Single-photon optomechanics in the strong coupling regime

We give a theoretical description of a coherently driven opto-mechanical system with a single added photon. The photon source is modeled as a cavity which initially contains one photon and which is irreversibly coupled to the opto-mechanical system. We show that the probability for the additional photon to be emitted by the opto-mechanical cavity will exhibit oscillations under a Lorentzian envelope, when the driven interaction with the mechanical resonator is strong enough. Our scheme provides a feasible route towards quantum state transfer between optical photons and micromechanical resonators.Comment: 14 pages, 6 figure

Creating and Verifying a Quantum Superposition in a Micro-optomechanical System

Micro-optomechanical systems are central to a number of recent proposals for realizing quantum mechanical effects in relatively massive systems. Here we focus on a particular class of experiments which aim to demonstrate massive quantum superpositions, although the obtained results should be generalizable to similar experiments. We analyze in detail the effects of finite temperature on the interpretation of the experiment, and obtain a lower bound on the degree of non-classicality of the cantilever. Although it is possible to measure the quantum decoherence time when starting from finite temperature, an unambiguous demonstration of a quantum superposition requires the mechanical resonator to be in or near the ground state. This can be achieved by optical cooling of the fundamental mode, which also provides a method to measure the mean phonon number in that mode. We also calculate the rate of environmentally induced decoherence and estimate the timescale for gravitational collapse mechanisms as proposed by Penrose and Diosi. In view of recent experimental advances, practical considerations for the realization of the described experiment are discussed.Comment: 19 pages, 8 figures, published in New J. Phys. 10 095020 (2008); minor revisions to improve clarity; fixed possibly corrupted figure

Macroscopic superpositions via nested interferometry: finite temperature and decoherence considerations

Recently there has been much interest in optomechanical devices for the production of macroscopic quantum states. Here we focus on a proposed scheme for achieving macroscopic superpositions via nested interferometry. We consider the effects of finite temperature on the superposition produced. We also investigate in detail the scheme's feasibility for probing various novel decoherence mechanisms.Comment: 12 pages, 2 figure

Design, fabrication, and characterization of deep-etched waveguide gratings

One-dimensional (1-D) deep-etched gratings on a specially grown AlGaAs wafer were designed and fabricated. The gratings were fabricated using state-of-the-art electron beam lithography and high-aspect-ratio reactive ion etching (RIE) in order to achieve the required narrow deep air slots with good accuracy and reproducibility. Since remarkable etch depths (up to 1.5 /spl mu/m), which completely cut through the waveguide core layer, have been attained, gratings composed of only five periods (and, thus, shorter than 6 /spl mu/m) have a bandgap larger than 100 nm. A defect was introduced by increasing the width of the central semiconductor tooth to create microcavities that exhibit a narrow transmission peak (less than 7 nm) around the wavelength of 1530 nm. The transmission spectra between 1460 and 1580 nm have been systematically measured, and the losses have been estimated for a set of gratings, both with and without a defect, for different periods and air slot dimensions. Numerical results obtained via a bidirectional beam propagation code allowed the evaluation of transmissivity, reflectivity, and diffraction losses. By comparing experimental results with the authors' numerical findings, a clear picture of the role of the grating's geometric parameters in determining its spectral features and diffractive losses is illustrated

A microchip optomechanical accelerometer

The monitoring of accelerations is essential for a variety of applications ranging from inertial navigation to consumer electronics. The basic operation principle of an accelerometer is to measure the displacement of a flexibly mounted test mass; sensitive displacement measurement can be realized using capacitive, piezo-electric, tunnel-current, or optical methods. While optical readout provides superior displacement resolution and resilience to electromagnetic interference, current optical accelerometers either do not allow for chip-scale integration or require bulky test masses. Here we demonstrate an optomechanical accelerometer that employs ultra-sensitive all-optical displacement read-out using a planar photonic crystal cavity monolithically integrated with a nano-tethered test mass of high mechanical Q-factor. This device architecture allows for full on-chip integration and achieves a broadband acceleration resolution of 10 \mu g/rt-Hz, a bandwidth greater than 20 kHz, and a dynamic range of 50 dB with sub-milliwatt optical power requirements. Moreover, the nano-gram test masses used here allow for optomechanical back-action in the form of cooling or the optical spring effect, setting the stage for a new class of motional sensors.Comment: 16 pages, 9 figure

A chip-scale integrated cavity-electro-optomechanics platform

We present an integrated optomechanical and electromechanical nanocavity, in which a common mechanical degree of freedom is coupled to an ultrahigh-Q photonic crystal defect cavity and an electrical circuit. The sys- tem allows for wide-range, fast electrical tuning of the optical nanocavity resonances, and for electrical control of optical radiation pressure back-action effects such as mechanical amplification (phonon lasing), cooling, and stiffening. These sort of integrated devices offer a new means to efficiently interconvert weak microwave and optical signals, and are expected to pave the way for a new class of micro-sensors utilizing optomechanical back-action for thermal noise reduction and low-noise optical read-out.Comment: 11 pages, 7 figure

Helicity conservation by flow across scales in reconnecting vortex links and knots

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation

Helicity within the vortex filament model

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments

Dynamical Coupling between a Bose-Einstein Condensate and a Cavity Optical Lattice

A Bose-Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe bistability already below the single photon level and strong back-action dynamics which tunes the system periodically out of resonance.Comment: 5 pages, 4 figure

Decoherence of a Pointer by a Gas Reservoir

We study the effect of the environment on the process of the measurement of a state of a microscopic spin half system. The measuring apparatus is a heavy particle, whose center of mass coordinates can be considered at the end of the measurement as approximately classical, and thus can be used as a pointer. The state of the pointer, which is the result of its interaction with the spin, is transformed into a mixed state by the coupling of the pointer to the environment. The environment is considered to be a gas reservoir, whose particles interact with the pointer. This results in a Fokker-Planck equation for the reduced density matrix of the pointer. The solution of the equation shows that the quantum coherences, which are characteristic to the entangled state between the probabilities to find the pointer in one of two positions, decays exponentially fast in time. We calculate the exponential decay function of this decoherence effect, and express it in terms of the parameters of the model.Comment: 41 pages, 1 figur