1. Institute of Theoretical Physics and State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China 2. Department of Physics and Key Laboratory of Optical Field Manipulation of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou 310018, China
The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberNc ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.
D. Lee T. , Huang K. , N. Yang C. . Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties. Phys. Rev., 1957, 106( 6): 1135 https://doi.org/10.1103/PhysRev.106.1135
Li Y. , Chen Z. , Luo Z. , Huang C. , Tan H. , Pang W. , A. Malomed B. . Two-dimensional vortex quantum droplets. Phys. Rev. A, 2018, 98( 6): 063602 https://doi.org/10.1103/PhysRevA.98.063602
H. Luo Z. , Pang W. , Liu B. , Y. Li Y. , A. Malomed B. . A new form of liquid matter: Quantum droplets. Front. Phys., 2021, 16( 3): 32201 https://doi.org/10.1007/s11467-020-1020-2
11
I. Mistakidis S. G. Volosniev A. E. Barfknecht R. Fogarty T. Busch Th. Foerster A. Schmelcher P. T. Zinner N., Cold atoms in low dimensions − a laboratory for quantum dynamics, arXiv: 2202.11071 ( 2022)
12
Ferrier-Barbut I. , Kadau H. , Schmitt M. , Wenzel M. , Pfau T. . Observation of quantum droplets in a strongly dipolar Bose gas. Phys. Rev. Lett., 2016, 116( 21): 215301 https://doi.org/10.1103/PhysRevLett.116.215301
13
Schmitt M. , Wenzel M. , Böttcher F. , Ferrier-Barbut I. , Pfau T. . Self-bound droplets of a dilute magnetic quantum liquid. Nature, 2016, 539( 7628): 259 https://doi.org/10.1038/nature20126
Y. Zheng Y. , T. Chen S. , P. Huang Z. , X. Dai S. , Liu B. , Y. Li Y. , R. Wang S. . Quantum droplets in two-dimensional optical lattices. Front. Phys., 2021, 16( 2): 22501 https://doi.org/10.1007/s11467-020-1011-3
17
Chomaz L. Ferrier-Barbut I. Ferlaino F. Laburthe-Tolra B. L. Lev B. Pfau T., Dipolar physics: A review of experiments with magnetic quantum gases, arXiv: 2201.02672 ( 2022)
18
E. Wilson K. , Guttridge A. , Segal J. , L. Cornish S. . Quantum degenerate mixtures of Cs and Yb. Phys. Rev. A, 2021, 103( 3): 033306 https://doi.org/10.1103/PhysRevA.103.033306
19
R. Cabrera C. , Tanzi L. , Sanz J. , Naylor B. , Thomas P. , Cheiney P. , Tarruell L. . Quantum liquid droplets in a mixture of Bose−Einstein condensates. Science, 2018, 359( 6373): 301 https://doi.org/10.1126/science.aao5686
A. Norcia M. , Politi C. , Klaus L. , Poli E. , Sohmen M. , J. Mark M. , N. Bisset R. , Santos L. , Ferlaino F. . Two-dimensional supersolidity in a dipolar quantum gas. Nature, 2021, 596( 7872): 357 https://doi.org/10.1038/s41586-021-03725-7
22
Cheiney P. , R. Cabrera C. , Sanz J. , Naylor B. , Tanzi L. , Tarruell L. . Bright soliton to quantum droplet transition in a mixture of Bose−Einstein condensates. Phys. Rev. Lett., 2018, 120( 13): 135301 https://doi.org/10.1103/PhysRevLett.120.135301
23
Semeghini G. , Ferioli G. , Masi L. , Mazzinghi C. , Wolswijk L. , Minardi F. , Modugno M. , Modugno G. , Inguscio M. , Fattori M. . Self-bound quantum droplets of atomic mixtures in free space. Phys. Rev. Lett., 2018, 120( 23): 235301 https://doi.org/10.1103/PhysRevLett.120.235301
24
Ferioli G. , Semeghini G. , Masi L. , Giusti G. , Modugno G. , Inguscio M. , Gallemi A. , Recati A. , Fattori M. . Collisions of self-bound quantum droplets. Phys. Rev. Lett., 2019, 122( 9): 090401 https://doi.org/10.1103/PhysRevLett.122.090401
25
Cikojević V. , V. Markić L. , Pi M. , Barranco M. , Ancilotto F. , Boronat J. . Dynamics of equilibration and collisions in ultradilute quantum droplets. Phys. Rev. Res., 2021, 3( 4): 043139 https://doi.org/10.1103/PhysRevResearch.3.043139
26
Lao J. , Zhou Z. , Zhang X. , Ye F. , Zhong H. . Oscillatory stability of quantum droplets in PT-symmetric optical lattice. Commum. Theor. Phys., 2021, 73( 6): 065103 https://doi.org/10.1088/1572-9494/abf093
Parisi L. , Giorgini S. . Quantum droplets in one-dimensional Bose mixtures: A quantum Monte Carlo study. Phys. Rev. A, 2020, 102( 2): 023318 https://doi.org/10.1103/PhysRevA.102.023318
29
I. Mistakidis S. , Mithun T. , G. Kevrekidis P. , R. Sadeghpour H. , Schmelcher P. . Formation and quench of homonuclear and heteronuclear quantum droplets in one dimension. Phys. Rev. Res., 2021, 3( 4): 043128 https://doi.org/10.1103/PhysRevResearch.3.043128
30
B. Baizakov B. , A. Malomed B. , Salerno M. . Multidimensional solitons in a low-dimensional periodic potential. Phys. Rev. A, 2004, 70( 5): 053613 https://doi.org/10.1103/PhysRevA.70.053613
31
Lehtovaara L. , Toivanen J. , Eloranta J. . Solution of time-independent Schrödinger equation by the imaginary time propagation method. J. Comput. Phys., 2007, 221( 1): 148 https://doi.org/10.1016/j.jcp.2006.06.006
