Intrinsic noise in systems with switching environments

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.Comment: 15 pages, 11 figure

Feedback Control of Quantum Transport

The current through nanostructures like quantum dots can be stabilized by a feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles $n$. At large times, the feedback loop freezes the fluctuations of $n$ which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.Comment: 4 pages, 2 figure

Achievable Qubit Rates for Quantum Information Wires

Suppose Alice and Bob have access to two separated regions, respectively, of a system of electrons moving in the presence of a regular one-dimensional lattice of binding atoms. We consider the problem of communicating as much quantum information, as measured by the qubit rate, through this quantum information wire as possible. We describe a protocol whereby Alice and Bob can achieve a qubit rate for these systems which is proportional to N^(-1/3) qubits per unit time, where N is the number of lattice sites. Our protocol also functions equally in the presence of interactions modelled via the t-J and Hubbard models

Advanced control with a Cooper-pair box: stimulated Raman adiabatic passage and Fock-state generation in a nanomechanical resonator

The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage (STIRAP) should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechnical resonator by vacuum-stimulated adiabatic passage with the superconducting nanocircuit coupled to the resonator

Driven transport on parallel lanes with particle exclusion and obstruction

We investigate a driven two-channel system where particles on different lanes mutually obstruct each other's motion, extending an earlier model by Popkov and Peschel Phys. Rev. E 64, 026126 (2001)]. This obstruction may occur in biological contexts due to steric hinderance where motor proteins carry cargos by "walking" on microtubules. Similarly, the model serves as a description for classical spin transport where charged particles with internal states move unidirectionally on a lattice. Three regimes of qualitatively different behavior are identified, depending on the strength of coupling between the lanes. For small and large coupling strengths the model can be mapped to a one-channel problem, whereas a rich phase behavior emerges for intermediate ones. We derive an approximate but quantitatively accurate theoretical description in terms of a one-site cluster approximation, and obtain insight into the phase behavior through the current-density relations combined with an extremal-current principle. Our results are confirmed by stochastic simulations

Simulating adiabatic evolution of gapped spin systems

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited state is any constant independent of n, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap doesn't scale with n. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change

The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently

We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap \Delta E between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins, where m is an O(1) constant, is locally the same as the ground state |\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to the ground state of H_n can be stored efficiently for all n. We formulate a conjecture that, if true, would imply our result applies to all noncritical 1D spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change