In the last three decades, we have witnessed incredible advances in laser technology and in the understanding of nonlinear laser-matter interactions, crowned recently by the award of the Nobel prize to Gérard Mourou and Donna Strickland [1,2]. It is now routinely possible to produce few-cycle femtosecond (1 fs = 10 −15 s) laser pulses in the visible and mid-infrared regimes [3,4]. By focusing such ultrashort laser pulses on gas or solid targets, possibly in a presence of nano-structures [5], the targets are subjected to an ultra-intense electric field, with peak field strengths approaching the binding field inside the atoms themselves. Such fields permit the exploration of the interaction between strong electromagnetic coherent radiation and an atomic or molecular system with unprecedented spatial and temporal resolution [6]. On one hand, HHG nowadays can be used to generate attosecond pulses in the extreme ultraviolet [7,8], or even in the soft X-ray regime [9]. Such pulses themselves may be used for dynamical spectroscopy of matter; despite carrying modest pulse energies, they exhibit excellent coherence properties [10,11]. Combined with femtosecond pulses they can also be used to extract information about the laser pulse electric field itself [12]. HHG sources therefore offer an important alternative to other sources of XUV and X-ray radiation: synchrotrons, free electron lasers, X-ray lasers, and laser plasma sources. Moreover, HHG pulses can provide information about the structure of the target atom, molecule or solid [13][14][15]. Of course, to decode such information from a highly nonlinear HHG signal is a challenge, and that is why a possibly perfect, and possibly "as analytical as possible" theoretical understanding of these processes is in high demand. Here is the first instance where SFA offers its basic services.Since electronic motion is governed by the waveform of the laser electric field, an important quantity to describe the electric field shape is the so-called absolute phase or carrier-envelope phase (CEP). Control over the CEP is paramount for extracting information about electron dynamics, and to retrieve structural information from atoms and molecules [13,16,17]. For instance, in HHG an electron is liberated from an atom or molecule through ionization, which occurs close to the maximum of the electric field. Within the oscillating field, the electron can thus accelerate along oscillating trajectories, which may result in recollision with the parent ion, roughly when the laser field approaches a zero value. Control over the CEP is particularly important for HHG, when targets are driven by laser pulses comprising only one or two optical cycles. In that situation the CEP determines the relevant electron trajectories, i.e. the CEP determines whether emission results in a single or in multiple attosecond bursts of radiation [16,18].The influence of the CEP on electron emission is also extremely important. It was demonstrated for instance in an anti-correlation experiment, in which the number of AT...

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.

Abstract. Recent tests of a single module of the Jagiellonian Positron Emission Tomography system (J-PET) consisting of 30 cm long plastic scintillator strips have proven its applicability for the detection of annihilation quanta (0.511 MeV) with a coincidence resolving time (CRT) of 0.266 ns. The achieved resolution is almost by a factor of two better with respect to the current TOF-PET detectors and it can still be improved since, as it is shown in this article, the intrinsic limit of time resolution for the determination of time of the interaction of 0.511 MeV gamma quanta in plastic scintillators is much lower. As the major point of the article, a method allowing to record timestamps of several photons, at two ends of the scintillator strip, by means of matrix of silicon photomultipliers (SiPM) is introduced. As a result of simulations, conducted with the number of SiPM varying from 4 to 42, it is shown that the improvement of timing resolution saturates with the growing number of photomultipliers, and that the 2 x 5 configuration at two ends allowing to read twenty timestamps, constitutes an optimal solution. The conducted simulations accounted for the emission time distribution, photon transport and absorption inside the scintillator, as well as quantum efficiency and transit time spread of photosensors, and were checked based on the experimental results. Application of the 2 x 5 matrix of SiPM allows for achieving the coincidence resolving time in positron emission tomography of ≈ 0.170 ns for 15 cm axial field-of-view (AFOV) and ≈ 0.365 ns for 100 cm AFOV. The results open perspectives for construction of a cost-effective TOF-PET scanner with significantly better TOF resolution and larger AFOV with respect to the current

Time crystals are quantum many-body systems that, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in condensed matter physics. In solid state physics properties of space crystals are often investigated with the help of external potentials that are spatially periodic and reflect various crystalline structures. A similar approach can be applied for time crystals, as periodically driven systems constitute counterparts of spatially periodic systems, but in the time domain. Here we show that condensed matter problems ranging from single particles in potentials of quasicrystal structure to many-body systems with exotic long-range interactions can be realized in the time domain with an appropriate periodic driving. Moreover, it is possible to create molecules where atoms are bound together due to destructive interference if the atomic scattering length is modulated in time.

By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.