Trapping and Cooling a Mirror to Its Quantum Mechanical Ground State

Abstract

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that its dynamics are perturbed mostly by the vacuum fluctuations of the optical fields. These improvements are expected to bring the task of achieving ground state occupation for the mirror closer to completion.PACS numbers: 42.50. Pq, 42.65.Sf, 85.85.+j, 04.80.Nn The observation of quantum dynamics in truly macroscopic objects is a challenging task that, although not yet achieved, has begun to look more and more feasible [1,2,3,4,5] as a result of recent experimental advances that include novel cooling techniques, progress in nanofabrication, and the improved control of decoherence. This is an exciting prospect, as it would enable us to explore the quantum-classical boundary [6] as well as to test quantum mechanics in an entirely new regime [7]. The implementation of characteristically quantum mechanical phenomena such as entanglement and superposition at a macroscopic scale [8] has broad implications, for instance in the impending merger of quantum optics with condensed matter physics [9]. It also signals direct technological benefits for areas like quantum measurement [10] and communication [11]. Additional potential applications include the interferometric detection of gravitational waves [12] and atomic force microscopy [13].A promising route to these objectives seems to be through the use of optomechanical systems, particularly of mirror cavities coupled to laser radiation [14,15,16]. Experimentally two-mirror cavities have been used, with one mirror held fixed and another mounted on a spring of frequency Ω M and damped at a rate Γ M [ Fig.1(a)]. It has been demonstrated that radiation pressure in the cavity can change these quantities to new values Ω eff and Γ eff [17]. To bring the mirror to its quantum mechanical ground state starting from temperature T the number of quanta [17] have to be reduced to < 1. Here k B and are Boltzmann's and Planck's constants. Most progress so far has been achieved by using the technique of cold damping where the thermal Brownian motion heating up the oscillator is countered by the effect of laser radiation, which increases the mirror damping while introducing very little noise [18]. As a result the ratio Γ M /Γ eff can be decreased to about 10 −4 either passively or by using active feedback cooling. This yields n ∼ 10 4 for typical parameters even if the base temperature is cryogenically reduced to T ∼ 4K [19]. We menti...

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