Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level system coupled to a quantum harmonic oscillator. Such devices may allow the exploration of parameter regimes outside the near-resonance and weak-coupling assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating other theoretical approaches. One such approach is an adiabatic approximation in the limit that the oscillator frequency is much larger than the characteristic frequency of the two-level system. A derivation of the approximation is presented and the time evolution of the two-level-system occupation probability is calculated using both thermal- and coherent-state initial conditions for the oscillator. Closed-form evaluation of the time evolution in the weak-coupling limit provides insight into the differences between the thermal- and coherent-state models. Finally, potential experimental observations in solid-state systems, particularly the Cooper-pair box--nanomechanical resonator system, are discussed and found to be promising.Comment: 16 pages, 11 figures; revised abstract; some text revisions; added two figures and combined others; added references. Submitted to Phys. Rev.

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radiofrequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position;back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550mK to 300mK-- an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these backaction effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.Comment: 28 pages, 7 figures; accepted for publication in Natur

Effect of positron-atom interactions on the annihilation gamma spectra of molecules

Calculations of gamma spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation gamma spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the gamma spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (thermalised, room-temperature) positron as a plane wave and gives annihilation gamma spectra that are about 40% broader than experiment, although the main chemical trends are reproduced. We show that this effective "narrowing" of the experimental spectra is due to the action of the molecular potential on the positron, chiefly, due to the positron repulsion from the nuclei. It leads to a suppression of the contribution of small positron-nuclear separations where the electron momentum is large. To investigate the effect of the nuclear repulsion, as well as that of short-range electron-positron and positron-molecule correlations, a linear combination of atomic orbital description of the molecular orbitals is employed. It facilitates the incorporation of correction factors which can be calculated from atomic many-body theory and account for the repulsion and correlations. Their inclusion in the calculation gives gamma spectrum linewidths that are in much better agreement with experiment. Furthermore, it is shown that the effective distortion of the electron momentum density, when it is observed through positron annihilation gamma spectra, can be approximated by a relatively simple scaling factor.Comment: 26 pages, 12 figure

Resonant Phenomena in Antihydrogen-Hydrogen Scattering

We present a treatment of cold hydrogen-antihydrogen collisions based on the asymptotic properties of atom-antiatom interactions. We derive general formulas for the elastic and inelastic cross sections and for the scattering lengths and analyze their sensitivity to the parameters characterizing the inelasticity of the collision process. Given the inelasticity, we obtain bounds for the complex scattering length. We investigate the influence of strong nuclear forces and the isotope effects in $\bar{\rm H}{\rm H}$ and $\bar{\rm H}{\rm D}$ collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow ${\rm H}\bar{\rm H}$ ($\bar{\rm H}{\rm D}$) states. The values of the elastic and inelastic cross-sections with simultaneous account of rearrangement and strong forces are presented. General expressions for the (complex) energies of the near-threshold $\rm{H}\bar{\rm H}$ states are obtained.Comment: 26 pages 7 figure

Low frequency current noise of the single-electron shuttle

Coupling between electronic and mechanical degrees of freedom in a single electron shuttle system can cause a mechanical instability leading to shuttle transport of electrons between external leads. We predict that the resulting low frequency current noise can be enhanced due to amplitude fluctuations of the shuttle oscillations. Moreover, at the onset of mechanical instability a pronounced peak in the low frequency noise is expected.Comment: 14 pages, 3 figures, 1 tabl

Convergent variational calculation of positronium-hydrogen-atom scattering lengths

We present a convergent variational basis-set calculational scheme for elastic scattering of positronium atom by hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed for achieving convergence. We report convergent results for scattering lengths in atomic units for both singlet ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.Comment: 11 pages, 1 postscript figure, Accepted in J. Phys. B (Letter

Damage profiles of ultrashallow B implants in Si and the Kinchin-Pease relationship

Damage distributions resulting from 0.1-2 keV B+ implantation at room temperature into Si(100) to doses ranging from 1×1014 to 2×1016 cm-2 have been determined using high-depth-resolution medium-energy-ion scattering in the double alignment mode. For all B+ doses and energies investigated a 3-4 nm deep, near-surface damage peak was observed while for energies at and above 1 keV, a second damage peak developed beyond the mean projected B+ ion range of 5.3 nm. This dual damage peak structure is due to dynamic annealing processes. For the near-surface peak it is observed that, at the lowest implant energies and doses used, for which recombination processes are suppressed due to the proximity of the surface capturing interstitials, the value of the damage production yield for low-mass B+ ions is equal or greater than the modified Kinchin-Pease model predictions [G. H. Kinchin and R. S. Pease, Rep. Prog. Phys. 18, 1 (1955); G. H. Kinchin and R. S. Pease, J. Nucl. Energy 1, 200 (1955); P. Sigmund, Appl. Phys. Lett. 14, 114 (1969)]

Beyond linear coupling in microwave optomechanics

We explore the nonlinear dynamics of a cavity optomechanical system. Our realization consisting of a drumhead nano-electro-mechanical resonator (NEMS) coupled to a microwave cavity, allows for a nearly ideal platform to study the nonlinearities arising purely due to radiation-pressure physics. Experiments are performed under a strong microwave Stokes pumping which triggers mechanical self-sustained oscillations. We analyze the results in the framework of an extended nonlinear optome-chanical theory, and demonstrate that quadratic and cubic coupling terms in the opto-mechanical Hamiltonian have to be considered. Quantitative agreement with the measurements is obtained considering only genuine geometrical nonlinearities: no thermo-optical instabilities are observed, in contrast with laser-driven systems. Based on these results, we describe a method to quantify nonlin-ear properties of microwave optomechanical devices. Such a technique, available now in the quantum electro-mechanics toolbox, but completely generic, is mandatory for the development of new schemes where higher-order coupling terms are proposed as a new resource, like Quantum Non-Demolition measurements, or in the search for new fundamental quantum signatures, like Quantum Gravity. We also find that the motion imprints a wide comb of extremely narrow peaks in the microwave output field, which could also be exploited in specific microwave-based measurements, potentially limited only by the quantum noise of the optical and the mechanical fields for a ground-state cooled NEMS device

Pulsed quantum optomechanics

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.Comment: 9 pages, 4 figure

Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme

We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonator's interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.Comment: Submitted to New Journal of Physics: Special Issue "Mechanical Systems at the Quantum Limit