Condensed Matter Theory

Abstract:

We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.

Abstract:

The resistance of DNA to stretch, twist and bend is broadly well estimated by experiments and is important for gene regulation and chromosome packing. However, their sequence-dependence and how bulk elastic constants emerge from local fluctuations is less understood. Here, we present SerraNA, which is an open software that calculates elastic parameters of double-stranded nucleic acids from dinucleotide length up to the whole molecule using ensembles from numerical simulations. The program reveals that global bendability emerge from local periodic bending angles in phase with the DNA helicoidal shape. We apply SerraNA to the whole set of 136 tetra-bp combinations and we observe a high degree of sequence-dependence with differences over 200% for all elastic parameters. Tetramers with TA and CA base-pair steps are especially flexible, while the ones containing AA and AT tend to be the most rigid. Thus, AT-rich motifs can generate extreme mechanical properties, which are critical for creating strong global bends when phased properly. Our results also indicate base mismatches would make DNA more flexible, while protein binding would make it more rigid. SerraNA is a tool to be applied in the next generation of interdisciplinary investigations to further understand what determines the elasticity of DNA.

Abstract:

In nature, interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviors. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors, and depleting agent. It shows a rich behavior evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.

Abstract:

Collective chemotaxis plays a key role in the navigation of cell clusters in e.g. embryogenesis and cancer metastasis. Using the active nematic continuum equations, coupled to a chemical field that regulates activity, we demonstrate and explain a physical mechanism that results in collective chemotaxis. The activity naturally leads to cell polarisation at the cluster interface which induces outwards flows. The chemical gradient then breaks the symmetry of the flow field, leading to a net motion. The velocity is independent of the cluster size in agreement with experiment.