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We present a formula for an infinite number of universal quantum logic gates, which are $4$ by $4$ unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order $n$. We then show that this {\it discrete} family, parametrized by integers $n$, is in fact, a small sub-class of a larger {\it continuous} family, parametrized by real numbers $\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian., Comment: 12 pages, no figures. Submitted to Physical Review A

We analyze the entanglement between two matter modes in a hybrid quantum system consists of a microcavity, a quantum well, and a mechanical oscillator. Although the exciton mode in the quantum well and the mechanical oscillator are initially uncoupled, their interaction through the microcavity field results in an indirect exciton-mode--mechanical-mode coupling. We show that this coupling is a Fano-Agarwal-type coupling induced by the decay of the exciton and the mechanical modes caused by the leakage of photons through the microcavity to the environment. Using experimental parameters and for slowly varying microcavity field, we show that the generated coupling leads to an exciton-mode--mechanical-mode entanglement. The maximum entanglement is achieved at the avoided level crossing frequency, where the hybridization of the two modes is maximum. The entanglement is also very robust against the phonon thermal bath temperature., Comment: 6 pages, 4 figures; published version

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with either the number of steps and the number of parties involved. The proof that the optimization of such correlation measure is a NP-problem is based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so called {\it nonlocality} for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures., Comment: 5 pages, 2 figures. Comments are welcome

The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of {\it classicality} as the non-violation of these classical inequalities by quantum states of several multiqubit systems and compare it with the non-violation of Bell inequalities, that is, {\it locality}. We explore --numerically and analytically-- the relationship between several other quantum measures and discover the deep connection existing between them. The results are surprising due to the fact that these measures are very different in their nature and application. The cases for $n=2,3,4$ qubits and a generalization to systems with arbitrary number of qubits are studied here when discriminated according to their degree of mixture., Comment: To appear in Quantum Information Processing

We analyze a scheme to entangle the movable mirrors of two spatially separated nanoresonators via a broadband squeezed light. We show that it is possible to transfer the EPR-type continuous-variable entanglement from the squeezed light to the mechanical motion of the movable mirrors. An optimal entanglement transfer is achieved when the nanoresonators are tuned at resonance with the vibrational frequencies of the movable mirrors and when strong optomechanical coupling is attained. Stationary entanglement of the states of the movable mirrors as strong as that of the input squeezed light can be obtained for sufficiently large optomechanical cooperativity, achievable in currently available optomechanical systems. The scheme can be used to implement long distance quantum state transfer provided that the squeezed light interacts with the nanoresonators., Comment: Published version

An analytic operator solution of a generalized quantum mechanical Hamiltonian of two-mode Bose Einstein condensates (BECs) is obtained and the same is used to investigate the nonclassical properties of the modes present in the system. Nonclassical characters are observed by means of single mode and intermodal squeezing, single mode and intermodal sub-Poissonian boson statistics and intermodal entanglement. In addition to the traditionally studied lower order nonclassical properties, signatures of higher order nonclassical characters of two-mode BEC systems are also obtained by investigating the possibility of higher order antibunching and higher order entanglement. The mutual relation among the observed nonclassicalities and their evolution (variation) with rescaled time and the ratio of the single boson tunneling amplitude ($\varepsilon$) and the coupling constant for the intra-modal interaction ($\kappa$) are also reported., Comment: 9 pages, 7 figures

We study the control of quantum resonances in photonic crystals with electromagnetically induced transparency driven by microwave field. In addition to the control laser, the intensity and phase of the maser can alter the transmission and reflection spectra in interesting ways, producing hyperfine resonances through the combined effects of multiple scattering in the superstructure., Comment: 7 pages, 4 figures

We examine nonclassical properties of the field states generated by applying the photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal and coherent states. Effects of repeated applications of AC and of CA are also studied. We also discuss experimental schemes to realize AC and CA with a cavity system using atom-field interactions., Comment: To be published in Journal of the Optical Society of America B

The transient evolution of nonclassical radiation fields interacting with an atom in a cavity is correlated to the atomic dynamics. Connection between the atomic phases of collapse and revival, and the Wigner function pattern is explored. Initial classical coherent field can evolve into nonclassical field. Schrodinger cat state field is generate during the atomic collapse phase. For initial Schrodinger cat field state, the state dissolves with time but revives during the atomic phase that corresponds with the initial phase. More intricate but orderly characteristics are found between the collapse-revival dynamics and the patterns of the Wigner function for initial thermal field., Comment: 5 pages, 4 figures

The Doppler effect of moving atoms can create irreversibility of light. We show that the laser field in electromagnetic induced transparency (EIT) scheme with atomic motion can control the directional propagation of two counter-propagating probe fields in atomic gas cell. The quantum coherence effect serves as an optical transistor. Interference of the two output fields from the cell shows useful feature for determining the mean atomic velocity and can be useful as quantum velocimeter. We also find that the sign of the dispersive phase in EIT has a unique property, which helps to explain certain features in the interference., Comment: 5 pages, 5 figures

We study the effects of arbitrary laser pulse excitations on quantum correlation, entanglement and the role of quantum noise. The transient quantities are computed exactly using a method that provides exact solutions of the Langevin field operators for photon pairs produced by a double Raman atom driven by laser pulses. Short pulses with appropriate chirping, delay and/or detuning can generate broadband photon pairs and yield results that provide insights on how to generate very large nonclassical correlation. We find that short pulses are not favorable for entanglement. The quantity was previously found to be phase-sensitive and this is used with the pulse area concept to explain the rapid variations of entanglement with pulse width and strength. Photon correlation and entanglement are favored by exclusively two different initial conditions. Analysis reinforces our understanding of the two nonclassical concepts.

We show that an absolute coherent phase of a laser can be used to manipulate the entanglement of photon pairs of two-photon laser. Our focus is on the generation of a continuous source of entangled photon pairs in the double $\Lambda $ (or Raman) scheme. We study the dependence of steady state entanglement on the phase and laser parameters. We obtain a relationship between entanglement and two-photon correlation. We derive conditions that give steady state entanglement for the Raman-EIT scheme and use it to identify region of steady state macroscopic entanglement. No entanglement is found for the double resonant Raman scheme for any laser parameters., Comment: 6 pages (two-column), 4 figures. submitted to a journal on 14 February 2007

The atom fluctuations statistics of an ideal, mesoscopic, Bose-Einstein condensate is investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which weds the master equation/stochastic path integral analysis with the results obtained based on canonical ensemble quasiparticle formalism [V. V. Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures., Comment: 13 pages, 6 figures

We review the phenomenon of equilibrium fluctuations in the number of condensed atoms in a trap containing N atoms total. We start with a history of the Bose-Einstein distribution, the Einstein-Uhlenbeck debate concerning the rounding of the mean number of condensed atoms near a critical temperature, and a discussion of the relations between statistics of BEC fluctuations in the grand canonical, canonical, and microcanonical ensembles. Next we discuss different approaches capable of providing approximate analytical results and physical insight into the problem of fluctuations. In particular, we describe the master equation (similar to the quantum theory of the laser) and canonical-ensemble quasiparticle approaches which give the most accurate and physically transparent picture of the BEC fluctuations. In the last part we describe condensate fluctuations in the interacting Bose gas. In particular, we show that the canonical-ensemble quasiparticle approach works very well for the interacting gases and yields analytical formulas for the characteristic function and all moments of the condensate fluctuations. In most cases the ground-state occupation fluctuations are anomalously large and are not Gaussian even in the thermodynamic limit. We clarify a crossover between the ideal and weakly-interacting-gas statistics which is governed by a pair-correlation squeezing mechanism., Comment: 78 pages, 19 figures, review article

A general scheme for rotational cooling of diatomic heteronuclear molecules is proposed. It uses a superconducting microwave cavity to enhance the spontaneous decay via Purcell effect. Rotational cooling can be induced by sequentially tuning each rotational transition to cavity resonance, starting from the highest transition level to the lowest using an electric field. Electrostatic multipoles can be used to provide large confinement volume with essentially homogeneous background electric field., Comment: 10 pages, 6 figures

We propose a laser cooling concept for the translational motion of molecules which does not require repeated spontaneous emission by each molecule. The cooling works by repetition of three main steps: velocity selection of a narrow momentum width, deceleration of velocity selected molecules and accumulation of the decelerated molecules by an irreversible process, namely by single spontaneous emission. We develop a cooling model which enables analytical description of the transient populations and entropies for the total molecular system, the center of mass degree of freedom and the internal degrees of freedom. Simulation shows that the cooling process can reduce a large momentum width to a final width which in principle can be arbitrarily small. Center of mass entropy is reduced while the internal entropy is increased after cooling. We show that translational cooling can occur during coherent laser interactions. The entropies change in consistency with the Araki-Lieb inequality., Comment: 9 pages Revtex, 5 figures

Ceres, the only dwarf planet in the inner Solar System, appears to be a relict ocean world. Data collected by NASA's Dawn spacecraft provided evidence that global aqueous alteration within Ceres resulted in a chemically evolved body that remains volatile-rich(1). Recent emplacement of bright deposits sourced from brines attests to Ceres being a persistently geologically active world(2,3), but the surprising longevity of this activity at the 92-km Occator crater has yet to be explained. Here, we use new high-resolution Dawn gravity data to study the subsurface architecture of the region surrounding Occator crater, which hosts extensive young bright carbonate deposits (faculae). Gravity data and thermal modelling imply an extensive deep brine reservoir beneath Occator, which we argue could have been mobilized by the heating and deep fracturing associated with the Occator impact, leading to long-lived extrusion of brines and formation of the faculae. Moreover, we find that pre-existing tectonic cracks may provide pathways for deep brines to migrate within the crust, extending the regions affected by impacts and creating compositional heterogeneity. The long-lived hydrological system resulting from the impact might also occur for large impacts in icy moons, with implications for creation of transient habitable niches over time.High-resolution data of Ceres's bright spots (faculae), obtained by Dawn's second extended mission, suggest the existence of a deep brine-rich reservoir that emerged to the surface through long-lived cryovolcanic activity as a consequence of the impact that created Occator crater.