Quantum Zeno subspaces and dynamical superselection rules

The quantum Zeno evolution of a quantum system takes place in a proper subspace of the total Hilbert space. The physical and mathematical features of the "Zeno subspaces" depend on the measuring apparatus: when this is included in the quantum description, the Zeno effect becomes a mere consequence of the dynamics and, remarkably, can be cast in terms of an adiabatic theorem, with a dynamical superselection rule. We look at several examples and focus on quantum computation and decoherence-free subspaces.Comment: 35 pages, 5 figure

Three different manifestations of the quantum Zeno effect

Three different manifestations of the quantum Zeno effect are discussed, compared and shown to be physically equivalent. We look at frequent projective measurements, frequent unitary "kicks" and strong continuous coupling. In all these cases, the Hilbert space of the system splits into invariant "Zeno" subspaces, among which any transition is hindered.Comment: 16 pages, 4 figure

Berry phase due to quantum measurements

The usual, "static" version of the quantum Zeno effect consists in the hindrance of the evolution of a quantum systems due to repeated measurements. There is however a "dynamic" version of the same phenomenon, first discussed by von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which a system is forced to follow a given trajectory. A Berry phase appears if such a trajectory is a closed loop in the projective Hilbert space. A specific example involving neutron spin is considered and a similar situation with photon polarization is investigated.Comment: 6 pages, 2 figures. Contribution to the Sixth Central-European Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May 199

Modifying the lifetime of an unstable system by an intense electromagnetic field

We study the temporal behavior of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. We analyze the dependence of the lifetime of the initial state on the intensity of the laser field. The phenomenon we discuss is related to both electromagnetic induced transparency and quantum Zeno effect.Comment: 10 pages, 3 figures. Contribution to Sixth Central-European Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May 199

Unstable systems and quantum Zeno phenomena in quantum field theory

We analyze the Zeno phenomenon in quantum field theory. The decay of an unstable system can be modified by changing the time interval between successive measurements (or by varying the coupling to an external system that plays the role of measuring apparatus). We speak of quantum Zeno effect if the decay is slowed and of inverse quantum Zeno (or Heraclitus) effect if it is accelerated. The analysis of the transition between these two regimes requires close scrutiny of the features of the interaction Hamiltonian. We look in detail at quantum field theoretical models of the Lee type.Comment: 25 pages, 6 figure

Quantum Zeno dynamics: mathematical and physical aspects

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.Comment: 52 pages, 10 figure

Wigner function and coherence properties of cold and thermal neutrons

We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A "decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.Comment: 6 pages, 3 figures. Contribution to the Sixth Central-European Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May 199

Mesoscopic interference

We analyze a double-slit experiment when the interfering particle is "mesoscopic" and one endeavors to obtain Welcher Weg information by shining light on it. We derive a compact expression for the visibility of the interference pattern: coherence depends on both the spatial and temporal features of the wave function during its travel to the screen. We set a bound on the temperature of the mesoscopic particle in order that its quantum mechanical coherence be maintained.Comment: 16 pages, 14 figure