Session J30: Open Quantum Systems and Decoherence

Heisenberg scaling of time-limited quantum metrology with realistic decoherence

The prospect of using entanglement to improve various metrology tasks is one of the most promising avenues for a near-term real-world benefit from genuine quantum phenomena [1]. However, in the standard scenario, history-independent Markovian dephasing removes the quantum advantage [2]. We revisit the problem of quantum metrology using the model of trapped ions subject to non-Markovian phase damping decoherence caused by Gaussian noise with finite correlation length and time (a slight generalization of the model used in Ref. [3]). Assuming a fixed available measurement time shorter than the noise correlation time (the non-Markovian limit) and a noise source that is local in space, we recover Heisenberg scaling ($\sim$1/N). This allows one to measure an ``instantaneous'' frequency to a higher precision than the time-averaged noise amplitude and moreover to a higher precision than classically allowed. Interestingly, for this protocol we show that the optimal number of measurements to be performed within the measurement time is three. \\[4pt] [1] V. Giovannetti, S. Lloyd, and L. Maccone Nature Photonics 5, 222 (2011) \newline [2] S. F. Huelga et al. Phys. Rev. Lett. 79, 3865 (1997 \newline [3] T. Monz et al. Phys. Rev. Lett. 106, 130506 (2011)   

Entanglement and diffusive behavior of a driven Floquet system coupled to noise

Attempting to improve the persistence of quantum effects in systems interacting with a bath, we consider a periodically-driven quantum system and focus on its quantum dynamics in the Floquet space. As a toy model, we first consider a harmonic oscillator interacting with a bath and investigate the diffusive behavior in the statistics of observables in the presence of a periodic driving force and analyze the system within the Floquet theory. We then extend this analysis to look at the entanglement of two oscillators interacting with a bath, and investigate whether a periodic driving force can improve the persistence of entanglement between the two systems. We discuss possible experimental realization of our exactly-solvable model with trapped ions. We discuss a Lie-algebraic contraction scheme to map the oscillator properties to spin the systems in an environment. Extensions of our theory to more complicated driven quantum systems will also be discussed. This research is supported by JQI-PFC.   

A Lie-algebraic approach to decoherence in a quantum spin system

Quantum spin systems interacting with environment lose quantum coherence and information due to the debilitating effects of the noise. Quantitative description of decoherence even in the simplest spin-1/2 systems is technically complicated and the conventional approach (e.g., calculating $T_1$ and $T_2$) involves a number of strong approximations. In order to go beyond this approximation scheme and identify its regime of validity, we use the Lie-algebraic contraction, which reduces the su(2) algebra into the solvable oscillator algebra to connect the two dynamical systems. We take advantage of the general exact solution to the latter and build a regular expansion in the contraction parameter to describe dissipative quantum dynamics of the spin. This procedure allows for a controlled non-perturbative treatment of the non-Markovian effects. New interesting effects include deviations from pure diffusion due to bath spectrum and non-Markovian effects in both systems. Our approach could shed light on the spin decoherance problem and noise characterization in experiments relevant for quantum computing.   

Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes

In the initial stage of photosynthesis, light-harvested energy is transferred with remarkably high efficiency to a reaction center, with the vibrational environment assisting the transport mechanism. It is of great interest to mimic this process with present-day technologies. Here we propose an analog quantum simulator of open system dynamics, where noise engineering of the environment has a central role. In particular, we propose the use of superconducting qubits for the simulation of exciton transport in the Fenna-Matthew-Olson protein, a prototypical photosynthetic complex. Our method allows for a single-molecule implementation and the investigation of energy transfer pathways as well as non-Markovian and spatiotemporal noise-correlation effects.   

Quantum signatures of chaos in quantum tomography

We study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography. The record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find an increase in information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. Finally we discuss how this approach can be used in general as a benchmark for information gain in an experimental implementation based on nonlinear dynamics of atomic spins measured weakly by a the Faraday rotation of a laser probe.   

Non-Markovian behavior of small and large complex quantum systems

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the Bloch ball, leading to non-Markovian behavior, even in the limit of infinite environments. Two contributions are identified: one due to the density of states and the other due to correlations in the spectrum. Prototype examples, one for chaotic and the other for regular dynamics are explored.   

Quantum correlation of an optically controlled open quantum system

A precise time-dependent optical control of an open quantum system relies on an accurate account of the quantum interference among the system, the photon control and the dissipative environment. In the spirit of the Keldysh non-equilibrium Green's function approach, we develop a diagrammatic technique to precisely calculate this quantum correlation for a fast multimode coherent photon control against slow relaxation, valid for both Markovian and non-Markovian systems. We demonstrate how this novel formalism can lead to a better accuracy than existing approximations of the master equation. We also describe extensions to cases with controls by photon state other than the coherent Glauber state.   

Effects of counter rotating terms on quantum discord and entanglement between two atoms in a dissipative cavity

We have investigated the role of counter-rotating interaction terms in the Rabi Hamiltonian on the creation and dynamics of entanglement and quantum discord between two identical atoms interacting with a lossy single mode cavity field for a system initially in different product states. For some initial states, the counter-rotating terms are found to lead to steady states in the long time limit which can have high quantum discord, but have no entanglement. The effect of cavity decay rate on these steady states quantum discord has been also investigated, surprisingly the increase in cavity decay rate is found to enhance the steady state quantum discord. Moreover, for certain initial states the effect of counter rotating terms are found to be detrimental to the quantum correlations when counter rotating terms in interaction Hamiltonian are taken into account.   

Pointer state engineering in open quantum systems

Pointer states have a long history in fundamental quantum theory and a practical relevance as long-lasting high-fidelity states in open quantum systems. For generic dissipative dynamics, however, pointer states need not exist or, when they do, need not coincide with states of interest. I will show how open-loop control procedures may be used to engineer dissipation in such a way that any desired initial pure state can be guaranteed to survive with high minimum fidelity over time and retrieved on demand. Quantitative fidelity bounds and constructive control protocols will be presented, and validated through simulation in paradigmatic single- and two- qubit dissipative scenarios. I will also argued that the state selectivity observed in recent dynamical decoupling experiments can be naturally understood within the pointer state engineering framework.   

Crossover from adiabatic to antiadiabatic quantum pumping with dissipation

Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the anti-adiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency $\omega$. The solution allows following in a transparent way the evolution of pumped DC current from much smaller to much larger $\omega$ values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.   

Open Quantum Walks and Dissipative Quantum Computing

Open Quantum Walks (OQWs) have been recently introduced as quantum Markov chains on graphs [S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/]. The formulation of the OQWs is exclusively based upon the non-unitary dynamics induced by the environment. It will be shown that OQWs are a very useful tool for the formulation of dissipative quantum computing and quantum state preparation. In particular, it will be shown how to implement single qubit gates and the CNOT gate as OQWs on fully connected graphs. Also, OQWS make possible the dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell states. Finally, it will be shown how to reformulate efficiently a discrete time version of dissipative quantum computing in the language of OQWs.   

Non-Markovian dynamics of a solid-state charge qubit measured by a quantum point contact

We study a system of a charge qubit consisting of an electron in two coupled quantum dots (CQD's) detected by a quantum point contact (QPC). We derive perturbatively the non-Markovian quantum master equation for the CQD's system and calculate the transport current through the QPC (considered as a reservoir) to second order in the system-reservoir interaction. The non-Markovianity of the whole system comes from the energy-dependent tunneling amplitudes and energy-dependent densities of states of the QPC, which are modeled as a spectral density with a Lorentzian shape. In the non-Markovian case, the decay coefficients in the derived master equation and transport current are time-dependent and involve the real and imaginary parts of the contributions from the QPC reservoir correlation functions. In the wide-band limit (WBL), the various Markovian master equations in different parameter regimes are recovered, and the contributions of the imaginary parts are found to vanish. However, in the non-Markovian regime, the contributions of the imaginary parts significantly influence the dynamics of the charge qubit and thus the transport current. Especially, the non-Markovian transient currents through QPC differ significantly from the WBL Markovian counterparts and thus may serve as a witness for the non-Markovian behavior in the QPC-qubit system.   

Hierarchical equations of motion: A fundamental theory for quantum open systems

As a powerful alternative to the influence functional path integral formalism, HEOM has been exploited in the study of various systems. In this talk, I will present some recent advancement on the HEOM-based nonlinear/nonequilibrium response theory and efficient implementation methods. Numerical demonstrations include coherent two-dimensional spectroscopy signals of light-harvesting model systems, and transport current noise spectrums through Anderson model quantum dots, operated in high-order co-tunneling regime.   

Fidelity of the ground state in adiabatic quantum computation

The energy gap between the ground and excited states of a qubit register performing an adiabatic quantum computation (AQC) algorithm is expected to provide additional stability against decoherence by environmental noise. However, the precise quantitative magnitude of this effect is still an open question. In this work, we show that fidelity of the ground state provides the ultimate quantitative measure of the AQC stability against decoherence. Even if the qubit register is not driven out of the ground state by the time evolution of the algorithm, the ground state is deformed by the qubit-environment interaction. The extent of this deformation can be characterized by the same noise correlators that determine the relaxation rates in the gate-model QC. We derive finite-temperature expression for the ground-state fidelity and calculate it numerically for the 16-qubit instances of adiabatic quantum optimization.