Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

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.

Spin squeezing, macrorealism and the heisenberg uncertainty principle

169 p.

Entanglement generation in harmonic chains: Tagging by squeezing

We address the problem of springlike coupling between bosons in an open-chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long-distance entanglement distribution.

Squeezing of mechanical motion via qubit-assisted control

We propose a feedback control mechanism for the squeezing of the phononic mode of a mechanical oscillator. We show how, under appropriate working conditions, a simple adiabatic approach is able to induce mechanical squeezing. We then go beyond the limitations of such a working point and demonstrate the stationary squeezing induced by using repeated measurements and reinitialization of the state of a two-level system ancilla coupled to the oscillator. Our nonadaptive feedback loop offers interesting possibilities for quantum state engineering and steering in open-system scenarios.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spin squeezing and entanglement via finite-dimensional discrete phase-space description

We show how mapping techniques inherent to N2-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson- Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations → entanglement → squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems. © 2013 World Scientific Publishing Company.

Squeezing of Pore-water from Core Samples of DGR Boreholes: Feasibility Study

Three archived core samples from boreholes DGR-4, DGR-5 and DGR-6 from the Salina F Unit, Queenston Formation and the Georgian Bay Formation were subjected to squeezing tests at pressures of up to 500 MPa. Two samples did not yield any water, while a total of 0.88 g pore water was obtained from a clay-rich sample from the Blue Mountain Formation (water content = 2.8 wt.%, porosity = 8 %). This water mass was sufficient for a full chemical and water-isotope analysis – the first direct determination of pore-water composition in rocks from the DGR boreholes. The results are generally in reasonable agreement with those of independent methods, or the observed differences can be explained. Ancillary investigations included the determination of water content, densities and mineralogy, aqueous extraction of squeezed cores, and SEM investigations to characterise the microtexture of unsqueezed and squeezed rock materials. It is concluded that squeezing is a promising method of pore-water extraction and characterisation and is recommended as an alternative method for future studies. Selection criteria for potentially squeezable samples include high clay-mineral content (correlating in a high water content) and low carbonate content (low stiffness, limited cementation). Potential artefacts of the method, such as ion filtration or pressure solution, should be explored and quantified in future efforts.

Pore-water squeezing from indurated shales

High-pressure mechanical squeezing was applied to sample pore waters from a sequence of highly indurated and overconsolidated sedimentary rocks in a drillcore from a deep borehole in NE Switzerland. The rocks are generally rich in clay minerals (28–71 wt.%), with low water contents of 3.5–5.6 wt.%, resulting in extremely low hydraulic conductivities of 10− 14–10− 13 m/s. First pore-water samples could generally be taken at 200 MPa, and further aliquots were obtained at 300, 400 and 500 MPa. Chemical and isotopic compositions of squeezed waters evolve with increasing pressure. Decreasing concentrations of Cl−, Br−, Na+ and K+ are explained by ion filtration due to the collapse of the pore space during squeezing. Increasing concentrations of Ca2 + and Mg2 + are considered to be a consequence of pressure-dependent solubilities of carbonate minerals in combination with sorption/desorption reactions. The pressure dependence was studied by model calculations considering equilibrium with carbonate minerals and the exchanger population on clay surfaces, and the trends observed in the experiments could be confirmed. The compositions of the squeezed waters were compared with results of independent methods, such as aqueous extraction and in-situ sampling of ground and pore waters. On this basis, it is concluded that the chemical and isotopic composition of pore water squeezed at the lowest pressure of 200 MPa closely represents that of the in-situ pore water. The feasibility of sampling pore waters with water contents down to 3.5 wt.% and possibly less opens new perspectives for studies targeted at palaeo-hydrogeological investigations using pore-water compositions in aquitards as geochemical archives.