Iterative path integral calculations of non-linear spectra and entanglement dynamics

Sahrapour, Mohammad

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https://hdl.handle.net/2142/44307 Copy

Description

Title

Iterative path integral calculations of non-linear spectra and entanglement dynamics

Author(s)

Sahrapour, Mohammad

Issue Date

2013-05-24T22:07:15Z

Director of Research (if dissertation) or Advisor (if thesis)

Makri, Nancy

Doctoral Committee Chair(s)

Ryu, Shinsei

Committee Member(s)

• Makri, Nancy
• Eckstein, James N.
• DeMarco, Brian L.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Path Integral
• Entanglement
• Quantum Dynamics
• Non linear Spectroscopy

Abstract

We review an iterative path integral method that allows the computation of exact, long-time dynamics of small systems interacting with a dissipative bath. The method takes advantage of the finite memory of large environments at finite temperature to allow an iterative evaluation of the dynamics, thereby replacing an exponential scaling in simulation time with a linear scaling. This method is applied to calculate the dynamics of two model systems. The first consists of two-qubits interacting with a common bath. In this case we observe a variety of entanglement effects. If the qubits are initially separable, through an indirect coupling, the bath can create steady state entanglement between the qubits. This effect is due to the existence of a decoherence-free subspace as a result of the form of the qubit Hamiltonian and system-bath coupling. Entanglement created by the bath is shown to decrease with increasing temperature and system-bath coupling strength. However large system-bath coupling causes a faster increase in the entanglement. Initially entangled qubits lose their entanglement as a result of interactions with the bath, an effect that is heightened at higher temperatures. Direct coupling between the qubits is shown to slow the decay of entanglement and preserve some entanglement at long times; however at high temperatures this steady state entanglement becomes negligible. The second system we consider is vibrational degree of freedom coupled to a bath of harmonic oscillators or two-level systems. We compute four-time correlation functions which are used to calculate response functions relevant to third order infrared or seventh order Raman experiments for harmonic, Morse, and quadratic-quartic potentials. Our calculations reveal the role of potential features (anharmonicity and eigenvalue spectrum), both on short and long time scales, on the response function. Further, thermal excitation causes dramatic changes in the appearance of the response function, introducing symmetry with respect to the main diagonal. Finally, coupling to harmonic dissipative baths leads to decay of the response function (primarily along the t3 direction) and a broadening of the peaks in its Fourier transform. At high temperatures two-level-system baths are less efficient in destroying coherence than harmonic baths of similar parameters.

Graduation Semester

2013-05

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http://hdl.handle.net/2142/44307

Copyright and License Information

Copyright 2013 Mohammad M. Sahrapour

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