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Ciurla D, Forgács P, Lukács Á, Romańczukiewicz T. Negative radiation pressure in Bose-Einstein condensates. Phys Rev E 2024; 109:014228. [PMID: 38366411 DOI: 10.1103/physreve.109.014228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
In two-component nonlinear Schrödinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is nonvanishing only in the orthogonal component to that of the embedded dark soliton, its acceleration is in the opposite direction to that of the incoming wave. This somewhat surprising phenomenon can be attributed to the well-known negative effective mass of the dark soliton. When a dark-bright soliton, whose effective mass is also negative, is hit by an incoming wave nonvanishing in the component corresponding to the dark soliton, the direction of its acceleration coincides with that of the incoming wave. This implies that the net force acting on it is in the opposite direction to that of the incoming wave. This rather counterintuitive effect is a yet another manifestation of negative radiation pressure exerted by the incident wave, observed in other systems. When a dark-bright soliton interacts with an incoming wave in the component of the bright soliton, it accelerates in the opposite direction; hence the force is pushing it now. We expect that these remarkable effects, in particular the negative radiation pressure, can be experimentally verified in Bose-Einstein condensates.
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Affiliation(s)
- Dominik Ciurla
- Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Péter Forgács
- Wigner RCP RMI, POB 49, 1525 Budapest, Hungary
- Institut Denis-Poisson, UMR No. 7013, CNRS, Université de Tours, Parc de Grandmont, 37200 Tours, France
| | - Árpád Lukács
- Wigner RCP RMI, POB 49, 1525 Budapest, Hungary
- Department of Mathematical Sciences, Durham University, Stockton Road, Durham DH1 3LE, United Kingdom
| | - Tomasz Romańczukiewicz
- Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
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Molchan MA. Nonlocal solitons in the parametrically driven nonlinear Schrödinger equation: stability analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:056603. [PMID: 22181532 DOI: 10.1103/physreve.84.056603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2011] [Indexed: 05/31/2023]
Abstract
We study analytically and numerically the linear stability of weakly nonlocal solitons in the parametrically driven nonlinear Schrödinger equation. Two exact solutions are derived in an implicit form. We show analytically that despite the well-known stabilizing properties of nonlocality one of the solitons remains unstable even in the nonlocal case for any values of the dissipation, the damping, and the degree of nonlocality. The second soliton, as compared to its local counterpart, attains wider stable regions in the space of the parameters of the system.
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Affiliation(s)
- Maxim A Molchan
- Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch 7701, South Africa.
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Barashenkov IV, Zemlyanaya EV, van Heerden TC. Time-periodic solitons in a damped-driven nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056609. [PMID: 21728684 DOI: 10.1103/physreve.83.056609] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Indexed: 05/31/2023]
Abstract
Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton's response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton's temporal chaos to the homoclinic bifurcation.
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Affiliation(s)
- I V Barashenkov
- Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
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Dror N, Malomed BA. Spontaneous symmetry breaking in coupled parametrically driven waveguides. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:016605. [PMID: 19257158 DOI: 10.1103/physreve.79.016605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2008] [Indexed: 05/27/2023]
Abstract
We introduce a system of linearly coupled parametrically driven damped nonlinear Schrödinger equations, which models a laser based on a nonlinear dual-core waveguide with parametric amplification symmetrically applied to both cores. The model may also be realized in terms of parallel ferromagnetic films, in which the parametric gain is provided by an external field. We analyze spontaneous symmetry breaking (SSB) of fundamental and multiple solitons in this system, which was not studied systematically before in linearly coupled dissipative systems with intrinsic nonlinearity. For fundamental solitons, the analysis reveals three distinct SSB scenarios. Unlike the standard dual-core-fiber model, the present system gives rise to a vast bistability region, which may be relevant to applications. Other noteworthy findings are restabilization of the symmetric soliton after it was destabilized by the SSB bifurcation, and the existence of a generic situation with all solitons unstable in the single-component (decoupled) model, while both symmetric and asymmetric solitons may be stable in the coupled system. The stability of the asymmetric solitons is identified via direct simulations, while for symmetric and antisymmetric ones the stability is verified too through the computation of stability eigenvalues, families of antisymmetric solitons being entirely unstable. In this way, full stability maps for the symmetric solitons are produced. We also investigate the SSB bifurcation of two-soliton bound states (it breaks the symmetry between the two components, while the two peaks in the shape of the soliton remain mutually symmetric). The family of the asymmetric double-peak states may decouple from its symmetric counterpart, being no longer connected to it by the bifurcation, with a large portion of the asymmetric family remaining stable.
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Affiliation(s)
- Nir Dror
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Barashenkov IV, Woodford SR, Zemlyanaya EV. Interactions of parametrically driven dark solitons. I. Néel-Néel and Bloch-Bloch interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026604. [PMID: 17358433 DOI: 10.1103/physreve.75.026604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2005] [Revised: 11/03/2006] [Indexed: 05/14/2023]
Abstract
We study interactions between the dark solitons of the parametrically driven nonlinear Schrödinger equation, Eq. 1 . When the driving strength, h , is below sqrt[gamma(2)+1/9], two well-separated Néel walls may repel or attract. They repel if their initial separation 2z(0) is larger than the distance 2zu between the constituents in the unstable stationary complex of two walls. They attract and annihilate if 2z(0) is smaller than 2zu. Two Néel walls with h lying between sqrt[gamma(2)+1/9] and a threshold driving strength hsn attract for 2z(0)<2zu and evolve into a stable stationary bound state for 2z(0)>2zu. Finally, the Néel walls with h greater than hsn attract and annihilate-irrespective of their initial separation. Two Bloch walls of opposite chiralities attract, while Bloch walls of like chiralities repel-except near the critical driving strength, where the difference between the like-handed and oppositely handed walls becomes negligible. In this limit, similarly handed walls at large separations repel while those placed at shorter distances may start moving in the same direction or transmute into an oppositely handed pair and attract. The collision of two Bloch walls or two nondissipative Néel walls typically produces a quiescent or moving breather.
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Affiliation(s)
- I V Barashenkov
- Department of Physics, University of Bayreuth, D-95440 Bayreuth, Germany.
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Barashenkov IV, Woodford SR. Interactions of parametrically driven dark solitons. II. Néel-Bloch interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026605. [PMID: 17358434 DOI: 10.1103/physreve.75.026605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2006] [Indexed: 05/14/2023]
Abstract
The interaction between a Bloch and a Néel wall in the parametrically driven nonlinear Schrödinger equation is studied by following the dissociation of their unstable bound state. Mathematically, the analysis focuses on the splitting of a fourfold zero eigenvalue associated with a pair of infinitely separated Bloch and Néel walls. It is shown that a Bloch and a Néel wall interact as two classical particles, one with positive and the other one with negative mass.
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Affiliation(s)
- I V Barashenkov
- Department of Physics, University of Bayreuth, D-95440 Bayreuth, Germany.
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Barashenkov IV, Woodford SR. Complexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026613. [PMID: 15783447 DOI: 10.1103/physreve.71.026613] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2004] [Revised: 11/15/2004] [Indexed: 05/24/2023]
Abstract
The parametrically driven Ginsburg-Landau equation has well-known stationary solutions-the so-called Bloch and Ne el, or Ising, walls. In this paper, we construct an explicit stationary solution describing a bound state of two walls. We also demonstrate that stationary complexes of more than two walls do not exist.
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Affiliation(s)
- I V Barashenkov
- Department of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
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Proukakis NP, Parker NG, Barenghi CF, Adams ACS. Parametric driving of dark solitons in atomic Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2004; 93:130408. [PMID: 15524690 DOI: 10.1103/physrevlett.93.130408] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2004] [Indexed: 05/24/2023]
Abstract
A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.
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Affiliation(s)
- N P Proukakis
- Department of Physics, University of Durham, South Road, Durham, DH1 3LE, United Kingdom
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Pérez-Arjona I, Silva F, Valcárcel GJD, Roldán E, Sánchez-Morcillo VJ. The Ising–Bloch transition in degenerate optical parametric oscillators. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/1464-4266/6/5/026] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Barashenkov IV, Cross S, Malomed BA. Multistable pulselike solutions in a parametrically driven Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056605. [PMID: 14682904 DOI: 10.1103/physreve.68.056605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2003] [Indexed: 05/24/2023]
Abstract
It is well known that pulselike solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilized by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilizing agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient c), starting from the nonlinear Schrödinger limit (for which c=0). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.
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Affiliation(s)
- I V Barashenkov
- Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
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Jo TC, Armbruster D. Localized solutions in parametrically driven pattern formation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:016213. [PMID: 12935231 DOI: 10.1103/physreve.68.016213] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2002] [Indexed: 05/24/2023]
Abstract
The Mathieu partial differential equation (PDE) is analyzed as a prototypical model for pattern formation due to parametric resonance. After averaging and scaling, it is shown to be a perturbed nonlinear Schrödinger equation (NLS). Adiabatic perturbation theory for solitons is applied to determine which solitons of the NLS survive the perturbation due to damping and parametric forcing. Numerical simulations compare the perturbation results to the dynamics of the Mathieu PDE. Stable and weakly unstable soliton solutions are identified. They are shown to be closely related to oscillons found in parametrically driven sand experiments.
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Affiliation(s)
- Tae-Chang Jo
- Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804, USA
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Barashenkov IV, Woodford SR, Zemlyanaya EV. Parametrically driven dark solitons. PHYSICAL REVIEW LETTERS 2003; 90:054103. [PMID: 12633360 DOI: 10.1103/physrevlett.90.054103] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2002] [Indexed: 05/24/2023]
Abstract
We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.
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Affiliation(s)
- I V Barashenkov
- Department of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
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de Valcárcel GJ, Pérez-Arjona I, Roldán E. Domain walls and ising-BLOCH transitions in parametrically driven systems. PHYSICAL REVIEW LETTERS 2002; 89:164101. [PMID: 12398725 DOI: 10.1103/physrevlett.89.164101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2000] [Revised: 06/27/2002] [Indexed: 05/24/2023]
Abstract
Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.
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Affiliation(s)
- Germán J de Valcárcel
- Departament d'Optica, Universitat de València, Dr. Moliner 50, 46100-Burjassot, Spain.
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Crawford C, Riecke H. Tunable front interaction and localization of periodically forced waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066307. [PMID: 12188828 DOI: 10.1103/physreve.65.066307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2000] [Revised: 01/17/2002] [Indexed: 05/23/2023]
Abstract
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We investigate wave pulses within the framework of coupled Ginzburg-Landau equations describing the traveling-wave amplitudes. We find that the introduction of resonant temporal forcing results in a tunable mechanism for stabilizing such wave pulses. In contrast to other localization mechanisms the temporal forcing can achieve localization by a repulsive as well as by an attractive interaction between the fronts. Systems for which the results are expected to be relevant include binary-mixture convection and electroconvection in nematic liquid crystals.
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Affiliation(s)
- Catherine Crawford
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA.
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Riecke H. Localized Structures In Pattern-Forming Systems. PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS 1999. [DOI: 10.1007/978-1-4612-1558-5_17] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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van Hecke M, de Wit E, van Saarloos W. Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation. PHYSICAL REVIEW LETTERS 1995; 75:3830-3833. [PMID: 10059742 DOI: 10.1103/physrevlett.75.3830] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Gluzman S. Parametric excitation of nonlinear waves in a one-dimensional system of interacting magnons. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:13809-13812. [PMID: 9975587 DOI: 10.1103/physrevb.50.13809] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Hagberg A, Meron E. Domain walls in nonequilibrium systems and the emergence of persistent patterns. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:705-708. [PMID: 9960649 DOI: 10.1103/physreve.48.705] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Elphick C, Ierley GR, Regev O, Spiegel EA. Interacting localized structures with Galilean invariance. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:1110-1122. [PMID: 9906060 DOI: 10.1103/physreva.44.1110] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Glazier JA, Kolodner P. Interactions of nonlinear pulses in convection in binary fluids. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4269-4280. [PMID: 9905528 DOI: 10.1103/physreva.43.4269] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Shi ZP, Huang G, Tao R. Envelope-kink excitations in a quantum anisotropic antiferromagnetic Heisenberg chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:8583-8586. [PMID: 9996490 DOI: 10.1103/physrevb.43.8583] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Schofield SA, Oxtoby DW. Diffusion disallowed crystal growth. I. Landau–Ginzburg model. J Chem Phys 1991. [DOI: 10.1063/1.459889] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Elphick C, Meron E. Comment on "Solitary waves generated by subcritical instabilities in dissipative systems". PHYSICAL REVIEW LETTERS 1990; 65:2476. [PMID: 10042559 DOI: 10.1103/physrevlett.65.2476] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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