Nonclassicality tests for macroscopic massive objects

The predictions of quantum mechanics differ in a very fundamental way from those of classical physics or even more general hidden variable theories. This can be most clearly seen in the violation of Bell- or Leggett-Garg type inequalities or tests of quantum contextuality. These predictions are accurately confirmed on a microscopic level in experiments with photons and atoms, but similar tests with more massive systems --where quantum physics conflicts with our daily life perceptions as well as with alternative theories and (gravity-induced) collapse models -- are still challenging. In a recent work [Phys. Rev. Lett. 112, 190402 (2014)] we have proposed a new and conceptually simple method for testing Leggett-Garg inequalities for macroscopic nanomechanical resonators. In our approach we use a single two-level system (e.g., an electronic spin or superconducting qubit, etc.) to probe the motion of the resonator via Ramsey interference measurements and identify distinct quantum mechanical features by looking at temporal correlations between two or multiple measurement outcomes. More generally, this scheme enables the measurement of modular variables, which play an important role for non-locality and non- classicality tests for continuous variable systems. Since this method can be implemented with a large variety of qubit-resonator systems that are currently implemented in experiments, it might find a wide range of applications for the generation and verification of non-classical motional states. In this project I will explore the broad potential utility of Ramsey interference measurements for fundamental tests of macroscopic quantum superposition states. First of all, this includes a thorough investigation of the implementation of these measurement protocols with state-of-the-art nanomechanical and trapped ion systems. More importantly, it is the aim of this project to identify new measurement protocols, which also allow entanglement verification between multiple mechanical modes and ultimately the violation of Bell inequalities between two space-like separated mechanical resonators. The following objectives, which will be pursued within this Erwin-Schrödinger fellowship, are: The development of schemes for motional state tomography and witnessing non- classical states using Ramsey measurements and the study of possible implementations of these protocols with nanomechanical and trapped ion systems. The design of Kochen-Specker tests for continuous variable (CV) systems using sequential Ramsey measurements. The derivation of methods for generation and detection of entangled Schrödinger cat states using Ramsey measurements and the identification of suitable entanglement witnesses using modular variables. The proposal of a Bell-type inequality in terms of modular variables for testing the nonlocality of space-like separated mechanical resonators.

Quantum mechanics predicts stunning features for microscopic systems which are far from our classical every-day life experience. For example, an electron can be in many different places at the same time, known as superposition, or it can be strongly correlated with a remote electron, called entanglement, which is stronger than any classical correlation. These nonclassical phenomena are already experimentally tested in microscopic systems successfully. In early stage of the project we put forward experimentally feasible schemes of nonclassicality tests of quantum mechanics such as nonlocality and contextuality for more massive and macroscopic systems. Furthermore, the mathematical constructions and the methodology we developed in early stages enabled us to develop efficient and experimentally accessible criteria for characterizing and detecting entanglement in various quantum systems.