Showing papers by "Alejandro Romanelli published in 2009"
TL;DR: In this paper, the authors generalize the discrete quantum walk on the line using a time-dependent unitary coin operator and find an analytical relation between the long-time behaviors of the standard deviation and the coin operator.
Abstract: We generalize the discrete quantum walk on the line using a time-dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, subdiffusive, and localized.
36 citations
TL;DR: In this article, the authors studied the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription and built a classical map based on the trace of the evolution operator.
Abstract: We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription We build for this system a classical map based on the trace of the evolution operator The sub-ballistic behavior of this quantum walk is connected with the power-law decay of the time correlations of the trace map
24 citations
TL;DR: A continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model, in which the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states.
Abstract: We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.
10 citations
TL;DR: In this paper, the authors studied the quantum kicked rotor in resonance subjected to a unitary noise defined through Kraus operators and showed that this type of decoherence does not, in general, lead to the classical diffusive behavior.
Abstract: We study the quantum kicked rotor in resonance subjected to a unitary noise defined through Kraus operators. We show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior; however, the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential-law decay for the coherence.
8 citations
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TL;DR: In this paper, the authors studied the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, and showed that this type of decoherence does not, in general, lead to the classical diffusive behavior.
Abstract: We study the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, we show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior, however the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential law decay for the coherence.
6 citations
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TL;DR: In this paper, the authors propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model, where the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states.
Abstract: We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.
14 Jun 2009
TL;DR: In this paper, a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors was considered.
Abstract: In this communication we study in depth the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking discussed for the first time in [1]. The idea can be put in short as follows. Consider a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM 10 mode with an arbitrary orientation (measured by θ at Fig. 1) emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane. Quantum effects are then quite intuitive: as any orientation is allowed, quantum noise is able to randomly rotate the generated pattern; this implies an indefiniteness in the angular orientation of the TEM 10 mode, what (invoking now the uncertainty principle) may lead to the perfect determination of its orbital angular momentum, which in this case coincides with the π/2 phase shifted TEM 10 mode orthogonal to the macroscopically generated one. Thus, perfect noise reduction is expected in the phase quadrature of this classically “empty” TEM 10 mode irrespectively of the pump level.