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arXiv:quant-ph/9911069 · Journal of Optics B Quantum and Semiclassical Optics

Motional squashed states

Stefano Mancini, David Vitali, Paolo Tombesi

Published Apr 1, 2000• 6 citations
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Abstract

We show that by using a feedback loop it is possible to reduce the fluctuations in one quadrature of the vibrational degree of freedom of a trapped ion below the quantum limit. The stationary state is not a proper squeezed state, but rather a squashed state, since the uncertainty in the orthogonal quadrature, which is larger than the standard quantum limit, is unaffected by the feedback action.

DOI
10.1088/1464-4266/2/2/322

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We show that by using a feedback loop it is possible to reduce the fluctuations in one quadrature of the vibrational degree of freedom of a trapped ion below the quantum limit. The stationary state is not a proper squeezed state, but rather a squashed state, since the uncertainty in the orthogonal quadrature, which is larger than the standard quantum limit, is unaffected by the feedback action.
Using a feedback loop it is possible to reduce the fluctuations in one quadrature of an in-loop field without increasing the fluctuations in the other. This effect has been known for a long time, and has recently been called `squashing' (Buchler et al 1999 Opt. Lett. 24 259), as opposed to the `squeezing' of a free field in which the conjugate fluctuations are increased. In this paper I present a general theory of squashing, including simultaneous squashing of both quadratures and simultaneous squeezing and squashing. I show that a two-level atom coupled to the in-loop light feels the effect of the fluctuations as calculated by the theory. In the ideal limit of light squeezed in one quadrature and squashed in the other, the atomic decay can be completely suppressed.
A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation.However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable.Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state.We obtain squeezing of one quadrature amplitude 1.1 Æ 0.4 dB below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object.
We present a simple method that can be used to directly measure the squeezing of the quantum motional states of a trapped ion. Through the use of the interaction between the trapped ion and classical lasers, one can design a required coupling between the internal electronic and external vibrational degrees of freedom of the ion and can transfer information of the expectation value of a vibrational operator to the atomic internal populations. Thus measurement of squeezing on the quantum motional state can directly be realized. By adjusting the phases of the interacting lasers, one can measure the squeezing of both position and momentum quadratures.
A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation. However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable. Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state. We obtain squeezing of one quadrature amplitude 1.1±0.4 dB below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object.