Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers

Marchukov, Oleksandr V.; Malomed, Boris A.; Dunjko, Vanja; Ruhl, Joanna; Olshanii, Maxim; Hulet, R. G.; Yurovsky, Vladimir

doi:10.1103/physrevlett.125.050405

Cited by 27 publications

(14 citation statements)

References 64 publications

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“…In the true 1D system, the collapse does not occur with the increase of the number of atoms. However, the realistic 1D limit is not tantamount to the ideal NLS equation, the deviation from which makes the collapse possible [7,34]. Nevertheless, in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Extensive research work on nonlinear dynamics of atomic matter waves in Bose-Einstein condensates (BECs), such as dark [1][2][3] bright [3][4][5], and breather [6,7] solitons, rogue waves (RWs) [8,9], gap solitons and other coherent modes in optical lattices [10,11], four-wave mixing [12], and, most recently, quantum droplets in binary [13,14] and dipolar [15] BEC set these topics at the forefront of current experimental and theoretical studies in soft-matter physics and nonlinear science. A commonly adopted dynamical model of BEC is the Gross-Pitaevskii (GP) equation (including the Lee-Huang-Yang corrections that account for the beyond-mean-field effects helping to stabilize quantum droplets [13]).…”

Section: Introductionmentioning

confidence: 99%

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Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential

Kengne,

Malomed,

Liu

2021

Preprint

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We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front of the cubic term and inverted parabolic potential. Under a special condition imposed on the coefficients, a combination of phase-imprint and modified lens-type transformations converts the GP equation into the integrable Kundu-Eckhaus (KE) one with constant coefficients, which contains the quintic nonlinearity and the Raman-like term producing the self-frequency shift. The condition for the baseband modulational instability of CW states is derived, providing the possibility of generation of chirped rogue waves (RWs) in the underlying matter-wave (BEC) model. Using known RW solutions of the KE equation, we present explicit first-and second-order chirped RW states. The chirp of the first-and second-order RWs is independent of the phase imprint. Detailed solutions are presented for the following configurations: (i) the nonlinearity exponentially varying in time; (ii) time-periodic modulation of the nonlinearity; (iii) a stepwise time modulation of the strength of the expulsive potential. Singularities of the local chirp coincide with valleys of the corresponding RWs. The results demonstrate that the temporal modulation of the s-wave scattering length and strength of the inverted parabolic potential can be used to manipulate the evolution of rogue matter waves in BEC.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential

Kengne,

Malomed,

Liu

2021

Preprint

Self Cite

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“…Nonlinear evolution equations (NLEEs) have been proposed to model certain nonlinear phenomena in nonlinear optics, fluid mechanics, plasma physics, etc [16][17][18][19][20][21][22]. As some NLEEs, shallow-water equations have been used to depict the horizontal structure of an atmosphere and the evolution of an incompressible fluid [23].…”

Section: Introductionmentioning

confidence: 99%

X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

Shen

Tian

Zhou

et al. 2021

Preprint

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Water waves are observed in the rivers, lakes, oceans, etc. Under investigation in this paper is a (2+1)-dimensional Hirota-Satsuma-Ito system arising in the shallow water waves. Via the Hirota method and symbolic computation, we derive some X-type and resonance Y-type soliton solutions. We also work out some hybrid solutions consisting of the resonance Y-type solitons, solitons, breathers and lumps. Graphics we present reveal that the hybrid solutions consisting of the resonance Y-type solitons and solitons/breathers/lumps describe the interactions between the resonance Y-type solitons and solitons/breathers/lumps, respectively. The obtained results rely on the water-wave coefficient in that system.

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“…Realizations of Bose-Einstein condensates (BECs) in 1995 for rubidium-87 [1], sodium-23 [2] and Lithium-7 [3] atoms had heralded the landmark of modern physics, then studies of coherent matter waves sparked renewed attention of scientists from various fields [4][5][6][7][8][9][10][11][12][13][14], evidenced by numerous theoretical predictions [15][16][17][18] and the subsequent experimental observations of novel quantum states of matter driven by BECs, which include degenerate quantum Fermi gases [19,20], Tonks-Girardeau gases with impenetrable (hard-core) bosons [21][22][23], spin-orbit-coupled BEC [24][25][26], and quantum droplets [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Particularly, quantum droplets [27,…”

Section: Introductionmentioning

confidence: 99%

One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates

Liu,

Zeng

2021

Preprint

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Lee-Huang-Yang (LHY) fluids are an exotic quantum matter emerged in a Bose-Bose mixture where the mean-field interactions, interspecies attraction (g 12 ) and intraspecies repulsive (g 11 , g 22 ), are tuned to cancel completely when g 12 = − √ g 11 g 22 and atom number N 2 = g 11 /g 22 N 1 , and as such the fluids are purely dominated by beyond mean-field (quantum many-body) effectquantum fluctuations. Three-dimensional LHY fluids were proposed in 2018 and demonstrated by the same group from Denmark in recent ultracold atoms experiments [T. G. Skov, et al., Phys. Rev. Lett. 126, 230404 (2021)], while their low-dimensional counterparts remain mysterious even in theory. Herein, we derive the Gross-Pitaevskii equation of one-dimensional LHY quantum fluids in two-component Bose-Einstein condensates, and reveal the formation, properties, and dynamics of matter-wave structures therein. An exact solution is found for fundamental LHY fluids. Considering a harmonic trap, approximate analytical results are obtained based on variational approximation, and higher-order nonlinear localized modes with nonzero nodes k = 1 and 2 are constructed numerically. Stability regions of all the LHY nonlinear localized modes are identified by linear-stability analysis and direct perturbed numerical simulations. Movements and oscillations of single localized mode, and collisions between two modes, under the influence of different incident momenta are also studied in dynamical evolutions. The predicted results are available to quantum-gas experiments, providing a new insight into LHY physics in low-dimensional settings.

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Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers

Cited by 27 publications

References 64 publications

Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential

Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential

X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates

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