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Physics Today

Can Phonons Squeeze their Way Into the Company of Photons?

Barbara Goss Levi

Published Jun 1, 1997• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.881762

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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.
Quantum optics experimenters have been pushing hard to generate greater “squeezing.” This drive was encouraged by last year's milestone demonstration at AT&T Bell Labs that the noise from an optical cavity had been measurably squeezed, that is, that the noise in one phase of the signal had been reduced below the level normally associated with quantum mechanical fluctuations in the vacuum field. Until then, that vacuum noise level had represented the fundamental quantum limit to precision in optical experiments. The Bell Labs experiment reduced the noise by 7–10% below this normal quantum limit (see PHYSICS TODAY, March 1986, page 17), and several experiments since then have achieved noise reductions of at least 20%. The most spectacular results to date have been obtained by a team at the University of Texas at Austin consisting of Ling-An Wu, Min Xiao, H. Jeffrey Kimble, John L. Hall (of the Joint Institute for Laboratory Astrophysics) and Huifa Wu, who have observed noise reductions to more than 60% below the normal level.
While it is true that quantum mechanics imposes strict limits on the precision of measurements, we can sometimes improve measurement precision without violating the uncertainty principle. The rub is that this improvement may be formidable to achieve in practice—and always comes at the expense of a loss in the precision of a complementary measurement. Last October a team at AT&T Bell Labs succeeded in reducing the noise observed from an optical cavity below the “shot noise”—the level of fluctuations associated with variations in the vacuum fields, which is the ultimate limit to accuracy that would be predicted by semiclassical models. Although the Bell Labs experiment reduced the noise below this level by only 7 to 10%, it bolstered hopes that continued progress might eventually yield reductions in noise by factors of ten. Manipulation of the quantum noise limitations might be absolutely critical to such precision measurements as detection of gravity waves, whose faint signals are likely to be near the measurement limit of laser interferometers or mechanical oscillators. The phenomenon might possibly find applications in optical communication or optical memory systems.
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.
Electromagnetic fields, with the noise on one quadrature component reduced to below the quantum mechanical zero-point fluctuation level and the noise on the other quadrature component enhanced to above it, are currently of great interest in quantum optics because of their potential applications to various precision measurements. Such squeezed states of light are usually produced by imposing nonlinear unitary evolution on coherent (or vacuum) states. On the other hand, squeezed states with reduced photon number noise and enhanced phase noise are generated directly by a constant current-driven semiconductor laser. This is the simplest scheme for the generation of nonclassical light, and so far it has yielded the largest quantum noise reduction. The mutual coupling between a lasing junction and an external electrical circuit provides opportunities for exploring the macroscopic and microscopic quantum effects in open systems.
Quantum statistical properties are derived for stimulated Raman scattering by squeezed phonons including squeezing of vacuum fluctuations in radiation modes and sub-Poisson photon behaviour.Initial radiation can be in squeezed thermalized and/or sub-Poisson states, phonon system can also be squeezed.In particular, effects of initial phase conditions, losses, initial nonclassical behaviour and phonon squeezing are demonstrated in terms of reduced factorial moments up to the fifth order in combined photon-photon and photon-phonon modes.Also photon number distribution, quadrature variances and principał squeeze parameters are shown.