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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

CLEO®/Europe-EQEC 2017 Shock Waves' Squeezing

Maria Chiara Braidotti, Antonio Mecozzi, Claudio Conti

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Summary form only given. Squeezed states are quantum states of light, which recently proved to play an important role in modern physics due to their connection with quantum information and their employment in quantum computation and gravitational wave detection [1,2].Here we show that squeezed states appear during the development of a classical optical shock phenomenon. Dispersive shock waves emerge during the wave propagation when a discontinuity in their derivative arises as a consequence of an abrupt jump in some of the quantities involved. These waves are singular solutions of hyperbolic partial differential equations, which describe a wide variety of wave-like phenomena in physics, ranging from fluido-dynamics to plasmas and Bose-Einstein condensation (see e.g. [4,5]).

DOI
10.1109/cleoe-eqec.2017.8087727

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Summary form only given. Squeezed states are quantum states of light, which recently proved to play an important role in modern physics due to their connection with quantum information and their employment in quantum computation and gravitational wave detection [1,2].Here we show that squeezed states appear during the development of a classical optical shock phenomenon. Dispersive shock waves emerge during the wave propagation when a discontinuity in their derivative arises as a consequence of an abrupt jump in some of the quantities involved. These waves are singular solutions of hyperbolic partial differential equations, which describe a wide variety of wave-like phenomena in physics, ranging from fluido-dynamics to plasmas and Bose-Einstein condensation (see e.g. [4,5]).
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.
Light flow in nonlinear media can exhibit quantum hydrodynamical features which are profoundly different from those of classical fluids. We show that rather extremes regime of quantum hydrodynamics can be accessed by exploring two paradigmatic problems in fluid dynamics. The first one is the piston problem for light, and its generalization, named after the celebrated mathematician Riemann, where the piston acts on a concomitant abrupt change of photon density. Our experiment reveals regimes featuring optical rarefaction (retracting piston) or shock (pushing piston) wave pairs, and most importantly the transition to a peculiar type of flow, occurring above a precise critical piston velocity, where the light shocks are smoothly interconnected by a large contrast, periodic, fully nonlinear wave. The second one is the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the step-like input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state.Our results show that fiber-based optical systems are peerless testbeds to investigate the extension of gas dynamics problems to superfluid regimes by taking benefit of the analogy between optics and fluid dynamics supported by the universality of the nonlinear Schrodinger equation.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information, and simulation. However the implications of the quantum nature of light in nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in a highly nonlocal regime. These results lead to advances in the quantum photon fluids research and may inspire applications in fields like metrology and analogs of quantum gravity.
We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a Bose-Einstein condensate.