Theory of Quantum Pulse Position Modulation and Related Numerical Problems

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find optimal (or suboptimal) measurement operators and to evaluate the corresponding error probability. For PPM, the correct formulation of quantum states is given by the tensorial product of m identical Hilbert spaces, where m is the PPM order. The presence of mixed states, due to thermal noise, generates an optimization problem involving matrices of huge dimensions, which already for 4-PPM, are of the order of ten thousand. To overcome this computational complexity, the currently available methods of quantum detection, which are based on explicit results, convex linear programming and square root measurement, are compared to find the computationally less expensive one. In this paper a fundamental role is played by the geometrically uniform symmetry of the quantum PPM format. The evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart.Comment: 10 pages, 7 figures, accepted for publication in IEEE Trans. on Communication

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.Comment: 20 pages, 13 figure

Study of the spatial and temporal coherence of high order harmonics

We apply the theory of high-order harmonic generation by low-frequency laser fields in the strong field approximation to the study of the spatial and temporal coherence properties of the harmonics. We discuss the role of dynamically induced phases of the atomic polarization in determining the optimal phase matching conditions and angular distributions of harmonics. We demonstrate that the phase matching and the spatial coherence can be controlled by changing the focusing parameters of the fundamental laser beam. Then we present a detailed study of the temporal and spectral properties of harmonics. We discuss how the focusing conditions influence the individual harmonic spectra and time profiles, and how the intensity dependence of the dynamically induced phase leads to a chirp of the harmonic frequency. This phase modulation can be used to control the temporal and spectral properties of the harmonic radiation. Temporally, the harmonic chirped pulse can be recompressed to very small durations. Spectrally, chirping of the fundamental beam may be employed to compensate for the dynamically induced chirp and to control the individual harmonic spectrum. Finally, we discuss the short pulse effects, in particular nonadiabatic phenomena and the possibility of generating attosecond pulses.Comment: Latex file with 37 pages, 25 postscript figures. to appear in Advances in Atomic, Molecular and Optical Physic

Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors

We present the first demonstration of reproducible harmonic mode-locked operation from a novel design of monolithic semiconductor laser comprising a compound cavity formed by a 1-D photonic-bandgap (PBG) mirror. Mode-locking (ML) is achieved at a harmonic of the fundamental round-trip frequency with pulse repetition rates from 131 GHz up to a record high frequency of 2.1 THz. The devices are fabricated from GaAs-Al-GaAs material emitting at a wavelength of 860 nm and incorporate two gain sections with an etched PBG reflector between them, and a saturable absorber section. Autocorrelation studies are reported which allow the device behavior for different ML frequencies, compound cavity ratios, and type and number of intra-cavity reflectors to be analyzed. The highly reflective PBG microstructures are shown to be essential for subharmonic-free ML operation of the high-frequency devices. We have also demonstrated that the single PBG reflector can be replaced by two separate features with lower optical loss. These lasers may find applications in terahertz; imaging, medicine, ultrafast optical links, and atmospheric sensing

Classical and quantum spreading of a charge pulse

With the technical progress of radio-frequency setups, high frequency quantum transport experiments have moved from theory to the lab. So far the standard theoretical approach used to treat such problems numerically--known as Keldysh or NEGF (Non Equilibrium Green's Functions) formalism--has not been very successful mainly because of a prohibitive computational cost. We propose a reformulation of the non-equilibrium Green's function technique in terms of the electronic wave functions of the system in an energy-time representation. The numerical algorithm we obtain scales now linearly with the simulated time and the volume of the system, and makes simulation of systems with 10^5 - 10^6 atoms/sites feasible. We illustrate our method with the propagation and spreading of a charge pulse in the quantum Hall regime. We identify a classical and a quantum regime for the spreading, depending on the number of particles contained in the pulse. This numerical experiment is the condensed matter analogue to the spreading of a Gaussian wavepacket discussed in quantum mechanics textbooks.Comment: 4 pages, 5 figures; to be published in IEEE Xplore, in Proceedings to IEEE 17th International Workshop on Computational Electronics 2014, June 3 - 6, 2014, Paris, France. Correction of typographic mistakes and update of ref. 1