First-order coherence versus entanglement in a nano-mechanical cavity

The coherence and correlation properties of effective bosonic modes of a nano-mechanical cavity composed of an oscillating mirror and containing an optical lattice of regularly trapped atoms are studied. The system is modeled as a three-mode system, two orthogonal polariton modes representing the coupled optical lattice and the cavity mode, and one mechanical mode representing the oscillating mirror. We examine separately the cases of two-mode and three-mode interactions which are distinguished by a suitable tuning of the mechanical mode to the polariton mode frequencies. In the two-mode case, we find that the occurrence of entanglement between one of the polariton modes and the mechanical mode is highly sensitive to the presence of the first-order coherence between the modes. In particular, the creation of the first-order coherence among the modes is achieved at the expense of entanglement between the modes. In the three-mode case, we show that no entanglement is created between the independent polariton modes if both modes are coupled to the mechanical mode by the parametric interaction. There is no entanglement between the polaritons even if the oscillating mirror is damped by a squeezed vacuum field. The interaction creates the first-order coherence between the polaritons and the degree of coherence can, in principle, be as large as unity. This demonstrates that the oscillating mirror can establish the first-order coherence between two independent thermal modes. A further analysis shows that two independent thermal modes can be made entangled in the system only when one of the modes is coupled to the intermediate mode by a parametric interaction and the other is coupled by a linear-mixing interaction.Comment: Published versio

Universal contact and collective excitations of a strongly interacting Fermi gas

We study the relationship between Tan's contact parameter and the macroscopic dynamic properties of an ultracold trapped gas, such as the frequencies of the collective oscillations and the propagation of sound in one-dimensional (1D) configurations. We find that the value of the contact, extracted from the most recent low-temperature measurements of the equation of state near unitarity, reproduces with accuracy the experimental values of the collective frequencies of the radial breathing mode at the lowest temperatures. The available experiment results for the 1D sound velocities near unitarity are also investigated.Comment: 5 pages, 3 figure

Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space \Real^3.Comment: 11 page

The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations

In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm with arbitrary phase rotations. We also showed that the phase condition: identical rotation angles, is a sufficient but not a necessary phase condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a table. Corrected the formula for kol on page 10. No figure

Sexually transmitted infection testing and self-reported diagnoses among a community sample of men who have sex with men, in Scotland

Introduction To examine sexually transmitted infection (STI) testing and self-reported diagnoses among men who have sex with men (MSM), in Scotland. Methods Cross-sectional survey of seven Glasgow gay bars in July 2010 (n=822, 62% response rate); 693 are included in the analyses. Results 81.8% reported ever having had an STI test; 37.4% had tested in the previous 6 months; 13.2% reported having an STI in the previous 12 months. The adjusted odds of having ever tested were significantly higher for men who had 6+ sexual partners in the previous 12 months (adjusted OR=2.66), a maximum sexual health knowledge score (2.23), and had talked to an outreach worker/participated in counselling (1.96), and lower for men reporting any high-risk unprotected anal intercourse (UAI) in the previous 12 months (0.51). Adjusted odds of recent testing were higher for men who had 6+ sexual partners (2.10), talked to an outreach worker/participated in counselling (1.66), maximum sexual health knowledge (1.59), and higher condom use knowledge (1.04), and lower for men aged ≥25 years (0.46). Adjusted odds of having had an STI in the previous 12 months were higher for men who had 6+ sexual partners (3.96) and any high-risk UAI in the previous 12 months (2.24) and lower for men aged ≥25 years (0.57). Conclusions STI testing rates were relatively high, yet still below the minimum recommended for MSM at high risk. Consideration should be given to initiating recall systems for men who test positive for STIs, and to developing behavioural interventions which seek to address STI transmission

Ratcheting Heat Flux against a Thermal Bias

Merely rocking the temperature in one heat bath can direct a steady heat flux from cold to hot against a non-zero thermal bias in stylized nonlinear lattice junctions that are sandwiched between two heat baths. Likewise, for an average zero-temperature difference between the two contacts a net, ratchet-like heat flux emerges. Computer simulations show that this very heat flux can be controlled and reversed by suitably tailoring the frequency ($\lesssim$ 100 MHz) of the alternating temperature field.Comment: 5 pages, 6 figure

Cusp Summations and Cusp Relations of Simple Quad Lenses

We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total images of a given source is a constant, we calculate the cusp summations for the five lens models. We find that the cusp summations are always larger than 0 for source on the major cusps, while can be larger or smaller than 0 for source on the minor cusps. We also find that if these lenses tend to the circular lens, the major and minor cusp summations will have infinite values, and with positive and negative signs respectively. The cusp summations do not change significantly if the sources are slightly deviated from the cusps. In addition, through the magnification invariants, we also derive the analytical signed cusp relations on the axes for three lens models. We find that both on the major and the minor axes the larger the lenses deviated from the circular lens, the larger the signed cusp relations. The major cusp relations are usually larger than the absolute minor cusp relations, but for some lens models with very large deviation from circular lens, the minor cusp relations can be larger than the major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA