We explore a single degenerate optical cavity supporting a synthetic two dimensional space, which includes the frequency and the orbital angular momentum axes of light. We create the effective gauge potential inside this synthetic space and show that the system exhibits topologicallyprotected one-way edge states along the OAM axis at the boundaries of the frequency dimension. In this synthetic space, we present a robust generation and manipulation of entanglement between the frequency and OAM of photons. Our work shows that a higher dimensional synthetic space involving multiple degrees of freedom of light can be achieved in a "zero" dimensional spatial structure, pointing towards a unique platform to explore topological photonics and to realize potential applications in optical communications and quantum information processing.
We investigate Casimir effect as well as thermal Casimir effect for a pair of parallel perfectly plates placed in general stationary space-time background. It is found that the Casimir energy is influenced by the 00-component of metric and the corresponding quantity in dragging frame. We give a scheme to renormalize thermal correction to free energy in curved space-time. It is shown that the thermal corrections to Casimir thermodynamic quantities not only depend on the proper temperature and proper geometrical parameters of the plates, but also on the determinant of space-time metric.
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:~the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties can, in special cases, be deduced from the quantum metric. In this work, we establish general and exact relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. In particular, we demonstrate that topological indices (Chern numbers or winding numbers) are bounded by the quantum volume determined by the quantum metric. Our theoretical framework, which builds on the Clifford algebra of Dirac matrices, is applicable to topological insulators and semimetals of arbitrary spatial dimensions, with or without chiral symmetry. This work clarifies the role of the Fubini-Study metric in topological states of matter, suggesting unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
The quantum coherence (QC) of two comoving atoms on a stationary trajectory is investigated. We develop a formalism to characterize the properties of atoms on a stationary trajectory. We give a criterion under which QC is frozen to a nonzero value. The frozen condition that vanishing super- or subradiant decay rate is not so sensitive to the initial condition of state. We show that enhanced QC and a subradiant state can be gained from the initial state.
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