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Modern Physics Letters B

ON THE QUANTUM NOISE REDUCTION OF A LASER-COOLED ION COUPLED TO A SOURCE OSCILLATOR

B. Baseia, CELIA M. A. DANTAS, Vanderlei Salvador Bagnato

Published Dec 20, 1994• 1 citation
Publisher

Abstract

In recent literature the treatment of the system constituted by a trapped laser-cooled ion coupled to the modes of a source oscillator is presented. Among several effects presented in this system, the transference of squeezing from the source oscillator to the cooled ion is investigated. In this paper we present an alternative and more elaborate approach for this problem considering mainly the generation and transference of squeezing in this coupled system. We find exact expression for the variances of the involved quadratures. Variations observed due to the change of the involved parameters are also discussed.

DOI
10.1142/s0217984994001746

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In recent literature the treatment of the system constituted by a trapped laser-cooled ion coupled to the modes of a source oscillator is presented. Among several effects presented in this system, the transference of squeezing from the source oscillator to the cooled ion is investigated. In this paper we present an alternative and more elaborate approach for this problem considering mainly the generation and transference of squeezing in this coupled system. We find exact expression for the variances of the involved quadratures. Variations observed due to the change of the involved parameters are also discussed.
A single trapped ion, laser cooled into its quantum ground state of motion, may be used as a very-low-temperature detector of radio-frequency signals applied to the trap end caps. If the signal source is a resonant oscillator of sufficiently high Q, the source may also be placed in its quantum ground state by coupling to the ion. Parametric couplings may be used to cool and detect source modes other than the mode directly coupled to the ion. A theoretical analysis of these cooling and detection processes is presented, and as an example, their application to single trapped electron and proton spectroscopy is examined. Squeezing and low noise detection of one quadrature component of the source oscillation are also discussed. The techniques discussed here may lead to radio-frequency measurements of improved accuracy and sensitivity. Cooling and detection of vibrations of macroscopic oscillators also appear possible.
We have demonstrated that, analogous to the use of quantum mechanical squeezing to beat the quantum shot noise limit, classical squeezing can be used to reduce the effect of thermal amplitude noise in precision measurements. The classical oscillator under study is a single ion in a Penning trap whose motion is cooled by coupling to a thermal bath. The thermal noise distribution is quadrature squeezed by parametric amplification. We observe 6 dB of noise reduction below the equilibrium value when the squeezing axis is 90\ifmmode^\circ\else\textdegree\fi{} out of phase with the coherent signal drive.
It is known from the recent literature that a quadratic oscillator (QO), in terms of the ladder operators â e â+ may exhibit various nonclassical effects, whereas a linear oscillator (LO) does not exhibit them. In this paper we find exact solutions for the system constituted by a LO coupled to a QO and show that nonclassical effects generated in the QO may contaminate the LO. The influence of the involved parameters of the system upon the generation and transference of different nonclassical effects, from the QO to the LO, is investigated. The analytical results are plotted numerically for various situations.
In a squeezed state, the variance in one canonical variable may be suppressed below that normally associated with either the ground state or a coherent state, at the expense of an expansion in the variance of the conjugate variable. Squeezed states are usually discussed in the context of quantized light fields. The principal properties of squeezed states are demonstrated using the motion of quantum mechanical simple harmonic oscillators. The motion of a single oscillator is discussed to introduce the key concepts of squeezing, including quadrature operators, and the error contours of the Wigner function describing the quantum quasiprobability distributions in phase space of the oscillator motion. The main topic of two-mode squeezing is then addressed, in which the fluctuations in a system of two oscillators are tightly correlated. The existence of squeezing is demonstrated in normal mode coordinates representing motion of superpositions of the motion of the two oscillators. The fluctuations within a single oscillator are shown to increase when squeezing increases in the normal modes, generating thermal noise in individual mode subsystems.