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We present a method to implement two-phonon interactions between mechanical resonators and spin qubits in hybrid setups, and show that these systems can be applied for the generation of nonclassical mechanical states even in the presence of dissipation. In particular, we demonstrate that the implementation of a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator: beyond a certain threshold in the driving amplitude, the driven-dissipative system sustains a mixed steady state consisting of a `jumping cat, i.e., a cat state undergoing random jumps between two phases. We consider realistic setups and show that, in samples within reach of current technology, the system features non-classical transient states, characterized by a negative Wigner function, that persist during timescales of fractions of a second.
Non-classical state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum non-demolition quadrature meas
Quantum optics - the creation, manipulation and detection of non-classical states of light - is a fundamental cornerstone of modern physics, with many applications in basic and applied science. Achieving the same level of control over phonons, the qu
We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are obtained. The anal
Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Pre
The generation of non-classical states of light via photon blockade with time-modulated input is analyzed. We show that improved single photon statistics can be obtained by adequately choosing the parameters of the driving laser pulses. An alternativ