Entropy Production of Doubly Stochastic Quantum Channels

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.Comment: 24 page

Relative Entropy Convergence for Depolarizing Channels

We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von-Neumann entropy. This result is compared to similar bounds obtained recently by Kim et al. and we show a version of Pinsker's inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer's inequality to prove a uniform lower bound.Comment: 21 pages, 3 figure

Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics

In this letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The non-demolition measurement technique gives access to the otherwise concealed intrinsic, low temperature electron spin relaxation time of n-doped GaAs (110) quantum wells and to the corresponding low temperature anisotropic spin relaxation. The Brownian motion of the electrons within the spin noise probe laser spot becomes manifest in a modification of the spin noise line width. Thereby, the spatially resolved observation of the stochastic spin polarization uniquely allows to study electron dynamics at equilibrium conditions with a vanishing total momentum of the electron system

GHz Spin Noise Spectroscopy in n-Doped Bulk GaAs

We advance spin noise spectroscopy to an ultrafast tool to resolve high frequency spin dynamics in semiconductors. The optical non-demolition experiment reveals the genuine origin of the inhomogeneous spin dephasing in n-doped GaAs wafers at densities at the metal-to-insulator transition. The measurements prove in conjunction with depth resolved spin noise measurements that the broadening of the spin dephasing rate does not result from thermal fluctuations or spin-phonon interaction, as previously suggested, but from surface electron depletion

Efficient Data Averaging for Spin Noise Spectroscopy in Semiconductors

Spin noise spectroscopy (SNS) is the perfect tool to investigate electron spin dynamics in semiconductors at thermal equilibrium. We simulate SNS measurements and show that ultrafast digitizers with low bit depth enable sensitive, high bandwidth SNS in the presence of strong optical background shot noise. The simulations reveal that optimized input load at the digitizer is crucial for efficient spin noise detection while the bit depth influences the sensitivity rather weakly

Crunching Biofilament Rings

We discuss a curious example for the collective mechanical behavior of coupled non-linear monomer units entrapped in a circular filament. Within a simple model we elucidate how multistability of monomer units and exponentially large degeneracy of the filament's ground state emerge as a collective feature of the closed filament. Surprisingly, increasing the monomer frustration, i.e., the bending prestrain within the circular filament, leads to a conformational softening of the system. The phenomenon, that we term polymorphic crunching, is discussed and applied to a possible scenario for membrane tube deformation by switchable dynamin or FtsZ filaments. We find an important role of cooperative inter-unit interaction for efficient ring induced membrane fission

A red/far-red light-responsive bi-stable toggle switch to control gene expression in mammalian cells

Growth and differentiation of multicellular systems is orchestrated by spatially restricted gene expression programs in specialized subpopulations. The targeted manipulation of such processes by synthetic tools with high-spatiotemporal resolution could, therefore, enable a deepened understanding of developmental processes and open new opportunities in tissue engineering. Here, we describe the first red/far-red light-triggered gene switch for mammalian cells for achieving gene expression control in time and space. We show that the system can reversibly be toggled between stable on- and off-states using short light pulses at 660 or 740 nm. Red light-induced gene expression was shown to correlate with the applied photon number and was compatible with different mammalian cell lines, including human primary cells. The light-induced expression kinetics were quantitatively analyzed by a mathematical model. We apply the system for the spatially controlled engineering of angiogenesis in chicken embryos. The system's performance combined with cell- and tissue-compatible regulating red light will enable unprecedented spatiotemporally controlled molecular interventions in mammalian cells, tissues and organisms