Entanglement between motional states of a single trapped ion and light

Abstract

We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-Q cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic relative phases. 32.80.Lg, The investigation of trapped ions manipulated by laser beams [1] is of importance not only due to the fundamental physics involved, but also because of potential aplications, such as precision spectroscopy [2] and quantum computation [3]. The laser fields couple the (quantized) internal degrees of freedom in the ion to the (quantized) vibrational motion of the ion's center of mass, but the fields themselves are usually treated as classical. The quantization of the field of course brings new possibilities. Within that realm, it has been already investigated the influence of the field statistics on the ion dynamics [4,5], as well as the transfer of coherence between the motional states and light [6]. There is much interest in the generation of non product, entangled states, and trapped ions seem to constitute a suitable system for doing that [7]. Entangled states involving atoms rather than photons may also be used for testing Bell's inequality [8,9], as it has been already experimentally demonstrated [8]. In general, what has been achieved so far is either the entanglement between the internal degrees of freedom of a single ion (electronic states) with the vibrational motion states of the ion itself, or the entanglement between internal states of several ions [7,10]. Nevertheless, there are few discussions about possibilities of entanglement between the quantized field and the vibrational motion of the ion. This might be of special interest in quantum information; an entangled state of a subsystem that may store quantum information (vibrational motion) with a subsystem that can be used for the propagation of quantum information (light). As another example of entanglement between matter and light, we may refer to a recently reported scheme for entangling light with atoms in a Bose-Einstein condensate [11].In this contribution we present a simple scheme through which there could be produced entanglement between the (center of mass) vibrational motion of a single trapped ion and the electromagnetic field. We show that it is possible to generate the whole Bell state basis simply by choosing either the blue or the red sideband (with different relative phases between ionic states).We consider a single trapped ion, within a Paul trap, which is by its turn placed inside a high-Q cavity [12], so that the cavity mode couples to the internal electronic states of the ion as well as to the vibrational degrees of f...

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