# Poster session and reception

Tuesday, April 12, 2016 - 4:30pm - 6:00pm

Lind 400

**Fixed-point Engineering in Quasi-local Open-system Dynamics**

Lorenza Viola (Dartmouth College)

Techniques for quantum reservoir and dissipation engineering are playing an increasingly important role in controlling open quantum systems. Implications range from dissipative quantum state preparation and quantum computation, to non-equilibrium quantum phases of matter and quantum thermodynamics. In this poster, I describe progress toward developing a general control-theoretic framework for designing open quantum system dynamics that admits a desired (pure or mixed) quantum state as its unique fixed point, subject to physical quasi-locality constraints. Both rigorous results and illustrative examples are presented for quasi-local dissipative dynamics of interest, including both asymptotic stabilization under continuous-time frustration-free Lindblad dynamics, and finite-time stabilization under discrete-time Markov dynamics. Co-authors: Peter D. Johnson (Dartmouth College), Francesco Ticozzi (U. Padua & Dartmouth College)**Low Dimensional Manifolds for Efficient, Exact Representation of Quantum Systems**

Nikolas Tezak (Stanford University)

The stochastic evolution of dissipative quantum systems often exhibits strong localization of certain observables which confines the quantum state to within a low dimensional subspace of excitations around a generalized coherent state manifold. We present a general approach for deriving coupled stochastic dynamics between the quantum state and the coherent manifold coordinates that parametrize the locally employed basis. This method applies in a variety of different contexts, ranging from quantum feedback networks to the scattering of particles in the presence of a decohering background potential. Besides enabling efficient numerical schemes it can provide analytic insight into the interplay of coherent dynamics and dissipation as they affect key observables of a system.**Resonance Fluorescence from an Artificial Atom in Squeezed Vacuum**

David Toyli (University of California, Berkeley)

The accurate prediction of the fluorescence spectrum of a single atom under coherent excitation, comprising canonical phenomena such as the Mollow triplet, is a foundational success of quantum optics. Despite considerable efforts, experiments demonstrating strong modifications to resonance fluorescence spectra resulting from interactions with non-classical vacuum states have remained elusive, in part due to challenges in efficient light-matter coupling. Here we strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution using a near-quantum-limited parametric amplifier. We observe a dramatic dependence of the Mollow triplet spectrum on the relative phase of the squeezed vacuum environment and observe subnatural fluorescence linewidths that demonstrate up to 3.1 dB of squeezing below the standard vacuum limit [1]. In addition to realizing two seminal predictions for resonance fluorescence in squeezed vacuum, our work provides resource-efficient methods for characterizing squeezed states in cryogenic environments. In collaboration with A.W. Eddins and I. Siddiqi (UC Berkeley); S. Boutin, S. Puri, and A. Blais (Sherbrooke University); and D. Hover, V. Bolkhovsky, and W.D. Oliver (MIT Lincoln Laboratory).

[1] D.M. Toyli*, A.W. Eddins*, et al., arXiv:1602.03240**Modeling Large-Scale 1D and 2D Ising and XY Machines**

Ryan Hamerly (Stanford University)

We model the performance of OPO Ising and XY machines against several 1D and 2D problems. These problems are interesting because they simulate real physics, giving rise to domain walls, frustration and BKT-like vortex behavior. They are also simple to implement with a time-multiplexed OPO network using a small number of static delay lines. We have implemented the 1D Ising model using a 10,000-pulse four-wave mixing fiber OPO, and observe domain formation with statistics that match the theoretical model.**Optimizing Coherent Quantum Feedback Network for Squeezed-light Generation**

Constantin Brif (Sandia National Laboratories)

We study the squeezing spectrum of the output field from a system of two optical parametric oscillators (OPOs) coupled into a coherent quantum feedback network (CQFN). The performance of the CQFN as a high-bandwidth squeezed-light source is optimized by searching over the space of model parameters with experimentally motivated bounds. We use the QNET package to model the CQFN performance and the PyGMO package of global optimization algorithms to maximize the degree of squeezing at a selected bandwidth frequency. The use of global search methods is critical for identifying the best possible performance of the CQFN, especially for squeezing at higher bandwidths. The results demonstrate that the CQFN of two coupled OPOs makes it possible to vary the squeezing spectrum, effectively utilize available pump power, and overall significantly outperform a single OPO. Additionally, the Hessian eigenvalue analysis shows that the squeezing generation performance of optimal configurations of the CQFN is robust to small variations of phase parameters.**Experimental Demonstration of Frequency Autolocking an Optical Cavity Using a Time-varying Kalman Filter**

Ian Petersen (University of New South Wales)

We propose and demonstrate a new autolocking scheme using a three-mirror ring cavity consisting of a linear quadratic regulator and a time-varying Kalman filter. Our technique does not require a frequency scan to acquire resonance. We utilize the singular perturbation method to simplify our system dynamics and to permit the application of linear control techniques. The error signal combined with the transmitted power is used to estimate the cavity detuning. This estimate is used by a linear time-varying Kalman filter which enables the implementation of an optimal controller. Experimental results validate the controller design and we demonstrate improved robustness to disturbances and a faster locking time than a traditional proportional-integral controller. More importantly, the time-varying Kalman filtering approach automatically reacquires lock for large detunings, where the error signal leaves its linear capture range, a feat which linear time-invariant controllers cannot achieve.**Quantum Networks: Analysis, Simulation, and Applications**

Michael Goerz (Stanford University)

Quantum networks provide a rich framework for a wide variety of quantum technologies, with applications in quantum computing, communication, and sensing. We have developed a software toolchain that enables the design and analysis of quantum networks. At its core, the QNET package processes a description of the network, and performs computer-algebraic analysis and model reduction. The toolchain then provides several numerical backends to efficiently simulate the system dynamics as a quantum-stochastic differential equation on a high-performance-computing system. We consider two exemplary applications: entanglement distribution in lossy quantum communication networks, and distributed sensor networks for detecting differential mode disturbances. In both cases, we can provide a realistic numerical model that facilitates the design of a network implementation.**Entanglement Enhanced Quantum Control of Optomechanical Systems**

Sebastian Hofer (University of Vienna )

The optomechanical radiation pressure interaction provides the means to create entanglement between a mechanical oscillator and an electromagnetic field. Here we show how we can utilize this entanglement within the framework of time-continuous quantum control in order to engineer the quantum state of the mechanical system.

Specifically, we analyze how to prepare low-entropy mechanical states by feedback cooling operated in the blue detuned regime, the creation of bipartite mechanical entanglement via time-continuous entanglement swapping, and preparation of a squeezed mechanical state by time-continuous teleportation. Furthermore we discuss the implementation of a Kalman filter (an optimal estimation technique from classical estimation theory) for an existing optomechanical system. This constitutes the first step of an experimental implementation of the control schemes described above.**Imaging High-speed Friction at the Nano-scale**

David Haviland (Royal Institute of Technology (KTH))

Friction is a complicated phenomenon involving nonlinear dynamics at different scales. The origin of friction is poorly understood, due in part to a lack of methods for measuring the force acting on nanometer-scale asperities sliding at velocity of order cm/sec. Dispite enormous advances in experimental technique this combination of small length scale and high velocity remained illusive. We present a technique for measuring the velocity-dependence of frictional forces on a single asperity (an AFM tip) reaching velocities up to several cm/sec. The method is based on the measurement and analysis of intermodulation products, or frequency mixing of multiple drive tones near a high Q torsional resonance, which arrise due to nonlinear frictional force. The method gives the oscillation amplitude dependence of both conservative and dissipative dynamic force quadratures, revealing a transition between stick-slip and smooth sliding, characteristic of friction at very high speeds. We explain the measurements with a modified Prandtl-Tomlinson model that accounts for the viscous and elastic nature of the asperity. With its high force sensitivity for small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces to sub 10 nm spatial resolution.**Environment Assisted Tunneling**

Shanon Vuglar (University of Melbourne)

Environment Engineering presents an alternative approach to measurement based feedback control of quantum systems. Of interest, it may be more tractable for certain control problems. We use Operational Dynamic Modelling to find an environment described by a Lindblad superoperator that assists the tunneling of a wave packet through a potential barrier.**Charting the Circuit QED Design Landscape Using Optimal Control**

Michael Goerz (Stanford University)

Superconducting circuits provide an extremely versatile platform for quantum information processing. The system parameters may be engineered over a wide

range of values. This, however, also provides a challenge in choosing the parameters that most easily allow for the implementation of a universal set of quantum gates. Here, we chart the parameter landscape of the circuit-QED Hamiltonian of two non-tunable transmon qubits coupled via a shared cavity bus. Using a multi-stage optimal control procedure, we first identify suitable candidate points where entanglement can be both created and destroyed. We find the most suitable points to be outside of the usually considered dispersive regime. We then continue to optimize pulses for a complete set of universal quantum gates. While in general, the realization of a perfect entangler and specific local gates are conflicting requirements, we successfully realize a set of 50 ns gates with gate errors near the decoherence-imposed limit.**Probabilistic, Approximate Sketching of Large Quantum Systems**

Dmitri Pavlichin (Stanford University)**Error Bounds on Finite-Dimensional Approximations of Input-Output Open Quantum Systems**

Hendra Nurdin (University of New South Wales)

Many physical systems of interest that are encountered in practice are input-output open quantum systems described by quantum stochastic differential equations (QSDEs) and defined on an infinite-dimensional underlying Hilbert space. Most commonly, these systems involve coupling to a quantum harmonic oscillator as a system component. We are concerned with the error in the finite-dimensional approximation of input-output open quantum systems defined on an infinite-dimensional underlying Hilbert space. We present explicit error bounds between the time evolution of the state of a class of infinite-dimensional quantum systems and its approximation on a finite-dimensional subspace of the original, when both are initialized in the latter subspace.**On Realizations of Linear Quantum Stochastic Systems**

Symeon Grivopoulos (University of New South Wales)

In this work we investigate two issues of realization of the Dynamics of Linear Quantum Stochastic Systems (LQSSs). First, we look into the relation between Hamiltonian (direct) interactions of LQSSs and field-mediated (indirect) interactions. We prove, in particular, that every Hamiltonian interaction between LQSSs can be realized by a field mediated one. Second, we show that there exists a version of the Canonical Kalman Decomposition that is compatible with the particular structure of LQSSs, and we investigate its properties.**Trapped Modes in Linear Quantum Stochastic Networks with Delays**

Gil Tabak (Stanford University)

Networks of open quantum systems with feedback have become an active area of research for applications such as quantum control, quantum communication and coherent information processing. A canonical formalism for the interconnection of open quantum systems using quantum stochastic differential equations (QSDEs) has been developed by Gough, James and co-workers and has been used to develop practical modeling approaches for complex quantum optical, microwave and optomechanical circuits/networks. In this paper we fill a significant gap in existing methodology by showing how trapped modes resulting from feedback via coupled channels with finite propagation delays can be identified systematically in a given passive linear network. Our method is based on the Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued functions, which has been applied in the past to analog electronic networks. Our results provide a basis for extending the Quantum Hardware Description Language (QHDL) framework for automated quantum network model construction (Tezak et al. in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, 2012) to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay.**Single Molecule Force Spectroscopy Reveals Markedly Different Mechanical Behaviors for the Actin-binding and Dystroglycan-binding Halves of Utrophin**

Sayan Ghosal (University of Minnesota, Twin Cities)

The X-lined recessive disease Duchenne Muscular Dystrophy (DMD) is caused by mutations in the gene encoding the large (400 kDa) protein dystrophin. While dystrophin is thought to mechanically stabilize the sarcolemma of striated muscle by coupling the cortical actin cytoskeleton via its N-terminal half with the transmembrane protein b-dystroglycan at its C-terminus, only two studies have reported on the mechanical properties of recombinant dystrophin fragments. The fetal dystrophin homologue utrophin has been shown to compensate for dystrophin in a mouse model of DMD. In this study, we investigated the mechanical extensibility of recombinant utrophin constructs using atomic force microscopy (AFM). Protein molecules with one end attached to a substrate and the other end attached to an AFM probe were pulled at various speeds to force domain unfolding and reveal their mechanical stiffness properties. We measured strikingly different mechanical characteristics for a construct encoding the N-terminal actin-binding half of utrophin (UtrN-R10) versus the C-terminal dystroglycan binding half (UtrR11-CT). UtrN-R10 displayed a “brittle” behavior where the unfolding forces of individual repeats were remarkably uniform upon extension. In contrast, UtrR11-CT exhibited characteristics of a stiffening spring with unfolding forces increasing dramatically with extension. Our findings are even more surprising in light of previous thermodynamic studies that measured identical thermal denaturation profiles for UtrN-R10 and UtrR11-CT. Our study reveals striking differences in the mechanical behaviors for two structurally similar utrophin constructs that are both dominated by a repetitive spectrin-like motif.**Emergent Transport Properties of Molecular Motor Ensemble Affected by Single Motor Mutations**

Shreyas Bhaban (University of Minnesota, Twin Cities)

Motor proteins, such as kinesins and dyneins, are responsible for several fundamental transport functions inside the cell. Impaired functionality of motor proteins, possibly due to mutations, have been linked to disruptions in intracellular transport and neurodegeneration. Cargo transport inside the cell is known to be facilitated by teams of motor proteins. It is particularly significant to study transport of cargo by both wild-type and mutant motor proteins. An exhaustive experimental analysis of specific mutations and its effect on multiple motor based transport is prohibitively time consuming due to combinatorial nature of the study. Thus, there is a significant need for analytical/computational methods to inform experiments.

We addressed this by developing a semi-analytical method to compute average run-length and velocity when cargo is carried by multiple types of motor proteins. Instantiation of this method for a recently reported mutation, which indicated reduced single kinesin stall force, revealed surprising insights. Primarily, in cargoes carried by multiple wild-type and mutant kinesin, mutants determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to increased run-length when load on the cargo is in the vicinity of the mutant's stalling force or multiples of its stalling force. This can have several implications towards understanding the effect of mutations on coordinated transport and knowing which single motor characteristics, when altered, leads to impaired cargo transport.

Furthermore, unlike Monte Carlo based approaches, the unique nature of this method enables study of rare events and results whose accuracy is independent of the number of iterations. The methodology can be further extended to study the effect of other single motor mutations on coordinated cargo transport.