529 research outputs found
Quantum Zeno effect, adiabaticity and dynamical superselection rules
The evolution of a quantum system undergoing very frequent measurements takes
place in a proper subspace of the total Hilbert space (quantum Zeno effect).
When the measuring apparatus is included in the quantum description, the Zeno
effect becomes a pure consequence of the dynamics. We show that for continuous
measurement processes the quantum Zeno evolution derives from an adiabatic
theorem. The system is forced to evolve in a set of orthogonal subspaces of the
total Hilbert space and a dynamical superselection rule arises. The dynamical
properties of this evolution are investigated and several examples are
considered.Comment: 24 pages, 1 figur
The Role of Temperature in the occurrence of some Zeno Phenomena
Temperature can be responsible for strengthening effective couplings between
quantum states, determining a hierarchy of interactions, and making it possible
to establish such dynamical regimes known as Zeno dynamics, wherein a strong
coupling can hinder the effects of a weak one. The relevant physical mechanisms
which connect the structure of a thermal state with the appearance of special
dynamical regimes are analyzed in depth
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
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
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
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
Continuous quantum error correction by cooling
We describe an implementation of quantum error correction that operates
continuously in time and requires no active interventions such as measurements
or gates. The mechanism for carrying away the entropy introduced by errors is a
cooling procedure. We evaluate the effectiveness of the scheme by simulation,
and remark on its connections to some recently proposed error prevention
procedures.Comment: 8 pages, 5 figures. Published version. Minor change in conten
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