Some remarks on the quantum mechanical oscillator phase problem

Ludovico Latmiral, Federico Armata, Marco G. Genoni +2 more

We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation precision posed by quantum mechanics and compare it with the precision obtainable with feasible measurements such as homodyne and heterodyne detection on the cavity field. In particular we demonstrate that homodyne detection is nearly optimal in the limit of a large number of photons of the field and we discuss the estimation precision of small anharmonicities in terms of its signal-to-noise ratio.

F. Cros

Víctor Montenegro, Marco G. Genoni, Abolfazl Bayat +1 more

Optomechanical systems are promising platforms for controlled light-matter interactions.They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state.In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems.In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian.Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction.To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state.We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process.To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector.Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information.Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature.

Mariagiovanna Gianfreda, Giulio Landolfi, Matteo G. A. Paris

Kurt A. Jacobs, Re-Bing Wu, Xiaoting Wang +3 more

Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators, as well as in frequency conversion. We show that if there is no restriction on the size of the linear coupling between two oscillators, then there exist control protocols that will swap their respective states with high fidelity within a time much shorter than a single oscillation period. Standard gradient search methods fail to find these fast protocols. We were able to do so by augmenting standard search methods with a path-tracing technique, demonstrating that this technique has remarkable power to solve time-optimal control problems, as well as confirming the highly challenging nature of these problems. As a further demonstration of the power of path tracing, first introduced by Moore Tibbets et al. ( Phys. Rev. A , 86 (2012) 062309), we apply it to the generation of entanglement in a linear network.