Atom-mirror cooling and entanglement using cavity Electromagnetically Induced Transparency

We investigate a hybrid optomechanical system comprised of a mechanical oscillator and an atomic 3-level ensemble within an optical cavity. We show that a suitably tailored cavity field response via Electromagnetically Induced Transparency (EIT) in the atomic medium allows for strong coupling of the mechanical mirror oscillations to the collective atomic ground-state spin. This facilitates ground-state cooling of the mirror motion, quantum state mapping and robust atom-mirror entanglement even for cavity widths larger than the mechanical oscillator frequency

Rigorous Born Approximation and beyond for the Spin-Boson Model

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. We also explore the calculation of the next order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying Mathematica file. We compute the $O(\alpha)$ corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in $\alpha$. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.Comment: Greatly extended version of short paper cond-mat/0304118. Accompanying Mathematica notebook fop5.nb, available in Source, is an essential part of this work; it gives full details of the fourth-order Born calculation summarized in the text. fop5.nb is prepared in arXiv style (available from Wolfram Research

Metastability and anomalous fixation in evolutionary games on scale-free networks

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system's metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending on the network's degree distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter

Few-Qubit lasing in circuit QED

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e., the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit-resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a single- or few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.Comment: Prepared for the proceedings of the Nobel Symposium 2009, Qubits for future quantum computers, May 2009 in Goeteborg, Sweden. Published versio

On the Inelastic Collapse of a Ball Bouncing on a Randomly Vibrating Platform

We study analytically the dynamics of a ball bouncing inelastically on a randomly vibrating platform, as a simple toy model of inelastic collapse. Of principal interest are the distributions of the number of flights n_f till the collapse and the total time \tau_c elapsed before the collapse. In the strictly elastic case, both distributions have power law tails characterised by exponents which are universal, i.e., independent of the details of the platform noise distribution. In the inelastic case, both distributions have exponential tails: P(n_f) ~ exp[-\theta_1 n_f] and P(\tau_c) ~ exp[-\theta_2 \tau_c]. The decay exponents \theta_1 and \theta_2 depend continuously on the coefficient of restitution and are nonuniversal; however as one approches the elastic limit, they vanish in a universal manner that we compute exactly. An explicit expression for \theta_1 is provided for a particular case of the platform noise distribution.Comment: 32 page

Persistence of Quantum Information

There is an increasing interest in the role of macroscopic environments to our understanding of the basics of quantum theory. The knowledge of the implications of the quantum theory to other theories, especially to the statistical mechanics and the domain of validity has captivated scientists from the beginning of quantum description. In such a context, the presence of an environment is commonly thought as entanglement, decohering and mixing properties of quantum system. Generically, an environment is assumed to be a noisy reservoir or a heat bath. Whereas in common interpretation of statistical mechanics the heat bath is unspecified, in quantum systems a heat bath can also provide an indirect interaction between otherwise totally decoupled subsystems and consequently a means to entangle them \cite{cdkl,dvclp,bfp}. In simple example for the entanglement between two qubits due to the interaction with a common heat bath has been explicitly shown in \cite{b}. Whereas in that paper the bath is described by a collection of harmonic oscillators, it seems to be more reasonable to specify the bath by stochastic forces represented by stochastic fields. From a more general point of view we expect the bath should be better described in a stochastic manner and not by deterministic forces. In the present paper we consider a two level system (qubits) which are able to perform flip processes by a coupling to classical stochastic fields. Thus we bridge the gap between quantum and classical probability theory. This problem is related to many other questions of quantum optics and quantum electronics where quantum statistical aspects arising from the intrinsic quantum character of the system while the possible time-dependence of system parameters may be interpreted as the influence of classical thermal fluctuations.Comment: 5 page

Proton or Metal? The H/D Exchange of Arenes in Acidic Solvents

The H/D exchange of arenes in acidic media by transition-metal and main-group-metal complexes and common inorganic salts was studied. The influence of Lewis acidity, anions, charge, and ligands was evaluated. The results indicate that the determination of H/D exchange activity in acidic media is not related to the formation of metal–carbon bonds (i.e., C–H activation). The combined experimental data (regioselectivity, activation energy, kinetics, isotope effects, solvent effects) and DFT calculations point toward a proton catalysis mechanism. Thus, highly Lewis acidic metal compounds, such as aluminum(III) triflate, were extraordinarily active for the H/D exchange reactions. Indeed, the degree of H/D exchange reactivity allows for a comparative measurement of Lewis acidities

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.Comment: 12 pages, 8 figure