253 research outputs found
Sequential measurement of conjugate variables as an alternative quantum state tomography
It is shown how it is possible to reconstruct the initial state of a
one-dimensional system by measuring sequentially two conjugate variables. The
procedure relies on the quasi-characteristic function, the Fourier-transform of
the Wigner quasi-probability. The proper characteristic function obtained by
Fourier-transforming the experimentally accessible joint probability of
observing "position" then "momentum" (or vice versa) can be expressed as a
product of the quasi-characteristic function of the two detectors and that,
unknown, of the quantum system. This allows state reconstruction through the
sequence: data collection, Fourier-transform, algebraic operation, inverse
Fourier-transform. The strength of the measurement should be intermediate for
the procedure to work.Comment: v2, 5 pages, no figures, substantial improvements in the
presentation, thanks to an anonymous referee. v3, close to published versio
Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects
We study the dynamics of the classical and quantum mechanical scattering of a
wave packet from an oscillating barrier. Our main focus is on the dependence of
the transmission coefficient on the initial energy of the wave packet for a
wide range of oscillation frequencies. The behavior of the quantum transmission
coefficient is affected by tunneling phenomena, resonances and kinematic
effects emanating from the time dependence of the potential. We show that when
kinematic effects dominate (mainly in intermediate frequencies), classical
mechanics provides very good approximation of quantum results. Moreover, in the
frequency region of optimal agreement between classical and quantum
transmission coefficient, the transmission threshold, i.e. the energy above
which the transmission coefficient becomes larger than a specific small
threshold value, is found to exhibit a minimum. We also consider the form of
the transmitted wave packet and we find that for low values of the frequency
the incoming classical and quantum wave packet can be split into a train of
well separated coherent pulses, a phenomenon which can admit purely classical
kinematic interpretation
Coherent Control of Trapped Bosons
We investigate the quantum behavior of a mesoscopic two-boson system produced
by number-squeezing ultracold gases of alkali metal atoms. The quantum Poincare
maps of the wavefunctions are affected by chaos in those regions of the phase
space where the classical dynamics produces features that are comparable to
hbar. We also investigate the possibility for quantum control in the dynamics
of excitations in these systems. Controlled excitations are mediated by pulsed
signals that cause Stimulated Raman Adiabatic passage (STIRAP) from the ground
state to a state of higher energy. The dynamics of this transition is affected
by chaos caused by the pulses in certain regions of the phase space. A
transition to chaos can thus provide a method of controlling STIRAP.Comment: 17 figures, Appended a paragraph on section 1 and explained details
behind the hamiltonian on section
Proof of the generalized Lieb-Wehrl conjecture for integer indices larger than one
Gnutzmann and Zyczkowski have proposed the Renyi-Wehrl entropy as a
generalization of the Wehrl entropy, and conjectured that its minimum is
obtained for coherent states. We prove this conjecture for the Renyi index
q=2,3,... in the cases of compact semisimple Lie groups. A general formula for
the minimum value is given.Comment: 8 pages, typos fixed, published versio
On Randomness in Quantum Mechanics
The quantum mechanical probability densities are compared with the
probability densities treated by the theory of random variables. The relevance
of their difference for the interpretation of quantum mechanics is commented
Chaos assisted adiabatic passage
We study the exact dynamics underlying stimulated Raman adiabatic passage
(STIRAP) for a particle in a multi-level anharmonic system (the infinite
square-well) driven by two sequential laser pulses, each with constant carrier
frequency. In phase space regions where the laser pulses create chaos, the
particle can be transferred coherently into energy states different from those
predicted by traditional STIRAP. It appears that a transition to chaos can
provide a new tool to control the outcome of STIRAP
Measurement uncertainty relations
Measurement uncertainty relations are quantitative bounds on the errors in an
approximate joint measurement of two observables. They can be seen as a
generalization of the error/disturbance tradeoff first discussed heuristically
by Heisenberg. Here we prove such relations for the case of two canonically
conjugate observables like position and momentum, and establish a close
connection with the more familiar preparation uncertainty relations
constraining the sharpness of the distributions of the two observables in the
same state. Both sets of relations are generalized to means of order
rather than the usual quadratic means, and we show that the optimal constants
are the same for preparation and for measurement uncertainty. The constants are
determined numerically and compared with some bounds in the literature. In both
cases the near-saturation of the inequalities entails that the state (resp.
observable) is uniformly close to a minimizing one.Comment: This version 2 contains minor corrections and reformulation
Nature of phase transition(s) in striped phase of triangular-lattice Ising antiferromagnet
Different scenarios of the fluctuation-induced disordering of the striped
phase which is formed at low temperatures in the triangular-lattice Ising model
with the antiferromagnetic interaction of nearest and next-to-nearest neighbors
are analyzed and compared. The dominant mechanism of the disordering is related
to the formation of a network of domain walls, which is characterized by an
extensive number of zero modes and has to appear via the first-order phase
transition. In principle, this first-order transition can be preceded by a
continuous one, related to the spontaneous formation of double domain walls and
a partial restoration of the broken symmetry, but the realization of such a
scenario requires the fulfillment of rather special relations between the
coupling constants.Comment: 10 pages, 7 figures, ReVTeX
A super-Ohmic energy absorption in driven quantum chaotic systems
We consider energy absorption by driven chaotic systems of the symplectic
symmetry class. According to our analytical perturbative calculation, at the
initial stage of evolution the energy growth with time can be faster than
linear. This appears to be an analog of weak anti-localization in disordered
systems with spin-orbit interaction. Our analytical result is also confirmed by
numerical calculations for the symplectic quantum kicked rotor.Comment: 4 pages, 2 figure
A condition for any realistic theory of quantum systems
In quantum physics, the density operator completely describes the state.
Instead, in classical physics the mean value of every physical quantity is
evaluated by means of a probability distribution. We study the possibility to
describe pure quantum states and events with classical probability
distributions and conditional probabilities and prove that the distributions
can not be quadratic functions of the quantum state. Some examples are
considered. Finally, we deal with the exponential complexity problem of quantum
physics and introduce the concept of classical dimension for a quantum system
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