Optical wavelength conversion of quantum states with optomechanics

An optomechanical interface that converts quantum states between optical fields with distinct wavelengths is proposed. A mechanical mode couples to two optical modes via radiation pressure and mediates the quantum state mapping between the two optical modes. A sequence of optomechanical $\pi/2$ pulses enables state-swapping between optical and mechanical states as well as the cooling of the mechanical mode. Theoretical analysis shows that high fidelity conversion can be realized for states with small photon numbers in systems with experimentally achievable parameters. The pulsed conversion process also makes it possible to maintain high conversion fidelity at elevated bath temperatures.Comment: 4 pages, 4 figures, Fig. 4 looks weird (possible latex style problem

Adiabatic State Conversion and Pulse Transmission in Optomechanical Systems

Optomechanical systems with strong coupling can be a powerful medium for quantum state engineering. Here, we show that quantum state conversion between cavity modes with different wavelengths can be realized with high fidelity by adiabatically varying the effective optomechanical couplings. The fidelity for the conversion of gaussian states is derived by solving the Langevin equation in the adiabatic limit. We also show that photon pulses can be transmitted between input-output channels with different wavelengths via the effective optomechanical couplings and the output pulse shape can also be manipulated.Comment: 5 pages, 2 figures. Supplementary Materials at http://prl.aps.org/supplemental/PRL/v108/i15/e15360

Efficiency in index options markets and trading in stock baskets

Researchers have reported mispricing in index options markets. This study further examines the efficiency of the S&P 500 index options market by testing theoretical pricing relationships implied by no-arbitrage conditions. The effect of a traded stock basket, Standard and Poor's Depository Receipts (SPDRs), on the link between index and options markets is also examined. Pricing efficiency within options markets improves, and the evidence supports the hypothesis that a stock basket enhances the connection between markets. However, when transactions costs and short sales constraints are included, very few violations of the pricing relationships are reported.Options (Finance) ; Stock - Prices