Benjamin Russell

Dynamics and Spectra of Monolithic Mode-Locked Laser Diodes Under External Optical Feedback

In this paper, the effect of external optical reflection on the dynamic regimes and spectral properties of Fabry-Perot and distributed Bragg reflector monolithic mode-locked laser diodes is investigated numerically. The relation of the findings to experimental results is discussed, and optimizing the laser construction for reducing the feedback effects is also assessed.

APPLICATIONS OF FINSLER GEOMETRY TO SPEED LIMITS TO QUANTUM INFORMATION PROCESSING

We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Here, we discuss speed limits in the context of quantum computing. We review some relevant parts of the theory of Finsler metrics on Lie groups and homogeneous spaces such as the special unitary groups and complex projective spaces. We show how these constructions can be applied to analysing the limit to the speed of quantum information processing operations in constrained quantum systems with finite dimensional Hilbert spaces of states. We demonstrate the approach applied to a spin chain system.

Geometric Methods for Analysing Quantum Speed Limits: Time-Dependent Controlled Quantum Systems with Constrained Control Functions

We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Here, we discuss speed limits in the context of quantum computing. We derive some results in the familiar representation, then demonstrate that the same results may be derived more readily by transforming the problem description into an alternative representation. This transformed approach is more readily extended to time-dependent and constrained systems. We demonstrate the approach applied to a spin chain system.

The Geometry of Speed Limiting Resources in Physical Models of Computation

We study the maximum speed of quantum computation and how it is affected by limitations on physical resources. We show how the resulting concepts generalize to a broader class of physical models of computation within dynamical systems and introduce a specific algebraic structure representing these speed limits. We derive a family of quantum speed limit results in resource-constrained quantum systems with pure states and a finite dimensional state space, by using a geometric method based on right invariant action functionals on SU(N). We show that when the action functional is bi-invariant, the minimum time for implementing any quantum gate using a potentially time-dependent Hamiltonian is equal to the minimum time when using a constant Hamiltonian, thus constant Hamiltonians are time optimal for these constraints. We give an explicit formula for the time in these cases, in terms of the resource constraint. We show how our method produces a rich family of speed limit results, of which the generalized Margolus–Levitin theorem and the Mandelstam–Tamm inequality are special cases. We discuss the broader context of geometric approaches to speed limits in physical computation, including the way geometric approaches to quantum speed limits are a model for physical speed limits to computation arising from a limited resource.

Mode locked laser diodes in integrated optoelectronics: Some anticipated challenges and possible solutions

The effect of electrical (finite absorber response time) and optical (distant reflector) external effects on the performance of monolithic mode-locked lasers in a monolithically integrated environment is discussed and illustrated using numerical modeling. The relation of the findings to the recent experimental results is discussed, and some methods of reducing the feedback effects are assessed.

Dependence of the quantum speed limit on system size and control complexity

We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. It is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.

Control landscapes for a class of non-linear dynamical systems: sufficient conditions for the absence of traps

We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point control problems for a general class of non-linear control systems of the form of a linear time invariant term with an additional state dependent non-linear term. Trap free landscapes ensure that local optimization methods (such as gradient ascent) can achieve monotonic convergence to effective control schemes in both simulation and practice. Within a large class of non-linear control problems, each of the three conditions is shown to hold for all but a null set of cases. Furthermore, we establish a Lipschitz condition for two of these assumptions; under specific circumstances, we explicitly find the associated Lipschitz constants. A detailed numerical investigation using the D-MOPRH control optimization algorithm is presented for a specific family of systems which meet the conditions for possessing trap free control landscapes. The results obtained confirm the trap free nature of the landscapes of such systems.

Numerical Analysis of Quantum Speed Limits: Controlled Quantum Spin Chain Systems with Constrained Control Functions

We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Certain time bounds are known, but these are not tight bounds. For computation, we also need to consider bounds in the presence of control functions. Here, we use a numerical search approach to discover specific optimal control schemes. We present results for two coupled spins controlled in two scenarios: (i) a single control field influencing each spin separately; (ii) two orthogonal control fields influencing each spin.

External electrical and optical effects in the operation of monolithic mode-locked laser diodes and the potential of nanostructure technologies in reducing these effects

The effects of the electrical parasitics and external optical reflections on the dynamic regimes and spectral properties of Fabry-Perot and Distributed Bragg Reflector monolithic mode-locked laser diodes are investigated numerically. Reduction of the range of stable mode-locking by the screening of the applied electric field by photocarriers accumulated due to the finite absorber circuit response time is investigated. External optical feedback above a certain critical value is shown to affect the laser dynamic drastically, potentially resulting in a wide range of dynamic regimes depending on the external reflector strength and position and in most cases severely degrading the laser performance, in agreement with experimental findings. The potential of some methods of reducing unwanted external electrical and optical effects, including the use of nanostructures such as deep-etched reflectors and Quantum Dot active media, is discussed.

Travelling-wave modelling of optical feedback effect on mode-locked laser diodes and its reduction by amplifier-absorber modules.

A numerical study of the influence of optical feedback on the dynamics of high-bit-rate mode-locked laser diodes is presented. A wide variety of dynamic regimes is discovered, which is qualitatively different to both single-frequency and self-pulsing lasers. The relation of the findings to the recent experimental results is discussed, and the potential of absorber-amplifier modules as optical isolators investigated.