Oded Kenneth

Repulsive Casimir forces

We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.

Pushmepullyou: an efficient micro-swimmer

The swimming of a pair of spherical bladders that change their volumes and mutual distance is superior to other models of artificial swimmers at low Reynolds numbers. The swimming resembles the wriggling motion known as metaboly of certain protozoa.

Opposites Attract: A Theorem about the Casimir Force

We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives.

Casimir forces in a T operator approach

We explore the scattering approach to Casimir forces. Our main tool is the description of Casimir energy in terms of transition operators. The approach is valid for scalar fields as well as for electromagnetic fields. We provide several equivalent derivations of the formula presented by Kenneth and Klich [Phys. Rev. Lett. 97, 160401 (2006)]. We study the convergence properties of the formula and how to utilize it together with scattering data to compute the force. Next, we discuss the form of the formula in special cases such as the simplified form obtained when a single object is placed next to a mirror. We illustrate the approach by describing the force between scatterers in one dimension and three dimensions, where we obtain the interaction energy between two spherical bodies at all distances. We also consider the cases of scalar Casimir effect between spherical bodies with different radii as well as different dielectric functions.

A frictionless microswimmer

We investigate the self-locomotion of an elongated microswimmer by virtue of unidirectional tangential surface treadmilling. We show that the propulsion could be almost frictionless, as the microswimmer is propelled forward with the speed of the backward surface motion, i.e. it moves through an almost quiescent fluid. We investigate this swimming technique using the special spheroidal coordinates and also find an explicit closed-form optimal solution for a two-dimensional treadmiller via complex-variable techniques. Slender-object surface treadmilling is a particularly efficient mode of locomotion because the viscous drag is determined by the smallest length scale of the object rather than by the largest scale, as is the usual case for low Reynolds number flow.

Deterministic generation of a cluster state of entangled photons

Weaving an entangled cluster Entanglement is a powerful resource for quantum computation and information processing. One requirement is the ability to entangle multiple particles reliably. Schwartz et al. created an on-demand entangled cluster state of several photons by addressing a quantum dot with a sequence of laser pulses (see the Perspective by Briegel). They used an internal state of the quantum dot, a dark exciton, and its association with another internal state, a biexciton, to weave successive photons into an entangled cluster, generating entanglement between up to five photons. Science, this issue p. 434; see also p. 416 A quantum dot is used to realize entangled cluster states of up to five photons. Photonic cluster states are a resource for quantum computation based solely on single-photon measurements. We use semiconductor quantum dots to deterministically generate long strings of polarization-entangled photons in a cluster state by periodic timed excitation of a precessing matter qubit. In each period, an entangled photon is added to the cluster state formed by the matter qubit and the previously emitted photons. In our prototype device, the qubit is the confined dark exciton, and it produces strings of hundreds of photons in which the entanglement persists over five sequential photons. The measured process map characterizing the device has a fidelity of 0.81 with that of an ideal device. Further feasible improvements of this device may reduce the resources needed for optical quantum information processing.

Surface tank-treading: propulsion of Purcell's toroidal swimmer

In this work we address the “smoking ring” propulsion technique, originally proposed by Purcell [Am. J. Phys. 45, 3 (1977)] for self-locomotion at low Reynolds numbers. We first consider self-locomotion of a doughnut-shaped swimmer powered by surface rotation. Different modes of surface motion are assumed and propulsion velocity and swimming efficiency are determined. The swimmer is propelled against the direction of its outer surface motion, the inner surface having very little effect. The simplest swimming mode corresponding to constant angular velocity can achieve propulsion speeds of up to 66% of the surface tank-treading velocity and swimming efficiency of up to 13%. Higher efficiency is possible for more complicated modes powered by nonuniform twirling of extensible surface. A practical design of a necklace-shaped swimmer motivated by Purcell’s idea is proposed and demonstrated numerically. Finally, the explicit solution is found for the two-dimensional swimmer composed of two counter-rotating disks...

Optically induced rotation of an exciton spin in a semiconductor quantum dot.

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the excitons spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.A polarized picosecond laser pulse, which couples the bright exciton states to biexciton resonant states, is used to manipulate the exciton spin. We directly demonstrate this novel knob in a picosecond time-resolved two pulses experiment.

Undulatory locomotion of finite filaments: lessons from Caenorhabditis elegans

Undulatory swimming is a widespread propulsion strategy adopted by many small-scale organisms including various single-cell eukaryotes and nematodes. In this work, we report a comprehensive study of undulatory locomotion of a finite filament using (i) approximate resistive force theory (RFT) assuming a local nature of hydrodynamic interaction between the filament and the surrounding viscous liquid and (ii) particle-based numerical computations taking into account the intra-filament hydrodynamic interaction. Using the ubiquitous model of a propagating sinusoidal waveform, we identify the limit of applicability of the RFT and determine the optimal propulsion gait in terms of (i) swimming distance per period of undulation and (ii) hydrodynamic propulsion efficiency. The occurrence of the optimal swimming gait maximizing hydrodynamic efficiency at finite wavelength in particle- based computations diverges from the prediction of the RFT. To compare the model swimmer powered by sine wave undulations to biological undulatory swimmers, we apply the particle-based approach to study locomotion of the

Quantum response of dephasing open systems

We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give quantum response a geometric interpretation in terms of Hilbert space projections: For a two level system and, more generally, for systems with suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: The qubit, coherent states and a model of the integer quantum Hall effect.