95 research outputs found
Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems
We consider recurrence to the initial state after repeated actions of a
quantum channel. After each iteration a projective measurement is applied to
check recurrence. The corresponding return time is known to be an integer for
the special case of unital channels, including unitary channels. We prove that
for a more general class of quantum channels the expected return time can be
given as the inverse of the weight of the initial state in the steady state.
This statement is a generalization of the Kac lemma for classical Markov
chains
Quantized recurrence time in iterated open quantum dynamics
The expected return time to the original state is a key concept
characterizing systems obeying both classical or quantum dynamics. We consider
iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a
broad class of systems that includes classical Markov chains and unitary
discrete time quantum walks on networks. Starting from a pure state, the time
evolution is induced by repeated applications of a general quantum channel, in
each timestep followed by a measurement to detect whether the system has
returned to the original state. We prove that if the superoperator is unital in
the relevant Hilbert space (the part of the Hilbert space explored by the
system), then the expectation value of the return time is an integer, equal to
the dimension of this relevant Hilbert space. We illustrate our results on
partially coherent quantum walks on finite graphs. Our work connects the
previously known quantization of the expected return time for bistochastic
Markov chains and for unitary quantum walks, and shows that these are special
cases of a more general statement. The expected return time is thus a
quantitative measure of the size of the part of the Hilbert space available to
the system when the dynamics is started from a certain state
Collective excitations and instability of an optical lattice due to unbalanced pumping
We solve self-consistently the coupled equations of motion for trapped
particles and the field of a one-dimensional optical lattice. Optomechanical
coupling creates long-range interaction between the particles, whose nature
depends crucially on the relative power of the pump beams. For asymmetric
pumping, traveling density wave-like collective oscillations arise in the
lattice, even in the overdamped limit. Increasing the lattice size or pump
asymmetry these waves can destabilize the lattice.Comment: 5 pages, minor changes (SI units, new references
Quantum rings as electron spin beam splitters
Quantum interference and spin-orbit interaction in a one-dimensional
mesoscopic semiconductor ring with one input and two output leads can act as a
spin beam splitter. Different polarization can be achieved in the two output
channels from an originally totally unpolarized incoming spin state, very much
like in a Stern-Gerlach apparatus. We determine the relevant parameters such
that the device has unit efficiency.Comment: 4 pages, 3 figures; minor change
Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator
We develop a mean-field model describing the Hamiltonian interaction of
ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate
is properly defined by means of a grand-canonical approach. The model is
efficient because only the relevant excitation modes are taken into account.
However, the model goes beyond the two-mode subspace necessary to describe the
self-organization quantum phase transition observed recently. We calculate all
the second-order correlations of the coupled atom field and radiation field
hybrid bosonic system, including the entanglement between the two types of
fields.Comment: 10 page
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