Quantum decoherence of a single ion qubit induced by photon-number fluctuations

ABSTRACT Quantum measurement is based on the interaction between a quantum object and a meter entangled with theobject. While information about the object is being extracted by the interaction, the quantum uctuations of theobject are imprinted onto the meter as a form of decoherence. Here, we study the nondestructive reconstructionof the photon number in an optical cavity, harnessing the quantum decoherence. We consider a single 40 Ca + ion that is dispersively coupled to a high- nesse cavity. While the cavity is populated with weak coherentstates, Ramsey spectroscopy is performed on the qubit transition to identify the shift and the broadening ofthe atomic energy levels. The shift is due to the ac Stark e ect induced by cavity photons, and the broadeningis attributed to the photon-number uctuations of the cavity eld. We show theoretically that photon-numberdistributions of the intracavity elds can be reconstructed in a basis of up to eleven Fock states with the maximumlikelihood method. Furthermore, we show that the photon number of each polarization component can also bereconstructed, taking advantage of the rich energy-level structure of the ion. In combination with currentlyavailable mirror-coating technology, quantum non-demolition (QND) measurement of cavity photons will makeit possible to create and manipulate nonclassical cavity- eld states in the optical domain.Keywords: nondestructive measurement, quantum uctuations, quantum decoherence, trapped ions, cavityquantum electrodynamics