Jetlike tunneling from a trapped vortex

Abstract

We analyze the tunneling of vortex states from elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear Schrdinger) equation, we derive analytically and demonstrate numerically a novel type of quantum fluid flow: a jet-like singularity formed by the interaction between the vortex and the nonhomogenous field. For strongly elongated traps, the ellipticity overwhelms the circular rotation, resulting in the ejection of field in narrow, well-defined directions. These jets can also be understood as a formation of caustics since they correspond to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. They will appear in any coherent wave system with angular momentum and non-circular symmetry, such as superfluids, Bose-Einstein condensates, and light.PACS numbers: 74.25. Wx, 42.65.Hw,03.75.Lm Topological charges, such as vortices, are fundamental to the dynamics of coherent fields 1,2 . They appear in laser systems, carry charge in superconductors, characterize turbulence in quantum fluids, and hold potential for quantum memory 3 . To date, the main focus in vortex dynamics has been on transport, so that the charges could move and interact. (see e.g. Ref. 4) However, it is often desirable, and sometimes necessary, to confine and trap vortex structures. This is a basic problem in trapping theory, yet it has received very little attention. Here, we consider the dynamics of vortex decay in a potential and show that asymmetry in the potential can lead to the development of jets during wave tunneling. These formations concentrate wave density in the form of caustics and represent a new type of coherent structure for wave transport.The emphasis on vorticity implies that phase dynamics will be important to the tunneling process. Even in the context of simple wavefunctions, without angular momentum, phase can have profound effects. Examples include the recent prediction of "blips" in the outgoing matter through a trap 5-8 and the development of dispersive shock waves 9-12 , e.g. when tunneling through a barrier. 13 These latter structures are traveling waves with oscillating phase that are finding increasing importance in fluids 14,15 , optics 2,11 , and Bose-Einstein condensates 16,17 . In spatially inhomogeneous potentials, such as the elliptical wells typical of BEC experiments 18 , both shock waves and blips can go unstable and generate vortices. Here, we consider the simplest case of a circular vortex trapped in an elliptical well and examine the competition of symmetry during wavefunction tunneling.Tunneling problems are usually discussed within the framework of the WKB approximation, which looks for a solution of the Schrödinger equation (Nonlinear 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 1111111111111 1111111111111 1111111111111 1111111111111 111111...

Propagation of a quantum fluid of light in a cavityless nonlinear optical medium: General theory and response to quantum quenches

“…where χ 0 = χ(ω 0 ); the parameters β 0 = β(ω 0 ), v 0 = v(ω 0 ), and D 0 = D(ω 0 ) are respectively the propagation constant β(ω) = [1 + χ(ω)] 1/2 ω/c (c is the vacuum speed of light) of the laser wave in the z > 0 direction, the group velocity v(ω) = [dβ(ω)/dω] −1 of the photons in the medium, and the group-velocity dispersion D(ω) = d 2 β(ω)/dω 2 evaluated at the carrier's angular frequency ω 0 . The hydrodynamic interpretation of the propagation equation (3) is mostly well known in the limiting case of a purely monochromatic wave at ω 0 [17][18][19][20][21][22][23][24][25] and has offered a transparent physical interpretation to a number of nonlinear-optics experiments [30-36, 48, 49]. In this time-independent case, the first and second derivatives of the envelope E with respect to t vanish, in such a way that the propagation of the optical field decribed by Eq.…”

“…This framework has been used in a number of theoretical works where laser-physics problems have been reformulated in the hydrodynamics language [16], including, e.g., the investigation of superfluid-like behaviors in the flow of a photon fluid [17][18][19][20][21], of nonlinear phenomena with light waves [22][23][24][25], and of the so-called acoustic Hawking radiation [26][27][28][29]. From the experimental point of view, numerous works have been devoted to the study of nonlinear features that may appear in these systems, with a special attention dedicated to their relation to hydrodynamics and superfluidity aspects [30][31][32][33][34][35][36].…”

Persistent currents of superfluidic light in a four-level coherent atomic medium

“…In this context, typical superfluidic signatures are predicted to occur below the critical speed defined by the Landau criterion [7,17]. Recently, there have been theoretical and experimental advances on this subject, including the study of dissipationless motion [18], suppressed scattering [6,[18][19][20], and the formation of shock wave diffraction patterns by a defect, with both dark solitons and vortices [21][22][23][24]. Still, the study of these quantum phenomena is limited when using bulk nonlinear media, which are not suitable to reproduce other superfluidic signatures, including the hallmark of superfluidity: the existence of persistent currents.…”

Prethermalization in a quenched one-dimensional quantum fluid of light: Intrinsic limits to the coherent propagation of a light beam in a nonlinear optical fiber

“…Its group-velocity dispersion D 0 = D(ω 0 ) and its Kerr coefficient n 2 (ω 0 ) at the laser pump's angular frequency ω 0 are assumed to be of same sign to prevent the occurrence of dynamical instabilities (see the last paragraph of Sect. 3.2) in the 1D photon fluid, supposed to be well within the weakly interacting regime (29). The quasimonochromatic beam which illuminates the z = 0 entrance face of the waveguide is assumed to have a wide top-hat spatial profile in the x = (x, y) plane as well as a constant power all along the optical axis before entering the waveguide so that it can be legitimately seen as an infinite plane wave propagating without amplitude attenuations in the increasing-z direction.…”

“…This framework has been used in a number of experimental works devoted to the study of nonlinear features in propagating fluids of light, with a special attention dedicated to their relation to hydrodynamics and superfluidity aspects [14][15][16][17][18][19][20]. From the theoretical point of view, the nonlinear propagating geometry has also been subjected to numerous investigations, including, e.g., the study of superfluidlike behaviors in the flow of a photon fluid past a localized obstacle [21][22][23][24][25], of nonlinear phenomena with light waves [26][27][28][29], and of the so-called acoustic Hawking radiation from analog black-hole horizons [30][31][32][33], the latter being accompanied with experimental works (see, e.g., Refs. [34,35]).…”