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Physics-Uspekhi

Squeezed light and nonclassical motion in mechanics

Vladimir P Bykov

Published Sep 30, 1993• 5 citations
Publisher

Abstract

From the fact of observation of squeezed light follows the possibility of a nonperturbing or nondemolition measurement (observation) of a single microscopic object in a widely distributed quantum-mechanical state. Macroscopic bodies—objects of classical mechanics—are usually found in states with narrow wave packets, although quantum mechanics does not forbid them to be in states with wide wave packets. The absence of macroscopic bodies in such states requires explanation. In this article it is shown that in virtue of a special, geometrical nature of the gravitational field the absence in nature of macroscopic bodies in widely distributed states can be due to the focusing action of the self-gravitational field of a macroscopic body on its wave packet. Thus, the gravitational field can play an important role in the relaxation of the classical limit of quantum mechanics.

DOI
10.1070/pu1993v036n09abeh002309

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From the fact of observation of squeezed light follows the possibility of a nonperturbing or nondemolition measurement (observation) of a single microscopic object in a widely distributed quantum-mechanical state. Macroscopic bodies—objects of classical mechanics—are usually found in states with narrow wave packets, although quantum mechanics does not forbid them to be in states with wide wave packets. The absence of macroscopic bodies in such states requires explanation. In this article it is shown that in virtue of a special, geometrical nature of the gravitational field the absence in nature of macroscopic bodies in widely distributed states can be due to the focusing action of the self-gravitational field of a macroscopic body on its wave packet. Thus, the gravitational field can play an important role in the relaxation of the classical limit of quantum mechanics.
The existence of quantum correlations affects both microscopic and macroscopic systems. On macroscopic systems, they are difficult to observe and usually irrelevant for the system's evolution due to the frequent energy exchange with the environment. The world-wide network of gravitational-wave (GW) observatories exploits optical as well as mechanical systems that are highly macroscopic and largely decoupled from the environment. The quasi-monochromatic light fields in the kilometer-scale arm resonators have photon excitation numbers larger than 1019, and the mirrors that are quasi-free falling in propagation direction of the light fields have masses of around 40 kg. Recent observations on the GW observatories LIGO and Virgo clearly showed that the quantum uncertainty of one system affected the uncertainty of the other. Here, we review these observations and provide links to research goals targeted with mesoscopic optomechanical systems in other fields of fundamental physical research. These may have Gaussian quantum uncertainties as the ones in GW observatories or even non-Gaussian ones, such as Schrödinger cat states.
Newtonian and Schrödinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a “concentration” near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space.
According to Quantum Mechanics a narrow wave-packet of the center of mass of any macroscopic object should smear out after some time. The problem is usually waved out by assuming that due to their heavy masses this occurs over astronomical times. Without a clear definition of macroscopic objects this remains ambiguous. On the other hand, Quantum Mechanics allows and energetically even prefers largely smeared out c.m. states that never been seen. Why is this the real state of the world we know? Does it suggest a micro-macro threshold with different theoretical descriptions? Does offer micro-miniaturization a hope for answering these questions?
Optical analogies of macroscopic quantum effects (Schr\"odinger cat states, squeezing, collapse, and revival) for light beams propagating in an inhomogeneous linear medium are demonstrated theoretically using exact analytical solutions of the wave equation. It is shown that the coherent superposition of macroscopically distinguishable states is generated via mode interference from an initial off-axis single wave packet. Squeezed cat states with a fidelity >99% arise periodically and disappear rapidly within limited intervals of a propagation distance. Collapse and revival of wave packets at long-term nonparaxial evolution due to mode interference is demonstrated. Oscillations of the beam trajectory occur with extremely small amplitude, of the order of $10{}^{\ensuremath{-}19}$ m, which is typical of the estimated displacement caused by cosmic gravitational waves in gravity-wave detectors.
We report the experimental realization of squeezed quantum states of light, tailored for new applications in quantum communication and metrology. Squeezed states in a broad Fourier frequency band down to 1 Hz have been observed for the first time. Nonclassical properties of light in such a low frequency band are required for high efficiency quantum information storage in electromagnetically induced transparency ( EIT) media. The states observed also cover the frequency band of ultra-high precision laser interferometers for gravitational wave detection and can be used to reach the regime of quantum non-demolition interferometry. Furthermore, they cover the frequencies of motion of heavy macroscopic objects and might therefore support attempts to observe entanglement in our macroscopic world.
We report the experimental realization of squeezed quantum states of light, tailored for new applications in quantum communication and metrology. Squeezed states in a broad Fourier frequency band down to 1 Hz have been observed for the first time. Nonclassical properties of light in such a low frequency band are required for high efficiency quantum information storage in electromagnetically induced transparency (EIT) media. The states observed also cover the frequency band of ultra-high precision laser interferometers for gravitational wave detection and can be used to reach the regime of quantum non-demolition interferometry. Furthermore, they cover the frequencies of motion of heavy macroscopic objects and might therefore support attempts to observe entanglement in our macroscopic world.