Gian Luca Lippi

Bio: Gian Luca Lippi is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Laser & Lasing threshold. The author has an hindex of 17, co-authored 109 publications receiving 1375 citations. Previous affiliations of Gian Luca Lippi include Bryn Mawr College & University of Münster.

Instabilities in lasers with an injected signal

Abstract: We consider a laser with an injected signal, in which the polarization can be adiabatically eliminated, we study the stability of the steady-state solutions, and we discuss the time-dependent solutions. For the laser alone, the only possible solution is constant intensity. However, the introduction of an external field, with an amplitude that does not satisfy the injection-locking condition, destabilizes the system. In such a case, numerical results show the existence of a self-Q-switching process, which induces relaxation oscillations. The frequency of the giant pulses is directly related to the amplitude of the external field, whereas the frequency of the relaxation oscillations depends on the damping rates. We show also that, depending on the value assigned to control parameters, the interaction between these frequencies leads to a chaotic behavior through intermittency or period-doubling bifurcations. Finally, topological equivalence between our laser system and a unidimensional circle map is shown for some values of control parameters.

Critical slowing down at a bifurcation

Abstract: Critical slowing down near a bifurcation or limit point leads to a dynamical hysteresis that cannot be avoided by sweeping a control parameter slowly through the critical point. This paper analytically illustrates, with the help of a simple model, the bifurcation shift. We describe an inexpensive experiment using a semiconductor laser where this phenomenon occurs near the threshold of a semiconductor laser.

Bidirectional ring laser: Stability analysis and time-dependent solutions

Abstract: We provide a comprehensive analysis of the standard model of the bidirectional ring laser in which only one mode can be supported in each direction and in the limit that the polarization can be eliminated adiabatically. The interaction between the two counterpropagating modes can be derived and it is most naturally viewed as a coupling between them via scattering from a spatial grating formed in the population inversion. If the grating is a sufficiently small modulation of the spatial average of the population inversion, it can be approximated by a sinusoidal function. A systematic derivation of the model with only a sinusoidal grating for the homogeneously broadened case is presented that reveals and corrects errors in several previously published analyses. The stability of the steady-state solution is analyzed. The bidirectional steady-state solution is unstable and the unidirectional steady-state solutions may be stable or unstable depending on the parameters. The well-established result of bistability between the two modes when the cavity is tuned to resonance is recovered, a result that persists, in part, even when the losses between the two modes are different.

Early-warning signals for critical transitions

Abstract: Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

The Quantum Theory of Light

Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

Anticipating Critical Transitions

Abstract: Tipping points in complex systems may imply risks of unwanted collapse, but also opportunities for positive change. Our capacity to navigate such risks and opportunities can be boosted by combining emerging insights from two unconnected fields of research. One line of work is revealing fundamental architectural features that may cause ecological networks, financial markets, and other complex systems to have tipping points. Another field of research is uncovering generic empirical indicators of the proximity to such critical thresholds. Although sudden shifts in complex systems will inevitably continue to surprise us, work at the crossroads of these emerging fields offers new approaches for anticipating critical transitions.

Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data

Abstract: Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light

Abstract: Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories1, 2, 3, 4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.