Adiabatically steered open quantum systems: Master equation and optimal phase

We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a non-steered system in the first super-adiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.Comment: 8 pages, no figures, final versio

Coherent caloritronics in Josephson-based nanocircuits

We describe here the first experimental realization of a heat interferometer, thermal counterpart of the well-known superconducting quantum interference device (SQUID). These findings demonstrate, on the first place, the existence of phase-dependent heat transport in Josephson-based superconducting circuits and, on the second place, open the way to novel ways of mastering heat at the nanoscale. Combining the use of external magnetic fields for phase biasing and different Josephson junction architectures we show here that a number of heat interference patterns can be obtained. The experimental realization of these architectures, besides being relevant from a fundamental physics point of view, might find important technological application as building blocks of phase-coherent quantum thermal circuits. In particular, the performance of two different heat rectifying devices is analyzed.Comment: 34 pages, 15 figures, review article for Ultra-low temperatures and nanophysics ULTN2013. Microkelvin Proceeding

Coherent diffraction of thermal currents in Josephson tunnel junctions

We theoretically investigate heat transport in temperature-biased Josephson tunnel junctions in the presence of an in-plane magnetic field. In full analogy with the Josephson critical current, the phase-dependent component of the heat flux through the junction displays coherent diffraction. Thermal transport is analyzed in three prototypical junction geometries highlighting their main differences. Notably, minimization of the Josephson coupling energy requires the quantum phase difference across the junction to undergo \pi-slips in suitable intervals of magnetic flux. An experimental setup suited to detect thermal diffraction is proposed and analyzed.Comment: 6.5 pages, 4 color figures, updated versio

Non-Abelian geometric phases in ground state Josephson devices

We present a superconducting circuit in which non-Abelian geometric transformations can be realized using an adiabatic parameter cycle. In contrast to previous proposals, we employ quantum evolution in the ground state. We propose an experiment in which the transition from non-Abelian to Abelian cycles can be observed by measuring the pumped charge as a function of the period of the cycle. Alternatively, the non-Abelian phase can be detected using a single-electron transistor working as a charge sensor.Comment: 5 pages, 3 figures; added references and clarified discussion about earlier research on the fiel

Geometric quantum gates with superconducting qubits

We suggest a scheme to implement a universal set of non-Abelian geometric transformations for a single logical qubit composed of three superconducting transmon qubits coupled to a single cavity. The scheme utilizes an adiabatic evolution in a rotating frame induced by the effective tripod Hamiltonian which is achieved by longitudinal driving of the transmons. The proposal is experimentally feasible with the current state of the art and could serve as a first proof of principle for geometric quantum computing.Comment: 7 pages, 5 figure

Ground-state geometric quantum computing in superconducting systems

We present a theoretical proposal for the implementation of geometric quantum computing based on a Hamiltonian which has a doubly degenerate ground state. Thus the system which is steered adiabatically, remains in the ground-state. The proposed physical implementation relies on a superconducting circuit composed of three SQUIDs and two superconducting islands with the charge states encoding the logical states. We obtain a universal set of single-qubit gates and implement a non-trivial two-qubit gate exploiting the mutual inductance between two neighboring circuits, allowing us to realize a fully geometric ground-state quantum computing. The introduced paradigm for the implementation of geometric quantum computing is expected to be robust against environmental effects.Comment: 9 pages, 5 figures. Final version with notation and typos correcte

Decoherence in adiabatic quantum evolution - application to Cooper pair pumping

One of the challenges of adiabatic control theory is the proper inclusion of the effects of dissipation. Here, we study the adiabatic dynamics of an open two-level quantum system deriving a generalized master equation to consistently account for the combined action of the driving and dissipation. We demonstrate that in the zero temperature limit the ground state dynamics is not affected by environment. As an example, we apply our theory to Cooper pair pumping which demonstrates the robustness of ground state adiabatic evolution.Comment: 7 pages, derivation of the master equation in the appendi

Decoherence of adiabatically steered quantum systems

We study the effect of Markovian environmental noise on the dynamics of a two-level quantum system which is steered adiabatically by an external driving field. We express the master equation taking consistently into account all the contributions to the lowest non-vanishing order in the coupling to the Markovian environment. We study the master equation numerically and analytically and we find that, in the adiabatic limit, a zero-temperature environment does not affect the ground state evolution. As a physical application, we discuss extensively how the environment affects Cooper pair pumping. The adiabatic ground state pumping appears to be robust against environmental noise. In fact, the relaxation due to the environment is required to avoid the accumulation of small errors from each pumping cycle. We show that neglecting the non-secular terms in the master equation leads to unphysical results, such as charge non-conservation. We discuss also a possible way to control the environmental noise in a realistic physical setup and its influence on the pumping process.Comment: 13 pages, 11 figures. Final versio

The Coherent Crooks Equality

This chapter reviews an information theoretic approach to deriving quantum fluctuation theorems. When a thermal system is driven from equilibrium, random quantities of work are required or produced: the Crooks equality is a classical fluctuation theorem that quantifies the probabilities of these work fluctuations. The framework summarised here generalises the Crooks equality to the quantum regime by modeling not only the driven system but also the control system and energy supply that enables the system to be driven. As is reasonably common within the information theoretic approach but high unusual for fluctuation theorems, this framework explicitly accounts for the energy conservation using only time independent Hamiltonians. We focus on explicating a key result derived by Johan {\AA}berg: a Crooks-like equality for when the energy supply is allowed to exist in a superposition of energy eigenstates states.Comment: 11 pages, 3 figures; Chapter for the book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook", eds. F. Binder, L. A. Correa, C. Gogolin, J. Anders and G. Adess