Quantum Thermodynamics

Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.Comment: 48 pages, improved and expanded several sections. Comments welcom

Studies of Small Systems in Quantum Information

I study two topics in quantum information theory from the perspective of algebra and geometry. The first relates to exploring the geometry of unitary operators for small quantum systems, specifically three-level systems. Such an understanding of the space over which quantum systems evolve is central to understanding the detailed dynamics of quantum systems and to understand the correlation properties of subsystems that compose a given quantum system. The geometry of unitary operators also allows for the calculation of path-dependent phases called geometric phases. These geometric phases are central to understanding a variety of experiments. I present a general technique, called unitary integration to handle operator equations and employ it to study various physical systems in quantum optics and quantum information. Unitary integration employs an inductive program to solve for the time-evolution of a system in terms of a unitary integration solution of smaller systems. The solution to the smallest system involving just a phase is easily solved, hence truncating the program and providing a solution to the initial problem. Unitary integration is developed in chapters 2 and 3 and this technique is applied to three-level systems in chapter 4. The second topic involves quantum systems involving many subsystems. Understanding the correlation properties of the subsystems that compose such systems has been of interest in the recent past. A useful tool in furthering this understanding has been parametrized families of states. Such states depend on a smaller set of parameters than a general state in the system and hence are easier to study and manipulate. I will present an iterative procedure to define such a parametric family of states called X states. I discuss the algebraic characterization for such states and develop a geometric picture for the algebra of such states. This geometric picture involves generalizations of triangles called ``simplexes\u27. X states are developed along with their algebraic characterization and connections to geometry in chapters 5 and 6. The central theme that is common to both topics is the use of algebraic and geometric concepts to solve for various specific problems in quantum information iteratively. While the first topic deals with the iterative decomposition of operator equations, the second topic deals with the iterative definition of parametrized familes of quantum states

Real-time feedback control of a mesoscopic superposition

We show that continuous real-time feedback can be used to track, control, and protect a mesoscopic superposition of two spatially separated wave-packets. The feedback protocol is enabled by an approximate state-estimator, and requires two continuous measurements, performed simultaneously. For nanomechanical and superconducting resonators, both measurements can be implemented by coupling the resonators to superconducting qubits.Comment: 4 pages, revtex4, 1 png figur

Classical information driven quantum dot thermal machines

We analyze the transient response of quantum dot thermal machines that can be driven by hyperfine interaction acting as a source of classical information. Our setup comprises a quantum dot coupled to two contacts that drive heat flow while coupled to a nuclear spin bath. The quantum dot thermal machines operate both as batteries and as engines, depending on the parameter range. The electrons in the quantum dot interact with the nuclear spins via hyperfine spin-flip processes as typically seen in solid state systems such as GaAs quantum dots. The hyperfine interaction in such systems, which is often treated as a deterrent for quantum information processing, can favorably be regarded as a driving agent for classical information flow into a heat engine setup. We relate this information flow to Landauer's erasure of the nuclear spin bath, leading to a battery operation. We further demonstrate that the setup can perform as a transient power source even under a voltage bias across the dot. Focusing on the transient thermoelectric operation, our analysis clearly indicates the role of Landauer's erasure to deliver a higher output power than a conventional quantum dot thermoelectric setup and an efficiency greater than that of an identical Carnot cycle in steady state, which is consistent with recently proposed bounds on efficiency for systems subject to a feedback controller. The role of nuclear spin relaxation processes on these aspects is also studied. Finally, we introduce the Coulomb interaction in the dot and analyze the transient thermoelectric response of the system. Our results elaborate on the effective use of somewhat undesirable scattering processes as a non-equilibrium source of Shannon information flow in thermal machines and the possibilities that may arise from the use of a quantum information source.Comment: 10 pages, 7 figure

Generalized X states of N qubits and their symmetries

Several families of states such as Werner states, Bell-diagonal states and Dicke states are useful to understand multipartite entanglement. Here we present a [2^(N+1)-1]-parameter family of N-qubit "X states" that embrace all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a sub-algebra of su(2^(N)). We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry.Comment: 4 pages, 2 figure