Shaken not stirred: Creating exotic angular momentum states by shaking an optical lattice

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a four-level model for each well. The results are compared with numerical simulations of the full Schroedinger equation.Comment: 20 pages, 8 figure

Quantum state transfer via invariant based shortcuts to adiabaticity

Adiabatic processes in quantum mechanics are very useful to prepare and manipulate quantum states but have the drawback of requiring long operation times. Hence there is a long time for the system to interact with its environment which can lead to a loss of coherence of the final state. This decoherence is problematic for implementing future quantum technologies which require the state's quantum mechanical features. “Shortcuts to Adiabaticity"(STA) provides a toolbox of methods to improve on adiabatic processes. Using these methods one can derive alternative processes which work for much shorter times with perfect fidelity. Since adiabatic processes are ubiquitous in atomic, molecular and optical physics, there is a broad scope of application for STA. In this thesis, STA (especially those using Lewis-Riesenfeld invariants) are applied to a variety of quantum systems for the purpose of quantum state transfer. In particular I show that STA control schemes in two- and three-level systems can be optimised to be more stable against unwanted uncontrollable transitions than adiabatic methods with the same operation time. I also show that STA methods can be applied in a triple well ring system with complex tunnelling, in optical lattices for the purposes of generating a higher orbital state of neutral atoms and in Penning traps to quickly compress or expand the trapped ion wavefunction. Finally I also investigate the effect of classical Poisson white noise on adiabatic processes

Classical dissipative cost of quantum control

Protocols for non-adiabatic quantum control often require the use of classical time varying fields. Assessing the thermodynamic cost of such protocols, however, is far from trivial. In this letter we study the irreversible entropy produced by the classical apparatus generating the control fields, thus providing a direct link between the cost of a control protocol and dissipation. We focus, in particular, on the case of time-dependent magnetic fields and shortcuts to adiabaticity. Our results are showcased with two experimentally realisable case studies: the Landau-Zener model of a spin-1/2 particle in a magnetic field and an ion confined in a Penning trap

Universally Robust Quantum Control

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses which are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. We highlight the power of our results for error resistant single- and two-qubit gates.Comment: 14 pages, 6 figure

First Passage Times for Continuous Quantum Measurement Currents

The First Passage Time (FPT) is the time taken for a stochastic process to reach a desired threshold. It finds wide application in various fields and has recently become particularly important in stochastic thermodynamics, due to its relation to kinetic uncertainty relations (KURs). In this letter we address the FPT of the stochastic measurement current in the case of continuously measured quantum systems. Our approach is based on a charge-resolved master equation, which is related to the Full-Counting statistics of charge detection. In the quantum jump unravelling we show that this takes the form of a coupled system of master equations, while for quantum diffusion it becomes a type of quantum Fokker-Planck equation. In both cases, we show that the FPT can be obtained by introducing absorbing boundary conditions, making their computation extremely efficient. The versatility of our framework is demonstrated with two relevant examples. First, we show how our method can be used to study the tightness of recently proposed KURs for quantum jumps. Second, we study the homodyne detection of a single two-level atom, and show how our approach can unveil various non-trivial features in the FPT distribution.Comment: 8 pages, 2 figure

A systematic review and meta-regression analysis of the vitamin D intake-serum 25-hydroxyvitamin D relationship to inform European recommendations

The present study used a systematic review approach to identify relevant randomised control trials (RCT) with vitamin D and then apply meta-regression to explore the most appropriate model of the vitamin D intake–serum 25-hydroxyvitamin D (25(OH)D) relationship to underpin setting reference intake values. Methods included an updated structured search on Ovid MEDLINE; rigorous inclusion/exclusion criteria; data extraction; and meta-regression (using different model constructs). In particular, priority was given to data from winter-based RCT performed at latitudes >49•58°N (n 12). A combined weighted linear model meta-regression analyses of natural log (Ln) total vitamin D intake (i.e. diet and supplemental vitamin D) versus achieved serum 25(OH)D in winter (that used by the North American Dietary Reference Intake Committee) produced a curvilinear relationship (mean (95% lower CI) serum 25(OH)D (nmol/l) = 9•2 (8•5) Ln (total vitamin D)). Use of non-transformed total vitamin D intake data (maximum 1400 IU/d; 35µg/d) provided for a more linear relationship (mean serum 25(OH)D (nmol/l) = 0•044 × (total vitamin D) + 33•035). Although inputting an intake of 600 IU/d (i.e. the RDA) into the 95% lower CI curvilinear and linear models predicted a serum 25(OH)D of 54•4 and 55•2 nmol/l, respectively, the total vitamin D intake that would achieve 50 (and 40) nmol/l serum 25(OH)D was 359 (111) and 480 (260) IU/d, respectively. Inclusion of 95% range in the model to account for inter-individual variability increased the predicted intake of vitamin D needed to maintain serum 25(OH)D ≥50 nmol/l to 930 IU/d. The model used to describe the vitamin D intake–status relationship needs to be considered carefully when setting new reference intake values in Europe