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Atomic ions, confined in radio-frequency Paul ion traps, are a promisingcandidate to host a future quantum information processor. In this letter, wedemonstrate a method to couple two motional modes of a single trapped ion,where the coupling mechanism is based on applying electric fields rather thancoupling the ion's motion to a light field. This reduces the design constraintson the experimental apparatus considerably. As an application of thismechanism, we cool a motional mode close to its ground state without accessingit optically. As a next step, we apply this technique to measure the mode'sheating rate, a crucial parameter determining the trap quality. In principle,this method can be used to realize a two-mode quantum parametric amplifier.

Two mode coupling in a single ion oscillator via parametric resonance