Condensed Matter Theory

Abstract:

AbstractDNA self‐assembly allows the construction of nanometre‐scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single‐stranded loops embedded in a double‐stranded DNA template and is programmed by a set of double‐stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T‐junctions formed by hybridization of single‐stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T‐junction origami motifs and that assembly can be performed at room temperature.

Abstract:

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

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.