing. Quantum registers, consisting of arrays of vertically stacked self-assembled semiconductor QDs, are connected by chains of in-plane self-assembled dots. We propose an entanglement distributor, a device for producing and distributing maximally entangled qubits on demand, communicated through in-plane dot chains. This enables the transmission of entanglement to spatially separated register stacks, providing a resource for the realization of a sizeable quantum processor built from coupled register stacks of practical size. Our entanglement distributor could be integrated into many of the present proposals for self-assembled QD-based quantum computation (QC). Our device exploits the properties of simple, relatively short, spin-chains and does not require microcavities. Utilizing the properties of self-assembled QDs, after distribution the entanglement can be mapped into relatively long-lived spin qubits and purified, providing a flexible, distributed, off-line resource. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Spikes and diffusion waves in one-dimensional model of chemotaxis

We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity $u_t = u_{xx} - \left(u (K^\prime \ast u)\right)_{x}$ with a given kernel $K'\in L^1(\R)$. We show the existence of global-in-time nonnegative solutions and we study their large time asymptotics. Depending on $K'$, we obtain either linear diffusion waves ({\it i.e.}~the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as $t\to\infty$. Moreover, for certain aggregation kernels, we show a concentration of solution on an initial time interval, which resemble a phenomenon of the spike creation, typical in chemotaxis models

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

L\'evy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces

In this paper we investigate the existence and some useful properties of the L\'evy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter $H\in (1/3,1/2]$. We prove that this stochastic area has a H\"older-continuous version with sufficiently large H\"older-exponent and that can be approximated by smooth areas. In addition, we prove the stationarity of this area.Comment: 18 page

A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Storage Qubits and Their Potential Implementation Through a Semiconductor Double Quantum Dot

In the context of a semiconductor based implementation of a quantum computer the idea of a quantum storage bit is presented and a possible implementation using a double quantum dot structure is considered. A measurement scheme using a stimulated Raman adiabatic passage is discussed.Comment: Revised version accepted for publication in Phys.Rev. B. 19 pages, 4 eps figure