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arXiv:quant-ph/0702198 · Physical Review B

Influence of pure dephasing by phonons on exciton-photon interfaces: Quantum microscopic theory

Kunihiro Kojima, Akihisa Tomita

Published May 15, 2006• 7 citations
arXivHTMLPDF

Abstract

We have developed a full quantum microscopic theory to analyze the time evolution of transversal and longitudinal components of an exciton-single photon system coupled to bulk acoustic phonons. These components are subjected to two decay processes. One is radiative relaxation and the other is pure dephasing due to exciton-phonon interaction. The former results in a decay with an exponent linear to time, while the latter causes a faster initial decay than the radiative decay. We analyzed the dependence of the components on the duration of the input one-photon pulse, temperature, and radiative relaxation rates. Such a quantitative analysis is important for the developments of atom-photon interfaces which enable coherent transfer of quantum information between photons and atomic systems. We found that, for a GaAs spherical quantum dot in which the exciton interacts with bulk phonons, the maximal probability of the excited state can be increased up to 75%. This probability can be considered as the efficiency for quantum information transfer from photon to exciton.

DOI
10.1103/physrevb.73.195312

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We have developed a full quantum microscopic theory to analyze the time evolution of transversal and longitudinal components of an exciton-single photon system coupled to bulk acoustic phonons. These components are subjected to two decay processes. One is radiative relaxation and the other is pure dephasing due to exciton-phonon interaction. The former results in a decay with an exponent linear to time, while the latter causes a faster initial decay than the radiative decay. We analyzed the dependence of the components on the duration of the input one-photon pulse, temperature, and radiative relaxation rates. Such a quantitative analysis is important for the developments of atom-photon interfaces which enable coherent transfer of quantum information between photons and atomic systems. We found that, for a GaAs spherical quantum dot in which the exciton interacts with bulk phonons, the maximal probability of the excited state can be increased up to 75%. This probability can be considered as the efficiency for quantum information transfer from photon to exciton.
We analyse various phonon-assisted mechanisms which contribute to the decoherence of excitonic qubits in quantum dot systems coupled by the Förster-type transfer process. We show the significant loss of coherence accompanied by dissipation due to charge carrier oscillations between qubit states by using a model of one-phonon assisted Förster-type transfer process. We obtain explicit expressions for the relaxation and dephasing times for excitonic qubits interacting with acoustic phonons via both deformation potential and piezoelectric coupling. We compare the decoherence times of the GaAs/AlGaAs material system with half times of concurrence decay in a 2$\otimes$2 bipartite mixed excitonic qubit system. We extend calculations to determine the influence of phonon mediated interactions on the non-unitary evolution of Berry phase in quantum dot systems.
In a parabolic quantum dot (QD), the exciton vacuum state and the exciton ground state may be employed as a two-level quantum system——a qubit. The pure dephaseing due to deformation potential exciton-bulk longitudinal acoustic phonon (LAP) interaction for the exciton qubit is investigated by using the reduce density matrix. The dependence of dephasing factor on time and the confinement length of the QD and temperature is calculated. It is shown that the pure dephasing factor increases quickly with increasing time when time is smaller than 2.5ps, and the dephasing time is of the order of ps. Even at absolute zero temperature, exciton-LAP interaction still causes excitonic dephasing. The pure dephasing factor increases with increasing temperature quickly when temperature is higher than 3K. At the same time, it is found that the confinement length of the QD has important effects on pure dephasing of qubit, the smaller the quantum size, the faster the pure dephasing is. The results show that using appropriate QD size at low temperature and using ultra-fast laser technology can effectively suppress pure dephasing due to exciton-LAP interaction.
We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored'' electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
A full quantum microscopic theory is developed to analyze a biexciton radiative cascade coupled to bulk acoustic phonons in a quantum dot. By considering the phonon sub-system in coherent state representation a new approach is proposed for investigating the phonon effects. Via this approach it is possible to obtain an exact analytical result for the phonon kernel in this system. This approach is introduced in the context of an example: the process of generating polarization-entangled photon pairs from the biexciton cascade in a quantum dot. We calculate the exact density matrix (using quantum state tomography) of photons and their concurrence. We show that the exchange interaction and temperature have remarkable effects on the degree of entanglement of the emitted photons. The approach introduced provides an exact analytical result for finite discrete electron states interacting with phonons.