Related papers: Comment on Nongeometric Conditional Phase Shift vi…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a…
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 mechanics allows the emergence of nonstatic quantum light waves in the Fock state even in a transparent medium of which electromagnetic parameters do not vary over time. Such wave packets become broad and narrow in turn periodically…
Geometric phases and holonomies (their non-commuting generalizations) are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against noise and experimental…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus…
Recently, nonadiabatic geometric quantum computation has been received much attention, due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and…
Nonadiabatic holonomic quantum gates are high-speed and robust. Nevertheless, they were found to be more fragile than the adiabatic gates when systematic errors become dominant. Inspired by the dark-path scheme that was used to partially…
Geometric phase of an open quantum system that is interacting with a thermal environment (bath) is studied through some simple examples. The system is considered to be a simple spin-half particle which is weakly coupled to the bath. It is…
We clarify that the nonadiabatic scheme based on a parallel extension of the adiabatic scenario cannot realize the desired goal of quantum computation.
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
We obtain the ground-state energy level and associated geometric phase in the Dicke model analytically by means of the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The non-adiabatic…
A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are usually accompanied by dynamical phases and are thus not…
In Phys. Rev. Lett. {\bf 66}, 847 (1991), T. B. Kepler and M. L. Kagan derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show…
Electronic wave-functions in the adiabatic representation acquire nontrivial geometric phases (GPs) when corresponding potential energy surfaces undergo conical intersection (CI). These GPs have profound effects on the nuclear quantum…