Related papers: Geometric Phase and Quantum Phase Transition : Two…
We show the explicit expression of the geometric phase for $n$-partite Gaussian states. In our analysis, the covariance matrix can be obtained as a boundary term of the geometric phase.
We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
The quantum phase transition in an atom-molecule conversion system with atomic hopping between different hyperfine states is studied. In mean field approximation, we give the phase diagram whose phase boundary only depends on the atomic…
We introduce the notion of the geometrically equivalent quantum systems (GEQS) as quantum systems that lead to the same geometric phases for a given complete set of initial state vectors. We give a characterization of the GEQS. These…
The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are…
Quantum phase transitions in the one-dimensional extended quantum compass model in transverse field are studied by using the Jordan-Wigner transformation. This model is always gapful except at the critical surfaces where the energy gap…
It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a…
We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
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 investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Magnetometry is a powerful technique for the non-invasive study of biological and physical systems. A key challenge lies in the simultaneous optimization of magnetic field sensitivity and maximum field range. In interferometry-based…