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Journal of Physics Conference Series

Generation of squeezed phonon states by optical excitation of a quantum dot

Doris E. Reiter, Steffen Sauer, J. Huneke, Thomas Papenkort, T. Kühn, Alexei Vagov, V. M. Axt

Published Nov 1, 2009• 4 citations
Publisher

Abstract

A theoretical analysis of the fluctuation properties of optical phonons generated by the optical excitation of a quantum dot is presented. In particular we study whether squeezed states may be generated where either the fluctuations of the displacement or of the momentum fall below the vacuum level. The calculations are based on a generating functions formalism which provides analytical results for the case of excitation by ultrashort optical pulses. While after a single pulse excitation no squeezing occurs we find that after an excitation with two phase-locked pulses phonon states can be created where the uncertainties of displacement or momentum temporarily fall below their vacuum values.

DOI
10.1088/1742-6596/193/1/012121

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A theoretical analysis of the fluctuation properties of optical phonons generated by the optical excitation of a quantum dot is presented. In particular we study whether squeezed states may be generated where either the fluctuations of the displacement or of the momentum fall below the vacuum level. The calculations are based on a generating functions formalism which provides analytical results for the case of excitation by ultrashort optical pulses. While after a single pulse excitation no squeezing occurs we find that after an excitation with two phase-locked pulses phonon states can be created where the uncertainties of displacement or momentum temporarily fall below their vacuum values.
Abstract In this paper, the fluctuation properties of phonons after the optical excitation of a quantum dot with an ultrashort laser pulse are studied theoretically. When a single pulse with pulse area π creates an exciton in the system, a coherent phonon state builds up. Fluctuations of coherent states are time independent and equal to the vacuum fluctuations. By an excitation with a π/2 pulse a superposition of ground and exciton state is created. In this case the phonon system becomes entangled with the electronic system. In the phonon subsystem this leads to the formation of a statistical mixture of the vacuum and the coherent state. The fluctuations of this mixture oscillate in time with both the single and the double phonon frequency, but never exhibit squeezing. The discrepancies with the predictions made in a Raman tensor model are briefly discussed. All scenarios are illustrated using the Wigner function.
We present quantum kinetic calculations showing how squeezed phonon states can be generated in a biased quantum well by optical driving. In such states the uncertainty of the lattice displacement or momentum is reduced below its zero-point value. It is shown that quantitative results that are meaningful for real observations require accounting for the inevitably limited spatial resolution. Our simulations yield results for the strength of the squeezing and predict under which conditions it can occur: Optical excitations on the lowest absorption line need at least two pulses to generate squeezing, while a single pulse below the band gap may produce a squeezed state which has an almost minimum-value uncertainty product.
Time-dependent lattice fluctuations of an optically excited strongly confined quantum dot are investigated with the aim to analyze the characteristics commonly used for identifying the presence of squeezed phonon states. It is demonstrated that the appearance of fluctuations oscillating with twice the phonon frequency, commonly regarded as a clear indication of squeezed states, cannot be considered as such. The source of the discrepancy with earlier investigations is discussed. Conditions for generating a squeezed state by using a two-pulse excitation are analyzed.
We study squeezed states of phonons, which allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. We investigate the generation of squeezed phonon states using a second-order Raman scattering process. We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments.
We investigate coherent and squeezed quantum states of phonons. The latter allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent states. The expectation values and quantum fluctuations of both the atomic displacement and the lattice amplitude operators are calculated in these states---in some cases analytically. We also study the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach. \textcopyright{} 1996 The American Physical Society.
We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and lattice amplitude operators, and also investigate the possibility of generating squeezed phonon states using a three-phonon parametric amplification process based on phonon-phonon interactions. Furthermore, we also propose a detection scheme based on reflectivity measurements.