Session N19: Open Quantum Systems and Decoherence

Complementarity of information and the emergence of the classical world

We prove an anti-symmetry property relating accessible information about a system through some auxiliary system F and the quantum discord with respect to a complementary system F'. In Quantum Darwinism, where fragments of the environment relay information to observers -- this relation allows us to understand some fundamental properties regarding correlations between a quantum system and its environment. First, it relies on a natural separation of accessible information and quantum information about a system. Under decoherence, this separation shows that accessible information is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. Second, It shows that objective information becomes accessible to many observers only when quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality, and supports Bohr's intuition that quantum phenomena acquire classical reality only when communicated.   

Quantum Decoherence with Bath Size: Dynamics, Randomness, and Connectivity

The decoherence of a quantum system $S$ coupled to a quantum environment $E$ is considered, where $S+E$ is a closed quantum system. For typical states $X$ of the Hilbert space, i.e. for states chosen randomly from the Hilbert space unit hypersphere, we derive a scaling relation for the sum of the off-diagonal elements of the reduced density matrix $\rho_S$ of $S$. This sum is a measure of the decoherence of $S$, and decreases as $D_E^{-\frac{1}{2}}$ as the dimension of the environment Hilbert space $D_E$ increases. We present long-time calculations of the time dependent Schr\"odinger equation (TDSE) of spin $\frac{1}{2}$ particles comprising $S+E$ in order to test this scaling. The Hamiltonian has uniform or random Heisenberg couplings of a spin chain for $S+E$. Factors that affect the approach to the predicted scaling relation for the Heisenberg $d=1$ ring include how quickly and successfully the dynamics drives an initial configuration to an $X$ state, and this depends on the randomness of the coupling strengths in the Hamiltonian and the addition of other connections either within $E$ or between $S$ and $E$.   

Open Quantum Walks: Microscopic Derivation and Generalised Master Equation

Recently, a formalism for discrete time open quantum walks was introduced [S. Attal et al., J. Stat. Phys., 147 (2012) 832; S. Attal, F. Petruccione, I. Sinayskiy, Phys. Lett. A, 376 (2012) 1545]. This formalism is exclusively based on the non-unitary dynamics induced by the environment. This approach rests upon the implementation of appropriate completely positive maps. Open quantum walks include the classical random walk and through a realization procedure a connection to the Hadamard quantum walk is established. Open quantum walks allow for an unravelling in terms of quantum trajectories. It was shown [I. Sinayskiy and F. Petruccione, QIP 11 (2012) 1301] that open quantum walks can perform universal quantum computation and can be used for quantum state engineering. Here, we present the microscopic derivation of open quantum walks. A walk on a graph is considered and transitions between vertices are mediated by the interaction of the walker with a shared bosonic environment. The reduced dynamics of the walker is shown to be described in terms of a generalised Markovian master equation. The time discretization of the master equation gives raise to an open quantum walk. Based on the class of microscopic models considered here possible physical implementations are discussed.   

Efficient simulation of stochastically-driven quantum systems

The simulation of noisy quantum systems is critical for accurate modeling of many experiments, including those implementing quantum information tasks. The expansion of a stochastic equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically-driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Forster resonance transfer in Rydberg atoms with non-perturbative position fluctuations. \newline \newline The work was supported by the Sandia National Laboratories Directed Research and Development Program. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Realizing a lattice-based quantum simulator using circuit quantum electrodynamics

Recent experimental progress in circuit quantum electrodynamics (CQED) has triggered extensive theoretical research on using these systems to implement a CQED lattice-based quantum simulator for non-equilibrium physics. CQED systems are inherently open due to unavoidable photon loss and the ease of replenishing photons through driving. The focus of this research is to experimentally realize proposals focused on building lattice-based simulators, where each lattice site contains a single CQED element. Results will be presented on a kagome lattice of 49 niobium coplanar waveguide resonators, each coupled a single aluminum transmon qubit   

Decoherence and Thermalisation dynamics in many-body systems

An isolated quantum system prepared in a pure state will evolve coherently in time. However, local observables of the system can appear thermalised in the sense that the reduced density matrix of a small part of the system approaches the form expected from a thermal Gibbs distribution. This eigenstate thermalisation hypothesis has been demonstrated numerically. We explore the dynamics of how the system approaches this thermalised state. Our previous numerical work on the Hubbard model [Phys. Rev. Lett. 105, 260402 (2010)] has found two dynamical regimes with exponential and Gaussian decay towards the thermal state respectively. We discuss how this can be understood analytically in a generic theory. We will explore the impact of symmetry laws on the dynamics.   

Wigner distribution functions for complex dynamical systems: a path integral approach

Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynman's and Vernon's influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators.   

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem.   

Understanding the role of counter-rotating terms of Rabi Model under dissipation

Rabi Hamiltonian is one of the most complete quantum mechanical models that describe the interaction of a qubit with a quantized field which became more relevant with the recent developments in the circuit QED technologies that made possible to obtain strong coupling in the field-qubit interactions. In the dissipative regime, the standart Lindblandian quantum optical master equation with Rabi Hamiltonian leads to unphysical effects such as an increase of total excitation number in the qubit-field system with increasing cavity decay rate. Recently, a new Liouville superoperator describing the loses of the system have been derived [F.Beaudoin, J.M.Gambetta, A.Blais, Phys. Rev. A 84, 043832 (2011)] at the ultrastrong coupling regime. In this study, by using the new dissipators for cavity loses, we have investigated the role of counter-rotating terms on the dynamics of entanglement and quantum discord at ultrastrong coupling regime and provided a comprehensible picture for the role of counter-rotating terms on quantum correlations. Contrary to the standart dissipators case, the steady-state of the system is found to contain non-zero entanglement.   

Classical memoryless noise-induced maximally discordant mixed separable steady states

Noise is, generally, detrimental to quantum correlations. For some initial states, it has been shown that back-action of the environment or the memory in environment-system interactions can create and/or sustain some of the quantum correlations in the system. In the present study, we have investigated the dynamics of quantum discord and entanglement for two qubits subject to independent global transverse and/or longitudinal memoryless noisy classical fields and have shown that a classical memoryless noise can lead to maximally discordant mixed separable states. Moreover, two independent noises in the system are found to enhance both the steady state randomness and quantum discord in the absence of entanglement for some initial states.   

Decoherence effects of a charge detector on a nearby quantum dot

We study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of an adjacent spin-1/2 quantum dot (QD). The Coulomb interaction between electrons traversing the QPC and those within the QD contribute to charge fluctuations and decoherence of the Kondo state in the QD, which can be detected through conductance measurements. Modeling the QPC as two current leads coupled through a localized level near resonance with the Fermi level of the leads, one can explore different transport regimes of the detector: Coulomb blockade, ballistic resonant-transport, and a Kondo screening state (associated with the ``0.7 anomaly''). Transitions between different states are achieved by tuning the capacitive coupling $u$, or the local gates in the QPC. The transitions are studied using Varma--Yafet variational techniques, providing interesting insights into the different regimes. We employ numerical renormalization-group calculations to accurately evaluate the spectral densities and conductance behavior of the coupled QPC--QD system. We report the dependence of the Kondo temperatures of both subsystems on the capacitive coupling strength $u$, and describe the phases' signatures in the local spectral densities and the conductance profile of the QPC.   

Full Counting Statistics of Photons Emitted by a Double Quantum Dot

We analyze the full counting statistics of photons emitted by a double quantum dot (DQD) to a high-quality microwave resonator due to the dipole coupling. We show that at the frequency matching condition $\omega_0=\Delta E/\hbar$ for the energy splitting $\Delta E$ of the DQD and the resonator frequency $\omega_0$, photon statistics exhibits both a sub-Poissonian distribution and anti-bunching. In the ideal case, when the system decoherence stems only from photo-detection process, the photon noise is reduced to nearly one-half of the noise for the Poisson distribution. The photon distribution remains sub-Poissonian even at moderate decoherence in the DQD, but eventually become super-Poissonian in the regime of strong decoherence of the DQD.   

Dephasing by a Zero Temperature Detector and the Friedel Sum Rule

Detecting the passage of an interfering particle through one of the interferometer's arms, known as ``which path'' measurement, gives rise to interference visibility degradation (dephasing). Here we consider a detector at {\em equilibrium} [1]. At finite temperature dephasing is caused by thermal fluctuations of the detector. More interestingly, in the zero temperature limit, equilibrium quantum fluctuations of the detector give rise to dephasing of the out-of-equilibrium interferometer. This dephasing is a manifestation of an orthogonality catastrophe which differs qualitatively from Anderson's. Its magnitude is directly related to the Friedel sum rule.\\[4pt] [1] B.~Rosenow and Y.~Gefen, Phys. Rev. Lett. {\bf 108}, 256805 (2012).   

Quantum dynamics of a spin chain in the presence of engineered collective noise

We experimentally and theoretically investigate the effect of engineered collective noise on the quantum dynamics of a spin chain evolving under the double-quantum Hamiltonian. This Hamiltonian is related by a similarity transformation to the isotropic XX Hamiltonian, and is experimentally accessible in solid-state NMR using coherent averaging techniques. In the absence of noise, a localized magnetic moment is observed to move down the chain at a constant velocity. We show that this transport is disrupted by the presence of collective z-noise, and that the magnetic moment becomes localized at the initial site as the strength of the noise increases. The relevance to quantum information transport in spin chains is also discussed.