5,268 research outputs found
Dissipative Chaotic Quantum Maps: Expectation Values, Correlation Functions and the Invariant State
I investigate the propagator of the Wigner function for a dissipative chaotic
quantum map. I show that a small amount of dissipation reduces the propagator
of sufficiently smooth Wigner functions to its classical counterpart, the
Frobenius-Perron operator, if . Several consequences arise: The
Wigner transform of the invariant density matrix is a smeared out version of
the classical strange attractor; time dependent expectation values and
correlation functions of observables can be evaluated via hybrid
quantum-classical formulae in which the quantum character enters only via the
initial Wigner function. If a classical phase-space distribution is chosen for
the latter or if the map is iterated sufficiently many times the formulae
become entirely classical, and powerful classical trace formulae apply.Comment: 14 revtex pages including 4 ps figure
Large effects of boundaries on spin amplification in spin chains
We investigate the effect of boundary conditions on spin amplification in
spin chains. We show that the boundaries play a crucial role for the dynamics:
A single additional coupling between the first and last spins can
macroscopically modify the physical behavior compared to the open chain, even
in the limit of infinitely long chains. We show that this effect can be
understood in terms of a "bifurcation" in Hilbert space that can give access to
different parts of Hilbert space with macroscopically different physical
properties of the basis functions, depending on the boundary conditions. On the
technical side, we introduce semiclassical methods whose precision increase
with increasing chain length and allow us to analytically demonstrate the
effects of the boundaries in the thermodynamic limit.Comment: replaced figs. 6,10 and corrected corresponding numerical values for
initial slopes, added a new fig.7 and a section on total fidelitie
Efficiency of Producing Random Unitary Matrices with Quantum Circuits
We study the scaling of the convergence of several statistical properties of
a recently introduced random unitary circuit ensemble towards their limits
given by the circular unitary ensemble (CUE). Our study includes the full
distribution of the absolute square of a matrix element, moments of that
distribution up to order eight, as well as correlators containing up to 16
matrix elements in a given column of the unitary matrices. Our numerical
scaling analysis shows that all of these quantities can be reproduced
efficiently, with a number of random gates which scales at most as with the number of qubits for a given fixed precision
. This suggests that quantities which require an exponentially large
number of gates are of more complex nature.Comment: 18 pages, 10 figure
Spontaneous emission from a two--level atom tunneling in a double--well potential
We study a two-level atom in a double--well potential coupled to a continuum
of electromagnetic modes (black body radiation in three dimensions at zero
absolute temperature). Internal and external degrees of the atom couple due to
recoil during emission of a photon. We provide a full analysis of the problem
in the long wavelengths limit up to the border of the Lamb-Dicke regime,
including a study of the internal dynamics of the atom (spontaneous emission),
the tunneling motion, and the electric field of the emitted photon. The
tunneling process itself may or may not decohere depending on the wavelength
corresponding to the internal transition compared to the distance between the
two wells of the external potential, as well as on the spontaneous emission
rate compared to the tunneling frequency. Interference fringes appear in the
emitted light from a tunneling atom, or an atom in a stationary coherent
superposition of its center--of--mass motion, if the wavelength is comparable
to the well separation, but only if the external state of the atom is
post-selected.Comment: 24 pages, 4 figures; improved discussion on the limitations of the
theor
Decoherence-enhanced measurements
Quantum-enhanced measurements use highly non-classical quantum states in
order to enhance the precision of the measurement of classical quantities, like
the length of an optical cavity. The major goal is to beat the standard quantum
limit (SQL), i.e. a precision of order , where is the number of
quantum resources (e.g. the number of photons or atoms used), and to achieve a
scaling , known as the Heisenberg limit. Doing so would have tremendous
impact in many areas, but so far only three experiments have demonstrated a
slight improvement over the SQL. The required quantum states are generally
difficult to produce, and very prone to decoherence. Here we show that
decoherence itself may be used as an extremely sensitive probe of system
properties. This should allow for a new measurement principle with the
potential to achieve the Heisenberg limit without the need to produce highly
entangled states.Comment: 14 pages, 2 figure
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