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arXiv:1309.5855 · Journal of High Energy Physics

Quantum decoherence with holography

Shih-Hao Ho, Wei Li, Feng-Li Lin, Bo Ning

Published Jan 1, 2014• 11 citations
arXivHTMLPDF

Abstract

Quantum decoherence is the loss of a system’s purity due to its interaction with the surrounding environment. Via the AdS/CFT correspondence, we study how a system decoheres when its environment is a strongly-coupled theory. In the FeynmanVernon formalism, we compute the influence functional holographically by relating it to the generating function of Schwinger-Keldysh propagators and thereby obtain the dynamics of the system’s density matrix. We present two exactly solvable examples: (1) a straight string in a BTZ black hole and (2) a scalar probe in AdS5. We prepare an initial state that mimics Schrödinger’s cat and identify different stages of its decoherence process using the time-scaling behaviors of Rényi entropy. We also relate decoherence to local quantum quenches, and by comparing the time evolution behaviors of the Wigner function and Rényi entropy we demonstrate that the relaxation of local quantum excitations leads to the collapse of its wave-function.

DOI
10.1007/jhep01(2014)170

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Quantum decoherence is the loss of a system’s purity due to its interaction with the surrounding environment. Via the AdS/CFT correspondence, we study how a system decoheres when its environment is a strongly-coupled theory. In the FeynmanVernon formalism, we compute the influence functional holographically by relating it to the generating function of Schwinger-Keldysh propagators and thereby obtain the dynamics of the system’s density matrix. We present two exactly solvable examples: (1) a straight string in a BTZ black hole and (2) a scalar probe in AdS5. We prepare an initial state that mimics Schrödinger’s cat and identify different stages of its decoherence process using the time-scaling behaviors of Rényi entropy. We also relate decoherence to local quantum quenches, and by comparing the time evolution behaviors of the Wigner function and Rényi entropy we demonstrate that the relaxation of local quantum excitations leads to the collapse of its wave-function.
Abstract Noise sources are ubiquitous in Nature and give rise to a description of quantum systems in terms of stochastic Hamiltonians. Decoherence dominates the noise-averaged dynamics and leads to dephasing and the decay of coherences in the eigenbasis of the fluctuating operator. For energy-diffusion processes stemming from fluctuations of the system Hamiltonian the characteristic decoherence time is shown to be proportional to the heat capacity. We analyze the decoherence dynamics of entangled CFTs and characterize the dynamics of the purity, and logarithmic negativity, that are shown to decay monotonically as a function of time. The converse is true for the quantum Renyi entropies. From the short-time asymptotics of the purity, the decoherence rate is identified and shown to be proportional to the central charge. The fixed point characterizing long times of evolution depends on the presence degeneracies in the energy spectrum. We show how information loss associated with decoherence can be attributed to its leakage to an auxiliary environment and discuss how gravity duals of decoherence dynamics in holographic CFTs looks like in AdS/CFT. We find that the inner horizon region of eternal AdS black hole is highly squeezed due to decoherence.
We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2 + 1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically, an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the travelling shell is brought in correspondence with the evolution of the pattern of entanglement in the dual field theory. We propose, thereafter, that the observed oscillations are the dual counterpart of the quantum revivals studied in the literature. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.
The dynamics of a particle influenced by strongly coupled quantum critical theories is studied by the holographic approach. Based upon the bottom-up approach a real-time prescription for the AdS/CFT correspondence in the context of nonequilibrium physics is developed in accordance with the field theoretic requirements, by which the associated holographic influence functional is obtained. We then study the decoherence dynamics of a particle induced by the quantum critical theories with a dynamical exponent zzz. We find that as zzz increases, the decoherence effect becomes less significant. Similar behavior is found as we heat up the environment. However, in this case the decoherence effect is enhanced not only by its strong coupling constant but also from the finite temperature effect. Finally a comparison is made with the result of a particle influenced by the free field.
It was found, by studying black holes, that the compatibility of the theory of gravity and the laws of quantum mechanics demands that the universe must act like a hologram. That is, all the information inside a region of the universe should be encoded on a so-called holographic screen of one-lesser dimension. This is termed the holographic principle. In a generic spacetime, such as an expanding universe, holographic screens depend on the choice of an observer, which is consistent with the notion that the observer is part of the system in cosmology. In the first part of this dissertation, we study the observer-dependence of holographic screens. This will help us understand how the fundamental description of the universe depends on the choice of the observer. Furthermore, we study the dynamics of the holographic screens and their geometry in the first part of this dissertation.An example where the holographic principle is manifest is the AdS-CFT correspondence. This correspondence connects quantum information quantities, like entanglement and complexity, to geometric quantities, like area and volume, respectively. In the second and the third part of this dissertation, we use the AdS-CFT correspondence as a tool to calculate the entanglement entropy and the computational complexity of a quenched CFT state. Studying the time evolution of the entanglement entropy following a quantum quench teaches us how a CFT state thermalizes. On the other hand, studying the time evolution of the computational complexity allows us to check the validity of various recent conjectures involving black holes and complexity.
We derive a Lindbladian description of holographic Brownian motion in the high-temperature regime. Starting from the influence functional for a trailing string endpoint, we identify the corresponding quantum master equation and prove that it is completely positive and trace-preserving. We determine the coefficients of the Lindbladian explicitly for two holographic backgrounds: the BTZ black hole and the AdS5_55​ black brane, restricting in the latter case to the endpoint fluctuation along the x1x^1x1-direction. We then analyze the time evolution of phase-space moments, energy relaxation, and steady states.
We study thermalization in the holographic (1 + 1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench models, but with some important distinctions. We observe that entanglement propagates along a sharp effective light cone from the points of initial excitations on the boundary. The characteristics of entanglement propagation in the global quench models such as entanglement velocity and the light cone velocity also have a meaning in the bilocal quench scenario. We also observe the loss of memory about the initial state during the equilibration process. We find that the memory loss reflects on the time behavior of the entanglement similarly to the global quench case, and it is related to the universal linear growth of entanglement, which comes from the interior of the forming black hole. We also analyze general two-point correlation functions in the framework of the geodesic approximation, focusing on the study of the late time behavior.