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arXiv:1405.1557 · New Journal of Physics

Exact decoherence dynamics of 1/ f noise

Md Manirul Ali, Ping-Yuan Lo, Wei-Min Zhang

Published Oct 8, 2014• 9 citations
arXivHTMLPDF

Abstract

In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by noise at finite temperature, where a full quantum description of the environment with noise (with ) is presented. The exact master equation and the associated non-equilibrium Greenʼs functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by noise. Our analysis is also applicable to other nano/micro mechanical oscillators. Finally, we demonstrate the non-Markovian decoherence dynamics of photon number superposition states using Wigner distribution that could be measured in experiments.

DOI
10.1088/1367-2630/16/10/103010

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In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by noise at finite temperature, where a full quantum description of the environment with noise (with ) is presented. The exact master equation and the associated non-equilibrium Greenʼs functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by noise. Our analysis is also applicable to other nano/micro mechanical oscillators. Finally, we demonstrate the non-Markovian decoherence dynamics of photon number superposition states using Wigner distribution that could be measured in experiments.
The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature are studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics are completely determined by the propagating (retarded) and correlation Green functions. Comparing the non-Markovian behavior at finite temperature with those at the zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergo a critical transition from the weak to the strong coupling due to the non-Markovian memory effect.
Based on the experiments [S. Putz et al., Nat. Phys. 10, 720 (2014); Nat. Photonics 11, 36 (2017)] on the hybrid quantum system of a superconducting microwave cavity coupled strongly to an inhomogeneous broadening spin ensemble, we use the exact master equation theory to investigate its non-Markovian decoherence dynamics under external driving fields. In the experiments, the spin ensemble is made of negatively charged nitrogen-vacancy defects in diamond. The exact master equation theory generalizes the fluctuation-dissipation relation and depicts in details the transient non-Markovian decoherence, in which the dissipation (relaxation) and fluctuations (noise or dephasing) dynamics is well described and the non-Markovian memory effect can be well characterized. We study the physical picture of the transient non-Markovian decoherence dynamics and explore how the non-Markovian decoherence induced by the inhomogeneous broadening of the spin ensemble is suppressed in the strong-coupling regime. We also show how the spectral hole burning generates localized bound states for the further decoherence suppression. Furthermore, we investigate the two-time correlations to show the relationships between quantum fluctuations and quantum memory.
I present an approach to calculate the finite-frequency quantum noise in systems strongly coupled to structured reservoirs based on the Markovian embedding. This technique consists of mapping of the non-Markovian dynamics of the original system onto the Markovian dynamics of the extended supersystem. The applicability of this method is demonstrated on a single electronic level coupled to a reservoir with an energy-dependent density of states. This model can be mapped onto an equivalent double-level system whose dynamics is governed by an exact Markovian master equation. It is demonstrated that the presented approach provides a way to describe genuinely quantum effects, such as the asymmetry of the absorption and the emission noise, as well as to deal with non-Markovian effects and intra-system interactions on equal footing.
A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.
We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared with the results in Markovian limit, it shows that the non-Markovian effect enhances the disentanglement to the initially entangled coherent state. Our analysis also shows that the decoherence behaviors of the entangled coherent states depend sensitively on the symmetrical properties of the entangled coherent states as well as the interactions between the system and the environment.
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.