We show that in an open optical system with one-photon dissipation formation of a stationary even coherent superposition state is possible, which is a consequence of the fact that the lifetime of the optical system in a coherent superposition state is different for even and odd states.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
In the quantum trajectory approach an open quantum system is represented by a stochastic pure-state wave function. The mixed-state density operator that satisfies the usual master equation is recovered from the quantum trajectories by performing either an ensemble average or, for stationary systems, an average over time. This unraveling of the master equation dynamics into pure-state trajectories provides new insight into the decay of quantum coherence in systems that are open to the environment. Under some conditions macroscopic superposition states are preserved as macroscopic superposition states along individual trajectories, but are reduced to mixtures by the trajectory average. Under other conditions one of the states in a macroscopic superposition becomes dominant (in amplitude) over the other along each quantum trajectory. We discuss the mechanisms that produce these dynamics and assess the implications for the observation of Schrodinger cat states in optics experiments. We present results for some specific examples of macroscopic superposition states generated by a cavity QED system. The system involves a small collection of atoms in an optical cavity driven by a coherent laser field. Under strong-coupling conditions this system produces a variety of Schrodinger cat states whose precise form depends on the number of atoms, the method of excitation (through a cavity mirror or from the side), the initial state of the atoms, and the position of the atoms in the cavity.
The process of the simultaneous absorption of three photons in a medium possessing weak one-photon absorption is analyzed. The mode experiencing absorption is perturbed externally via a three-photon parametric process. It is shown that a steady-state, three-component superposition state of light can exist in this system in the range where the amplitude of the state is small (small perturbations of the system). The latter condition is due to the fact that, in this range of interactions, the field spends significantly more time in one of three types of superposition states of light that form an ensemble of quantum trajectories of the system than in the other two.
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.