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Physical Review B

Optical excitation of squeezed longitudinal optical phonon states in an electrically biased quantum well

Thomas Papenkort, V. M. Axt, T. Kühn

Published Jun 22, 2012• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.85.235317

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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.
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.
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 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.
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.
Twelve years ago, Richart Slusher and his colleagues at AT&T Bell Labs produced light whose noise was below the vacuum quantum fluctuations, at least in part of the signal. Since then, researchers have been trying to squeeze the uncertainties out of other systems as well. So far they have succeeded in quieting a classical mechanical oscillator and both classical and nonclassical states of a vibrating, trapped ion. Now comes a report of squeezed phonons: By striking a crystal with a femtosecond laser pulse, a group at the University of Michigan believes it has excited an acoustic mode whose variance falls below the standard quantum limit. So far, the noise has been reduced by only 0.01% (the earliest experiments on optical squeezing yielded 20%), but just the concept of squeezed phonons has intrigued many observers.
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.