Tommaso Tufarelli

We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. We show how this interaction is realizable in many setups, including nanomechanical systems, ion traps, cavity QED and circuit QED, and in each context we provide quantitative estimates for the relevant parameters. The dynamics of the system is investigated through a master equation, including typical decoherence mechanisms resulting from the coupling of the qubit and oscillator to a thermal Markovian environment. We show how to solve the master equation by adopting a phase-space representation for the oscillator, and derive analytical and approximate solutions for many special cases of interest. Finally, our techniques are applied to a relevant example by studying the dynamics of qubit-oscillator entanglement and the preparation of oscillator states with negative Wigner function.

Setting off from the classic input-output formalism, we develop a theoretical framework to characterise the Gaussian quantum channels relating the initial correlations of an open bosonic system to those of properly identified output modes. We then proceed to apply our formalism to the case of quantum harmonic oscillators, such as the motional degrees of freedom of trapped ions or nanomechanical oscillators, interacting with travelling electromagnetic modes through cavity fields and subject to external white noise. Thus, we determine the degree of squeezing that can be transferred from an intra-cavity oscillator to light, and also show that the intra-cavity squeezing can be transformed into distributed optical entanglement if one can access both output fields of a two-sided cavity.

We introduce a scheme to reconstruct arbitrary states of networks composed of quantum oscillators--e.g., the motional state of trapped ions or the radiation state of coupled cavities. The scheme uses minimal resources, in the sense that it i) requires only the interaction between one-qubit probe and one constituent of the network; ii) provides the reconstructed state directly from the data, avoiding any tomographic transformation; iii) involves the tuning of only one coupling parameter. In addition, we show that a number of quantum properties can be extracted without full reconstruction of the state. The scheme can be used for probing quantum simulations of anharmonic many-body systems and quantum computations with continuous variables. Experimental implementation with trapped ions is also discussed and shown to be within reach of current technology.