Generating and Quantifying Macroscopic Quantum States of Atomic and Optical Systems

Abstract

We discuss a classification of quantum effects based on possibility of emergence in macroscopic scales. We regard a certain phenomena as a genuine macroscopic quantum effect, if it cannot be described by any classical physics nor an accumulation of microscopic quantum effects. A quantum state corresponding to such effect is called a macroscopic quantum state. One prominent aspect among various quantum effects is quantum entanglement. We investigate possibilities of generating macroscopic entanglement between an atom and a thermal state or even between multiple thermal states. We found entanglement is always risen for an arbitrarily large temperature of the thermal states. This indicates importance of coherent interactions rather than the necessity of initial purities. We also propose a generation scheme for hybrid entanglement, which is comprised of classical and quantum states, based on single–photon addition technique. The key idea is that adding a single photon into a coherent state makes another approximate coherent state with a larger amplitude. Since it does not require in–line nonlinear interactions, it is experimentally feasible compared to traditional schemes. Besides generating entanglement, we also attempt to quantify the macroscopic quantumness for arbitrary quantum states of spins. We construct a measure of macroscopic quantumness by counting oscillations of interference fringes in phase space. We apply the measure to typical and intuitive macroscopic quantum states and verify that the measure works properly. Remarkably, we show that quantum phase transition is a naturally occurring genuine macroscopic quantum effect in the spirit of Schr¨odingers cat.