Space-time wave packets (STWPs) are a new class of spatiotemporally structured light fields that are endowed with a host of unique properties, including diffraction-free propagation at controllable group velocity, self-healing, and dispersion-free propagation in dispersive media. These characteristics make STWPs useful candidates for free-space optical communications, particularly for quantum communications. We demonstrate here the first single-photon STWP produced in two different configurations from entangled-photon pairs produced through spontaneous parametric downconversion. In the first configuration, a spatiotemporal spectral modulator is placed in the path of the signal photon, whose arrival is heralded by detection of the idler photon, which we refer to as local STWP synthesis. In the second configuration, the signal photon after the modulator is detected to herald the arrival of the idler photon, which we refer to as remote STWP preparation. In both configurations, we observe the predicted diffraction-free propagation of single-photon STWPs. These results pave the way for quantum communications using spatiotemporally structured quantum states of light.
In quantum mechanics the situation is different because the uncertainty principle does not allow us to know the initial positions and momenta of the particles with desired accuracy. The individual particle is described by a wave packet. Since the wave packet is localized and spreading with time, it is impossible to distinguish two identical particles as their wave functions always overlap at any point in space. Quantum theory describes any object at energies below its excitation threshold with four degrees of freedom. The wave functions of all the states of a given system of identical particles must have the same symmetry; otherwise, the wave function of a state formally a superposition of states of different symmetry would be neither symmetrical nor antisymmetrical. Hence, for a system of identical particles, at high energies and low concentration, probable number of particles per quantum state will be very small. Wave functions of the particles are well separated.
In this work we study the effects of collapse and revival, as well as the zitterbewegung (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some Landau level
n0 of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and their evolution is visualized. Our computations demonstrate that due to the dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time
t=TR/2 its reshaping takes place first. It is shown that the behavior of the wave packet containing the states of both energy bands (with
En>0 and
En<0) is more complicated. At short times of a few classical periods such a packet splits into two parts, which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have a significant overlap that leads to ZB, and at the time of fractional revival each of two subpackets is decomposed into few packet fractions. However, at
t=TR each of the two subpackets (with positive or negative energy) restores at various points of the cyclotron orbit, which makes reshaping of the initial wave packet impossible, entirely unlike the wave packet which consists of states with energies
En>0 only. The obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where superhigh magnetic field has a value of the order
108−−109T, as well as for interpretation of experiments with trapped ions.