Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

Bougas, G.; Mistakidis, S. I.; Schmelcher, Peter

doi:10.1103/physreva.100.053602

Cited by 21 publications

(24 citation statements)

References 99 publications

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“…The three-body collisional complex mainly consists of two identical particles of either bosonic or fermionic symmetry and a third distinguishable one where their pairwise interactions are modeled via δ−function pseudopotentials. This setup constitutes a straightforward generalisation of the analytically tractable trapped two-body problem [35,[61][62][63]. These particular considerations permit us to investigate the dependence of two-/three-body correlations on the scattering lengths, the mass ratio of the particles as well as the impact of particle symmetry.…”

Section: Hamiltonian and Hyperspherical Frameworkmentioning

confidence: 99%

“…The latter are experimentally probed * gbougas@physnet.uni-hamburg.de via radio-frequency spectroscopy, time-of-flight expansion, and subsequent measurement of the structure factor with the aid of Bragg spectroscopy [27][28][29][30][31][32]. Their investigation sheds light into the microscopic properties of the system, especially the formation of two- [33][34][35][36] and three-body bound states (trimers) [26,33]. Importantly, the two-body contact satisfies universal relations regarding the energy, the two-body loss rate, and the radiofrequency spectra that hold regardless of the statistics and the dimensionality, in few-as well as in many-body settings [37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

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Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

Bougas,

Mistakidis,

Giannakeas

et al. 2021

Preprint

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Few-body correlations emerging in two-dimensional harmonically trapped mixtures, are comprehensively investigated. The presence of the trap leads to the formation of atom-dimer and trap states, in addition to trimers. The Tan's contacts of these eigenstates are studied for varying interspecies scattering lengths and mass ratio, while corresponding analytical insights are provided within the adiabatic hyperspherical formalism. The two-and three-body correlations of trimer states are substantially enhanced compared to the other eigenstates. The two-body contact of the atom-dimer and trap states features an upper bound regardless of the statistics, treated semi-classically and having an analytical prediction in the limit of large scattering lengths. Such an upper bound is absent in the three-body contact. Interestingly, by tuning the interspecies scattering length the contacts oscillate as the atom-dimer and trap states change character through the existent avoided-crossings in the energy spectra. For thermal gases, a gradual suppression of the involved two-and three-body correlations is evinced manifesting the impact of thermal effects. Moreover, spatial configurations of the distinct eigenstates ranging from localized structures to angular anisotropic patterns are captured. Our results provide valuable insights into the inherent correlation mechanisms of few-body mixtures which can be implemented in recent ultracold atom experiments and will be especially useful for probing the crossover from few-to many-atom systems.

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Section: Hamiltonian and Hyperspherical Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

Bougas,

Mistakidis,

Giannakeas

et al. 2021

Preprint

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“…Similar to above, the key step of our approach is to calculate free Green's function G 0 (E, ze z ) defined in Eq. (12). Since the result in Eq.…”

Section: General Case: Arbitrary Ementioning

confidence: 93%

“…The two-body problems of trapped interacting ultracold atoms are basic problems in cold atom physics [1][2][3][4][5][6][7][8][9][10][11][12][13]. They are of broad interest because of the following reasons.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement

Chen,

Xiao,

Zhang

et al. 2020

Preprint

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We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic equation J3D(E) = 1/a3D (J2D(E) = ln a2D) for the eigen-energy E of this system in the 3D (2D) case, with a3D and a2D being the corresponding s-wave scattering lengths, and provide the analytical expressions of the functions J3D(E) and J2D(E). In previous researches this type of equation was obtained for spherically or axially symmetric harmonic traps (T. Busch, et. al., Found. Phys. 28, 549 (1998); Z. Idziaszek and T. Calarco, Phys. Rev. A 74, 022712 ( 2006)). However, for our cases with a completely anisotropic trap, only the equation for the ground-state energy of some cases has been derived (J. Liang and C. Zhang, Phys. Scr. 77, 025302 ( 2008)). Our results in this work are applicable for arbitrary eigen-energy of this system, and can be used for the studies of dynamics and thermal-dynamics of interacting ultracold atoms in this trap, e.g., the calculation of the 2nd virial coefficient or the evolution of two-body wave functions. In addition, our approach for the derivation of the above equations can also be used for other two-body problems of ultracold atoms.

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“…While solving large many-body systems with approaches beyond mean-field is a very difficult task and only possible in special cases [12][13][14], few-particle systems can actually be amenable to exact treatments across the whole range of interactions and correlation strengths [15][16][17][18][19]. Several treatments of SOC in such systems have already been carried out [20][21][22][23][24][25][26] and, for example, a mapping to an effective spin model was recently suggested by a perturbative approach to account for weak Raman coupling [21].…”

Section: Introductionmentioning

confidence: 99%

Spin–orbit coupling in the presence of strong atomic correlations

et al. 2020

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We explore the influence of contact interactions on a synthetically spin-orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-ofmass momentum to relative momentum and also affects the global entanglement shared between the real-and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the ground state which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin-orbit coupling and therefore the system does not contain spin-spin entanglement.

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Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

Cited by 21 publications

References 99 publications

Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement

Spin–orbit coupling in the presence of strong atomic correlations

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