Search results for " Fourier"
showing 10 items of 478 documents
Arbitrary qudit gates by adiabatic passage
2013
We derive an adiabatic technique that implements the most general SU($d$) transformation in a quantum system of $d$ degenerate states, featuring a qudit. This technique is based on the factorization of the SU($d$) transformation into $d$ generalized quantum Householder reflections, each of which is implemented by a two-shot stimulated Raman adiabatic passage with appropriate static phases. The energy of the lasers needed to synthesize a single Householder reflection is shown to be remarkably constant as a function of $d$. This technique is directly applicable to a linear trapped ion system with $d+1$ ions. We implement the quantum Fourier transform numerically in a qudit with $d=4$ (defined…
Wavelet-like orthonormal bases for the lowest Landau level
1994
As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.
Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display.
2010
Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has b…
One-shot color digital holography based on the fractional talbot effect
2010
We present a simple method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. Experimental results are also shown.
Introduction: Signals and Transforms
2015
In this chapter we outline some well known facts about periodic signals and transforms, which are needed throughout the book. For details we refer to the classical textbook Oppenheim and Schafer [2].
Electric quantum walks in two dimensions
2015
We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x or y axes, it produces a transient trapping of the probability distribution along the direction of the field, while when it is directed along the diagonals, a perfect 2D trapping is frustrated. The analysis of the alternate walk helps to understand the behaviour of the Grover walk as both walks are partially equivalent; in particular, it helps to understand the role played by the existence of conical intersections in the dispersion relations, as we show th…
Teaching stable two-mirror resonators through the fractional Fourier transform
2009
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…
Fourier-Accelerated Polymer Dynamics
1994
Fourier acceleration methods are applied to simulations of two-dimensional isolated ring polymers of up to N = 64 monomers. Three simulation schemes are compared: (i) a simple Langevin simulation with local updating, (ii) a Langevin algorithm with Fourier acceleration, and (iii) a Fourier accelerated Langevin algorithm combined with Metropolis acceptance of the moves (Force Biased Monte Carlo). In contrast to (i) and (ii), method (iii) is not hampered by systematic discretization errors, which, in case (ii), seem to grow systematically with chain length N. The results on the correlation time 4 are not very accurate, however, the data are in rough agreement with τ s N z with z= 2.5 (Rouse mo…
Teaching Fourier optics through ray matrices
2005
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…
White-light optical implementation of the fractional fourier transform with adjustable order control.
2000
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.