Related papers: The Sub-Geometric Phases in Density Matrix
Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably…
A new definition and interpretation of geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected Principal Fibre Bundles, and the…
The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behaviour of the geometric phase during a linear quench caused by a gradual turning off of…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…
Berry monopoles always cancel when summing over a complete set of energy eigenstates. We demonstrate that analogous sum rules exist for geometric phases and their underlying 2-forms in non-adiabatic evolution. Our result has implications…
We use Abelian Bosonization and density matrix renormalization group method to study the effect of density on quantum phases of long range 1-D Bose-Hubbard model. We predict the existence of supersolid phase and also other quantum phases…
We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937-940, 2471] that…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von…
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy…
Off-diagonal mixed state phases based upon a concept of orthogonality adapted to unitary evolution and a proper normalisation condition are introduced. Some particular instances are analysed and parallel transport leading to the…
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield…
We derive the general form of the non-trivial geometric phase resulting from the unique combination of point group and time reversal symmetries. This phase arises e.g. when a magnetic adatom is adsorbed on a non-magnetic C$_n$ crystal…
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in…
The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the…
The level crossing problem and associated geometric terms are neatly formulated by the second quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete…