279 research outputs found
Non-monotonous short-time decay of the Loschmidt echo in quasi-one-dimensional systems
We study the short-time stability of quantum dynamics in quasi-one-dimensional systems with respect to small localized perturbations of the potential. To this end, we address, analytically and numerically, the decay of the Loschmidt echo (LE) during times short compared to the Ehrenfest time. We find that the LE is generally a non-monotonous function of time and exhibits strongly pronounced minima and maxima at the instants of time when the corresponding classical particle traverses the perturbation region. We also show that, under general conditions, the envelope decay of the LE is well approximated by a Gaussian, and we derive explicit analytical formulas for the corresponding decay time. Finally, we demonstrate that the observed non-monotonicity of the LE decay is only pertinent to one-dimensional (and, more generally, quasi-one-dimensional systems), and that the short-time decay of the LE can be monotonous in higher number of dimensions
Diffraction in time: An exactly solvable model
In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or “shutter,” that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as “diffraction in time.” Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules
Lyapunov spreading of semi-classical wave packets for the Lorentz Gas: theory and applications
We consider the quantum mechanical propagator for a particle moving in a -dimensional Lorentz gas, with fixed, hard sphere scatterers. To evaluate this propagator in the semi-classical region, and for times less than the Ehrenfest time, we express its effect on an initial Gaussian wave packet in terms of quantities analogous to those used to describe the exponential separation of trajectories in the classical version of this system. This result relates the spread of the wave packet to the rate of separation of classical trajectories, characterized by positive Lyapunov exponents. We consider applications of these results, first to illustrate the behavior of the wave-packet auto-correlation functions for wave packets on periodic orbits. The auto-correlation function can be related to the fidelity, or Loschmidt echo, for the special case that the perturbation is a small change in the mass of the particle. An exact expression for the fidelity, appropriate for this perturbation, leads to an analytical result valid over very long time intervals, inversely proportional to the size of the mass perturbation. For such perturbations, we then calculate the long-time echo for semi-classical wave packets on periodic orbits. This paper also corrects an earlier calculation for a quantum echo, included in a previous version of this paper. We explain the reasons for this correction
Manipulating quantum wave packets via time-dependent absorption
A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially localized quantum states. In particular, in the context of atom-optics experiments, we explicitly demonstrate how the proposed approach can be used to generate spatially shifted, split, squeezed, and cooled atomic wave packets. We expect our work to be useful in devising new interference experiments with atoms and molecules and, more generally, to enable new ways of coherent control of matter waves
Quantum backflow in a ring
Free motion of a quantum particle with the wave function entirely comprised
of plane waves with non-negative momenta may be accompanied by negative
probability current, an effect called quantum backflow. The effect is weak and
fragile, and has not yet been observed experimentally. Here we show that
quantum backflow becomes significantly more pronounced and more amenable to
experimental observation if, instead of letting the particle move along a
straight line, one forces it to move in a circular ring.Comment: 6 pages, 4 figure
Rotating Gaussian wave packets in weak external potentials
We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave packet center. Using a semiclassical approximation of the eikonal type, we derive an explicit formula for a time-dependent change of mean angular momentum of a wave packet induced by its interaction with a weak external potential. As an example, we apply our analytical approach to the scenario of a two-dimensional quantum particle crossing a tilted ridge potential barrier. In particular, we demonstrate that the initial orientation of the particle wave packet determines the sense of its rotation, and report a good agreement between analytical and numerical results
Origin of the exponential decay of the Loschmidt echo in integrable systems
We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement
Long-Time Coherence in Echo Spectroscopy with ---- Pulse Sequence
Motivated by atom optics experiments, we investigate a new class of fidelity
functions describing the reconstruction of quantum states by time-reversal
operations as . We show that the decay of
is quartic in time at short times, and that it freezes well
above the ergodic value at long times, when is not too large. The
long-time saturation value of contains easily extractable
information on the strength of decoherence in these systems.Comment: 5 pages, 3 figure
- …