Quantum squeezing of motion in a mechanical resonator

Quantum mechanics places limits on the minimum energy of a harmonic oscillator via the ever-present "zero-point" fluctuations of the quantum ground state. Through squeezing, however, it is possible to decrease the noise of a single motional quadrature below the zero-point level as long as noise is added to the orthogonal quadrature. While squeezing below the quantum noise level was achieved decades ago with light, quantum squeezing of the motion of a mechanical resonator is a more difficult prospect due to the large thermal occupations of megahertz-frequency mechanical devices even at typical dilution refrigerator temperatures of ~ 10 mK.

Kronwald, Marquardt, and Clerk (2013) propose a method of squeezing a single quadrature of mechanical motion below the level of its zero-point fluctuations, even when the mechanics starts out with a large thermal occupation. The scheme operates under the framework of cavity optomechanics, where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion. In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in Kronwald et. al. to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.

In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al.. We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 +/- 0.06 times the quantum zero-point motion.

In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 +/- 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.

Calculation of energy levels in InGaAs/GaAs quantum dot array

The subbands of the ground state E-c1, the first excited state E-c2 and heavy hole state E-HH1 are calculated by solving the eigenvalues of effective-mass Hamiltonian H-0 which is derived from eight-band k . p theory and the calculations are performed at k(x) = k, = k = 0 for the three-dimensional array of InGaAs/GaAs quantum dots (QDs). With indium content in InGaAs QDs gradually increasing from 30% to 100%,the intersubband transition wavelength of E-c2 to E-c1, blue-shifts from 18.50 to 11.87 mu m,while the transition wavelength of E-c1, to E-HH1, red-shifts from 1. 04 to 1. 73 mu m. With the sizes of Ir-0.5 Ga-0.5 As and InAs QDs increasing from 1.0 to 5.0 nm, the intersubband transition from E-c1, to E-C2 transforms from bound-state-to-continuum-state to bound-state-to-bound-state, and the corresponding intersubband transition wavelengths red-shift from 8.12 pm (5.90 pm) to 53.47 mu m (31.87 pm), respectively, and the transition wavelengths of E-C1 to E-HH1 red-shift from 1. 13 mu m (1.60 mu m) to 1.27 mu m (2.01 mu m), respectively.

Calculation of the current noise spectrum in mesoscopic transport: A quantum master equation approach

Based on our recent work on quantum transport [X. Q. Li , Phys. Rev. B 71, 205304 (2005)], we show how an efficient calculation can be performed for the current noise spectrum. Compared to the classical rate equation or the quantum trajectory method, the proposed approach is capable of tackling both the many-body Coulomb interaction and quantum coherence on an equal footing. The practical applications are illustrated by transport through quantum dots. We find that this alternative approach is in a certain sense simpler and more straightforward than the well-known Landauer-Buttiker scattering matrix theory.

Ground-state properties of an artificial molecule: a simple model calculation for the double quantum dot

The ground state of a double quantum-dot structure is studied by a simplified Anderson-type model. Numerical calculations reveal that the ground-state level of this artificial molecule increases with the increasing single particle level of the dot, and also increases with the decreasing transfer integrals. We show the staircase feature of the electron occupation and the properties of the ground-state eigenvector by varying the;single particle level of the dot.

Calculation of valence subband structures for strained GaInP/AlGaInP quantum wells without axial approximation

Usually in the calculation of valence subband structure for III-V direct bandgap material, axial approximation had been used in the Luttinger-Kohn model to simplify the computational efforts. In this letter, the valence subband structure for the GaInP/AlGaInP strained and lattice-matched quantum wells was calculated without axial approximation, on the basis of 6x6 Luttinger-Kohn Hamiltonian including strain and spin-orbit splitting effects. The numerical simulation results were presented with help of the finite-difference methods. The calculation results with/without axial approximation were compared and the effect of axial approximation on the valence subband structure was discussed in detail. The results indicated that there was a strong warping in the GaInP valence band, and axial approximation can lead to an error when k was not equal to zero, especially for compressively strained and lattice-matched GaInP/AlGaInP quantum wells.

Calculation of the band structure of semiconductor quantum wells using scattering matrices

The transfer-matrix method widely used in the calculation of the band structure of semiconductor quantum wells is found to have limitations due to its intrinsic numerical instability. It is pointed out that the numerical instability arises from free-propagating transfer matrices. A new scattering-matrix method is developed for the multiple-band Kane model within the envelope-function approximation. Compared with the transfer-matrix method, the proposed algorithm is found to be more efficient and stable. A four-band Kane model is used to check the validity of the method and the results are found to be in good agreement with earlier calculations.

Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6 * 6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6 * 6 Luttinger-Kohn model. The effect of the number and period of plane-waves used for expansion on the stability of energy eigenvalues is examined. For practical calculation, it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

Probing mechanical quantum coherence with an ultracold-atom meter

We propose a scheme to probe quantum coherence in the state of a nanocantilever based on its magnetic coupling (mediated by a magnetic tip) with a spinor Bose Einstein condensate (BEC). By mapping the BEC into a rotor, its coupling with the cantilever results in a gyroscopic motion whose properties depend on the state of the cantilever: the dynamics of one of the components of the rotor angular momentum turns out to be strictly related to the presence of quantum coherence in the state of the cantilever. We also suggest a detection scheme relying on Faraday rotation, which produces only a very small back-action on the BEC and is thus suitable for a continuous detection of the cantilever's dynamics.

Ground-state self-consistent calculation of quantum dots under magnetic fields: Addition spectrum

A density-functional self-consistent calculation of the ground-state electronic density of quantum dots under an arbitrary magnetic field is performed. We consider a parabolic lateral confining potential. The addition energy, E(N+1)-E(N), where N is the number of electrons, is compared with experimental data and the different contributions to the energy are analyzed. The Hamiltonian is modeled by a density functional, which includes the exchange and correlation interactions and the local formation of Landau levels for different equilibrium spin populations. We obtain an analytical expression for the critical density under which spontaneous polarization, induced by the exchange interaction, takes place.

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A novel self consistent calculation approach for the capacitance-voltage characteristics of semiconductor quantum wire transistors based on a split-gate configuration

Purpose - The purpose of this paper is to develop an efficient numerical algorithm for the self-consistent solution of Schrodinger and Poisson equations in one-dimensional systems. The goal is to compute the charge-control and capacitance-voltage characteristics of quantum wire transistors. Design/methodology/approach - The paper presents a numerical formulation employing a non-uniform finite difference discretization scheme, in which the wavefunctions and electronic energy levels are obtained by solving the Schrodinger equation through the split-operator method while a relaxation method in the FTCS scheme ("Forward Time Centered Space") is used to solve the two-dimensional Poisson equation. Findings - The numerical model is validated by taking previously published results as a benchmark and then applying them to yield the charge-control characteristics and the capacitance-voltage relationship for a split-gate quantum wire device. Originality/value - The paper helps to fulfill the need for C-V models of quantum wire device. To do so, the authors implemented a straightforward calculation method for the two-dimensional electronic carrier density n(x,y). The formulation reduces the computational procedure to a much simpler problem, similar to the one-dimensional quantization case, significantly diminishing running time.

Ventilated Stone Veneer: Mechanical Behaviour, Calculation Methodologies, Major Pathologies and Existing Tests

The increase of building pathologies related to the use of stone materials and the use of ventilated stone veneers, requires the reformulation of design concepts in building façades and also the reformulation of the architectural project. The aim of this paper is to identify, analyze and evaluate synthetically building pathologies in stone ventilated façades in order to obtain the main technical conditions to be considered in the architectural design, by interpreting its mechanical behavior and capabilities to prevent such pathologies and to ensure the proper features during the building lifetime. The methodology is based on both laboratory stone tests and in situ tests about construction systems, by analyzing physical and mechanical behavior of the outer layer in relation to other building requirements. The results imply the need of proper sizing, specific quality control and practical application of calculation methods, to control high concentration pressures in ventilated façades by reaching appropriate project solutions. In conclusion, the research about different pathologies of stone ventilated façades, the study of their mechanical behavior, their anchorage and their connection with their constructive aspects, will help to improve the construction quality of the stone ventilated façade in buildings and to enhance the use of natural stone in modern architecture.

Quantum nondemolition measurement of Fock states of mesoscopic mechanical oscillators

We investigate a scheme that makes a quantum nondemolition (QND) measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two beam bending modes. The nonlinear coupling between the two modes shifts the resonant frequency of the readout oscillator in proportion to the excitation level of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We derive an equation for the reduced density matrix of the system oscillator, and use this to study the conditions under which discrete jumps in the excitation level occur. The appearance of jumps in the actual quantity measured is also studied using the method of quantum trajectories. We consider the feasibility of the scheme for experimentally accessible parameters.