Related papers: Off-Diagonal Geometric Phases
We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how it could be implemented with superconducting charge qubits. While it may circumvent many of the drawbacks related to the…
The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one…
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…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket…
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous…
We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve…
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…
A magnetically trapped atom experiences an adiabatic geometric (Berry's) phase due to changing field direction. We investigate theoretically such an Aharonov-Bohm-like geometric phase for atoms adiabatically moving inside a storage ring as…
We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase…
Adiabatic evolution is an emergent design principle for time modulated metamaterials, often inspired by insights from topological quantum computing such as braiding operations. However, the pursuit of classical adiabatic metamaterials is…
A quantum system interacting with its environment is subject to dephasing which ultimately destroys the information it holds. Using a superconducting qubit, we experimentally show that this dephasing has both dynamic and geometric origins.…
We present a comprehensive analytical study that extends the conventional formulation of Berry curvature, highlighting its derivation in the context of problematic domains of definition of the operators. Our analysis reveals that handling…
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the…
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…
A periodic perturbation such as a laser field cannot induce transitions between two decoupled states for which the transition matrix element vanishes. We show, however, that if in addition some system parameters are varied adiabatically,…
We study classical and quantum phases in the adiabatic Born-Oppenheimer context. These include a classical astronomical case, the general dual description of the phases, a new "Paradox" connected to scattering Berry phase and its resolution…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric…
We investigate the geometric phase of an atom inside an adiabatic radio frequency (rf) potential created from a static magnetic field (B-field) and a time dependent rf field. The spatial motion of the atomic center of mass is shown to give…