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Exploring Macroscopic Quantum Mechanics in Optomechanical Devices pp 127–139Cite as

Universal Entanglement Between an Oscillator and Continuous Fields

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Abstract

In the previous two chapters, we have studied the optomechanical entanglement between the optical cavity modes and the mechanical oscillator, both of which have finite degrees of freedom. In this chapter, we study the entanglement between a mechanical oscillator and a coherent continuous optical field which contains infinite degrees of freedom. This system is interesting because it lies in the heart of all optomechanical systems. With a rigorous functional analysis, we develop a new mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that quantum entanglement is always present between the oscillator and the continuous optical field-even when the environmental temperature is high, and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period, if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes, which are ordered by their entanglement strength, to better understand the entanglement structure, in analogy with the energy spectrum of an atomic system.

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Notes

  1. 1.

    An introduction of this method in solving a similar problem can be found in the appendix of Ref. [30].

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  1. Caltech M350-17, Theoretical Astrophysics, E. California Blvd 1200, Pasadena, CA, 91125, USA

    Haixing Miao

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Miao, H. (2012). Universal Entanglement Between an Oscillator and Continuous Fields. In: Exploring Macroscopic Quantum Mechanics in Optomechanical Devices. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25640-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-25640-0_8

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