Coupled multimode optomechanics in the microwave regime

The motion of micro- and nanomechanical resonators can be coupled to electromagnetic fields. This allows to explore the mutual interaction and introduces new means to manipulate and control both light and mechanical motion. Such optomechanical systems have recently been implemented in nanoelectromechanical systems involving a nanomechanical beam coupled to a superconducting microwave resonator. Here, we propose optomechanical systems that involve multiple, coupled microwave resonators. In contrast to similar systems in the optical realm, the coupling frequency governing photon exchange between microwave modes is naturally comparable to typical mechanical frequencies. For instance this enables new ways to manipulate the microwave field, such as mechanically driving coherent photon dynamics between different modes. In particular we investigate two setups where the electromagnetic field is coupled either linearly or quadratically to the displacement of a nanomechanical beam. The latter scheme allows to perform QND Fock state detection. For experimentally realistic parameters we predict the possibility to measure an individual quantum jump from the mechanical ground state to the first excited state.Comment: 6 pages, 4 figures, 1 tabl

The use of the Infection and Treatment Method vaccine in controlling East Coast Fever in Kenya: Does gender matter for adoption and impact?

United States Agency for International DevelopmentInternal Revie

Effective dynamics for particles coupled to a quantized scalar field

We consider a system of N non-relativistic spinless quantum particles (``electrons'') interacting with a quantized scalar Bose field (whose excitations we call ``photons''). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c= epsilon << 1). We show that dressed particle states exist (particles surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)^{2}. Beyond that order the effective dynamics are expected to be dissipative. The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum, which is not an eigenvalue. Nevertheless we construct approximate dressed electrons subspaces, which are adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln (v/c)^{-1}}. We also give an explicit expression for the non adiabatic transitions corresponding to emission of free photons. For the radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in Communications in Mathematical Physic

Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics

This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which has a particular property: the perturbation series for the ground-state energy vanishes to all orders in the coupling parameter, but the actual ground-state energy is positive and dominated by instanton configurations of the form exp(-a/g), where a is the instanton action. The instanton effects are most naturally taken into account within the modified Bohr-Sommerfeld quantization conditions whose expansion leads to the generalized perturbative expansions (so-called resurgent expansions) for the energy values of the Fokker-Planck potential. Until now, these resurgent expansions have been mainly applied for small values of coupling parameter g, while much less attention has been paid to the strong-coupling regime. In this contribution, we compare the energy values, obtained by directly resumming generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling expansion, for which we determine the first few expansion coefficients in powers of g^(-2/3). Detailed calculations are performed for a wide range of coupling parameters g and indicate a considerable overlap between the regions of validity of the weak-coupling resurgent series and of the strong-coupling expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck Hamiltonian, we also briefly discuss the computation of its eigenfunctions. These eigenfunctions may be utilized for the numerical integration of the (single-particle) time-dependent Schroedinger equation and, hence, for studying the dynamical evolution of the wavepackets in the double-well-like potentials.Comment: 13 pages; RevTe

Evidence of absence: no relationship between behaviourally measured prediction error response and schizotypy

Introduction: The predictive processing framework has attracted much interest in the field of schizophrenia research in recent years, with an increasing number of studies also carried out in healthy individuals with nonclinical psychosis-like experiences. The current research adopted a continuum approach to psychosis and aimed to investigate different types of prediction error responses in relation to psychometrically defined schizotypy. Methods: One hundred and two healthy volunteers underwent a battery of behavioural tasks including (a) a force-matching task, (b) a Kamin blocking task, and (c) a reversal learning task together with three questionnaires measuring domains of schizotypy from different approaches. Results: Neither frequentist nor Bayesian statistical methods supported the notion that alterations in prediction error responses were related to schizotypal traits in any of the three tasks. Conclusions: These null results suggest that deficits in predictive processing associated with clinical states of psychosis are not always present in healthy individuals with schizotypal traits

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Necessary Condition for the Quantum Adiabatic Approximation

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also give a necessary condition for the adiabatic approximation that depends on local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur

Control of microwave signals using circuit nano-electromechanics

Waveguide resonators are crucial elements in sensitive astrophysical detectors [1] and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-coshmechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [16-18], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [19]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [20-22], extending the toolbox of control techniques of the microwave field.Comment: 9 figure