Entanglement of mechanical oscillators coupled to a non-equilibrium environment

Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to non-equilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture

Theory of ground state cooling of a mechanical oscillator using dynamical back-action

A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical back-action is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum.Comment: 5 pages, 2 figure

Ground State Energy Fluctuations of a System Coupled to a Bath

It is often argued that a small non-degenerate quantum system coupled to a bath has a fixed energy in its ground state since a fluctuation in energy would require an energy supply from the bath. We consider a simple model of a harmonic oscillator (the system) coupled to a linear string and determine the mean squared energy fluctuations. We also analyze the two time correlator of the energy and discuss its behavior for a finite string.Comment: 5 pages, 2 eps figures, minor change

Many-body dephasing in a trapped-ion quantum simulator

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering

Hybrid-Entanglement in Continuous Variable Systems

Entanglement is one of the most fascinating features arising from quantum-mechanics and of great importance for quantum information science. Of particular interest are so-called hybrid-entangled states which have the intriguing property that they contain entanglement between different degrees of freedom (DOFs). However, most of the current continuous variable systems only exploit one DOF and therefore do not involve such highly complex states. We break this barrier and demonstrate that one can exploit squeezed cylindrically polarized optical modes to generate continuous variable states exhibiting entanglement between the spatial and polarization DOF. We show an experimental realization of these novel kind of states by quantum squeezing an azimuthally polarized mode with the help of a specially tailored photonic crystal fiber

The statistical mechanics of complex signaling networks : nerve growth factor signaling

It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort is being made to experimentally measure the rate constants for individual steps in these signaling networks, many of the parameters required to describe the behavior of these systems remain unknown, or at best, estimates. With these goals and caveats in mind, we use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. To establish the usefulness of our approach, we have applied our methods towards modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. Using our approach, we are able to extract predictions that are highly specific and accurate, thereby enabling us to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. We show that extracting biologically relevant predictions from complex signaling models appears to be possible even in the absence of measurements of all the individual rate constants. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems wherein particular ''soft'' combinations of parameters can be varied over wide ranges without impacting the final output and demonstrating that a few ''stiff'' parameter combinations center around the paramount regulatory steps of the network. We refer to this property -- which is distinct from robustness -- as ''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption for GIF), IOP style; supp. info/figs. included as brown_supp.pd

Derivative pricing under the possibility of long memory in the supOU stochastic volatility model

We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to observed market prices of plain vanilla options

Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler

We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport is dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at the same energy [P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001)]. We seek to revisit the transport of those nonlocal Cooper pairs as well as the efficiency of such an Andreev entangler when including the quantum noise (decoherence).Comment: 15 pages and 6 figures; final version to appear in Physical Review