Ultra-Strong Optomechanics Incorporating the Dynamical Casimir Effect

We propose a superconducting circuit comprising a dc-SQUID with mechanically compliant arm embedded in a coplanar microwave cavity that realizes an optomechanical system with a degenerate or non-degenerate parametric interaction generated via the dynamical Casimir effect. For experimentally feasible parameters, this setup is capable of reaching the single-photon, ultra-strong coupling regime, while simultaneously possessing a parametric coupling strength approaching the renormalized cavity frequency. This opens up the possibility of observing the interplay between these two fundamental nonlinearities at the single-photon level.Comment: 7 pages, 1 figure, 1 tabl

How Vocabulary is Learned

Vocabulary learning requires two basic conditions – repetition (quantity of meetings with words) and good quality mental processing of the meetings. Other factors also affect vocabulary learning. For example, learners may differ greatly in their motivation to engage in learning, and words may differ greatly in their learning burden. However, without quantity and quality of processing, learning cannot occur. The greater the number of repetitions, the more likely learning is to occur. The deeper and more thoughtful the quality of processing, the more likely learning is to occur. This paper explains quantity and quality, and shows how teachers and learners can increase the quantity and quality of their processing of vocabulary, thus increasing their vocabulary size

Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.Comment: 10 pages, 5 figure

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state

The Trilinear Hamiltonian: A Zero Dimensional Model of Hawking Radiation from a Quantized Source

We investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviations arise when the pump mode (black hole) has emitted nearly half of its initial energy into the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum gravitational degrees of freedom.Comment: 18 pages, 6 figures, Submitted to New Journal of Physics focus issue: "Classical and Quantum Analogues for Gravitational Phenomena and Related Effects

Do bilinguals have different concepts? The case of shape and material in Japanese L2 users of English

An experiment investigated whether Japanese speakers’ categorisation of objects and substances as shape or material is influenced by acquiring English, based on Imai and Gentner (1997). Subjects were presented with an item such as a cork pyramid and asked to choose between two other items that matched it for shape (plastic pyramid) or for material (piece of cork). The hypotheses were that for simple objects the number of shape-based categorisations would increase according to experience of English and that the preference for shape and material-based categorisations of Japanese speakers of English would differ from mono¬lingual speakers of both languages. Subjects were 18 adult Japanese users of English who had lived in English-speaking countries between 6 months and 3 years (short-stay group), and 18 who had lived in English-speaking countries for 3 years or more (long-stay group). Both groups achieved above criterion on an English vocabulary test. Results were: both groups preferred material responses for simple objects and substances but not for complex objects, in line with Japanese mono¬linguals, but the long-stay group showed more shape preference than the short-stay group and also were less different from Americans. These effects of acquiring a second language on categorisation have implications for conceptual representation and methodology