Session T1: Hybrid Systems, Optomechanics and Macroscopic Systems at the Quantum Limit II

Coupling propagating acoustic waves to quantum circuits

We present a method for coupling propagating Surface Acoustic Waves (SAW) to charge sensitive quantum circuits, by direct piezoelectric charge induction. Using an RF-Single Electron Transistor\footnote{R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, and D.E. Prober, Science.~{\bf 280}, 1238 (1998).} as a high-performance electrometer, and employing an on-chip mixing technique\footnote{R. Knobel, C.S. Yung, and A.N. Cleland, Appl. Phys. Lett.~{\bf 81}, 532 (2002).}, we demonstrate ultra-high displacement sensitivity in the gigahertz frequency range, and an averaged detection sensitivity below the single-phonon level. Based on these experimental results, we discuss how the method can be enhanced and extended to superconducting qubits, and what roles Surface Acoustic Waves could potentially play in novel hybrid quantum devices.   

Single Crystal Diamond Mechanical Resonators

We report on the fabrication and measurement of single crystal diamond mechanical resonators. This is an important step towards realizing diamond photonics, optomechanics, and diamond-based scanning magnetometers. We present measurements of mechanical quality factors in excess of 10,000 as well as estimates of the coupling to embedded nitrogen-vacancy (NV) centers through strain. Strain tuning the NV's zero-phonon line could facilitate coupling its spin state to a photonic network. We also discuss strain as a coupling mechanism between the spin and mechanical degree of freedom in a diamond based resonator.   

Resonant Optical Forces in Silicon Carbide Nanostructures

Silicon carbide (SiC) materials are widely used for their exceptional electronic, mechanical, and thermal properties. For example, given its high stiffness to density ratio, SiC is an ideal material for mechanical resonators, and it has been explored for applications in nanoelectromechanical systems (NEMS). SiC also supports strong surface phonon-polariton resonances in the infrared region, which could enable its use for optomechanics. Similar to surface plasmon-polaritons supported by metal-dielectric interfaces, these surface waves at a SiC-vacuum interface can be used to guide and confine intense electromagnetic energy. Here, we investigate the resonant optical forces induced by phonon-polariton modes in different SiC nanostructures. Specifically, we calculate optical forces using the Maxwell Stress Tensor for three geometries: spherical particles, slab waveguides, and rectangular waveguides. We find that the high quality factor phonon-polariton modes in SiC can produce very large forces, more than two orders of magnitude larger than the plasmonic forces in similar metal nanostructures. These strong resonant forces, combined with its mechanical and thermal properties, make SiC a promising material for optomechanical applications.   

Quantum Mechanical Scattering in Nanoscale Systems

We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.   

Modeling time domain spectroscopy of electron-phonon coupled systems out of equilibrium

Recent advances in Terahertz large-electric field generation and pump-probe spectroscopies resolving pico- and even femtosecond time scales allow to study the behavior of photoexcited solids out of equilibrium. The relaxation after the pump pulse typically involves very fast processes related to purely electronic degrees of freedom, but for the slower return back to equilibrium it is essential to understand the interplay of electronic and lattice degrees of freedom. We present a theoretical investigation of electron-phonon coupled systems out of equilibrium, with results for various quantities (electronic distribution function, time-resolved angle-resolved photoemission, charge current). Our results show that the experimentally observed behavior can be related to the underlying microscopic properties of the system.   

Modeling lattice interaction in non-equilibrium pump-probe experiments

In past years, advances is experimental laser technology have allowed for the study of materials at ever shorter timescales. In these pump-probe experiments, after excitation by the pulse, the systems evolve back to equilibrium through its inherent relaxation processes, which are typically temporally separated by their characteristic timescales. Among the slower processes are the electron-phonon interactions, which carry the majority of the energy transferred to the electrons away into the lattice. We present a direct calculation of the characteristic timescales for systems driven out of equilibrium via a short pulse and allowed to relax via electron-phonon interactions. We make a direct connection between the observable timescales and the microscopic specifics, both via decay rates and oscillations in various photon-spectroscopies.   

Fluctuation Induced Forces for Surface Relief Gratings

In 1948 H.~G.~B.~Casimir predicted that two flat parallel neutral perfectly conducting plates would attract each other due to the quantum fluctuations of the electromagnetic field. Since then progress has been made to allow one to calculate the interaction energy due to both quantum and thermal fluctuations between two objects of almost arbitrary shape and material properties. This work focuses on interaction with at least one object described by a surface relief grating. The Casimir energy is calculated using the scattering matrix approach, and the scattering matrix of the periodic surface is calculated using the C method from electromagnetic grating theory. The strengths and limitations of the method with regards to calculating the Casimir energy are discussed, and the results for simple 1-D and 2-D periodic structures are shown.   

Superfluid to Mott-Insulator Transition in Thermodynamic Limit of 1D Coupled Cavity Array

In recent years, there has been great interest in simulating condensed matter models with quantum optical systems, which are usually characterized by a high degree of experimental control. One such model is the Jaynes-Cummings-Hubbard (JCH) model, an analog for the Bose-Hubbard (BH) model, in which mobile photons interact with atoms localized within a regular lattice of weakly coupled cavities. Finite system Density Matrix Renormalization Group (DMRG) studies have predicted a superfluid (SF) to Mott insulator (MI) transition in the phase diagram of the JCH model, and finite-size scaling has been used to determine the phase boundary in the thermodynamic limit. In this work, we directly numerically investigate the JCH model in the thermodynamic limit using infinite-system DMRG. The preliminary results indicate that the properties of the expected SF state are not wholly consistent with those of a conventional superfluid.   

Dirac Exciton-Polariton Condensates in a Triangular Lattice

Microcavity exciton-polaritons are quantum bose particles arising from the strong light-matter coupling between cavity photons and quantum well excitons. Recently, we have investigated the behavior of condensates in artificial lattice geometries in two-dimension (2D). Coherent $p$- and $d$-orbital state in a 2D square lattice is recently observed. Here we investigate exciton-polariton condensates at Dirac points formed in a 2D triangular lattice and experimental mapping of Dirac dispersion and discuss the interaction effect. We anticipate that the preparation of high-orbital condensates can be further extended to probe dynamical quantum phase transition in a controlled manner as quantum simulation applications.   

Numerical Study of the Bose-Einstein Condensation of Exciton-Polaritons

Using the complex Gross-Pitaevskii equation (cGPE) with pumping and decay terms that models the Bose-Einstein condensate of exciton-polaritons, we numerically investigate the dynamics of instability of its radially symmetric steady solutions. We develop accurate algorithms for computing the steady state solution, the linear stability spectra, as well as the full nonlinear solutions of the cGPE. We accurately compute the thresholds of instability that depend, e.g. on the strength and size of the polariton pumping spot and observe the formation of vortices and such complex dynamics as the formation of vortex lattices and nucleation.   

Formation and decay of a Bose-Einstein condensate of trapped dipole excitons

We study the nonlinear dynamics of formation and decay of a Bose-Einstein condensate of dipole excitons trapped in an external confining potential in coupled quantum wells. The problem is considered within an analytical approach and in numerical simulations. The trap restricts the spatial distribution of excitons and results in non-uniform density distribution in the exciton cloud. We demonstrate that under typical experimental conditions, regardless of a long-range nonlocal interaction of the dipole excitons, the system can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, and we find the effective interaction constant. In the numerical simulations, we account for the finite lifetime of dipole excitons and generation of the excitons due to continuous laser pumping. We also discuss formation and decay of vortex states in the condensate.   

Measurement of Casimir force with magnetic materials Alexandr Banishev, Chia-Cheng Chang, Umar Mohideen Department of Physics and Astronomy, University of California, Riverside, USA

The Casimir effect is important in various fields from atomic physics to nanotechnology. According to the Lifshitz theory of the Casimir force, the interaction between two objects depends both on their dielectric permittivity and magenetic permeability. Thus the role of magnetic properties on the Casimir force is interesting particularly due to the possibility of a reduction the Casimir force. In this report we will present the results of a Casimir force measurement between a magnetic material such as nickel coated on SiO2 plate and a Au-coated sphere.   

Geometry and fluctuation induced (Casimir) forces

Since the original prediction of attraction between parallel, perfectly conducting plates by Casimir there has been significant amount of work done in extending the calculations to real materials, finite temperatures and micro or nanostructured geometries. Majority of the experimental work has been carried out in the sphere-plane geometry. In this talk we will present ongoing experimental work on sphere--cylinder and sphere--cone geometries using frequency modulated atomic force microscopy. We will discuss numerical results in the sphere cylinder geometry and the range of validity of the point force approximation(PFA).   

Temperature dependence of Casimir force

Most of the experimental work till date on Casimir forces have been performed at or near room temperature. We report on our measurements of Casimir forces performed at liquid helium and liquid nitrogen temperatures using gold coated sphere and plate. These measurements were performed on a home built Atomic Force Microscope with a phase locked loop to track the frequency shift. We will discuss the results in the context of current theoretical understanding of temperature dependence in the sphere -- plate geometry.   

Enhanced light-matter interactions of a single emitter coupled to a slot waveguide

Traditionally, enhanced light-matter interactions are achieved using either plasmonic structures or photonic crystals. However, these structures suffer from inherent metal losses or narrow operating bandwidth. Instead, here we use an all-dielectric waveguide structure with ultra-small mode volume and low-loss and broadband capabilities. A slot-waveguide architecture is used for deep sub-wavelength light confinement in a low-index material surrounded by high-index barriers. Individual colloidal quantum dots are controllably coupled to this waveguide mode. A large Purcell enhancement is observed from lifetime measurements of the spontaneous emission rate of the quantum dot before and after coupling to the waveguide. Second order intensity correlation measurements verify that the observed fluorescence is indeed due to a single quantum dot. The demonstrated system is a promising broadband and low-loss platform for quantum information applications.