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Bulletin of the American Physical Society

Efimov states embedded in a quenched unitary Bose-condensed gas.

V. E. Colussi, S. Musolino, S. J. J. M. F. Kokkelmans

Published May 29, 2018• 0 citations
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Abstract

Three identical bosons at unitarity may form a series of three-body bound states whose spectrum was first given by Efimov. Recently, a macroscopic population of Efimov molecules was measured for the first time in a Bose-condensed gas quenched to unitarity. Through the method of cumulants, we study three-body physics in the many-body context. We report preliminary results for the spectrum of two- and three-body bound states embedded in the quenched unitary Bose-condensed gas. This study is in preparation for studying the dependence of macroscopic observables on Efimov physics. Netherlands Organisation for Scientific Research (NWO) under Grant 680-47-623.

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Three identical bosons at unitarity may form a series of three-body bound states whose spectrum was first given by Efimov. Recently, a macroscopic population of Efimov molecules was measured for the first time in a Bose-condensed gas quenched to unitarity. Through the method of cumulants, we study three-body physics in the many-body context. We report preliminary results for the spectrum of two- and three-body bound states embedded in the quenched unitary Bose-condensed gas. This study is in preparation for studying the dependence of macroscopic observables on Efimov physics. Netherlands Organisation for Scientific Research (NWO) under Grant 680-47-623.
We study the structure of a Bose-condensed gas after quenching interactions to unitarity. Using the method of cumulants, we decompose the evolving gas in terms of clusters. Within the quantum depletion we observe the emergence of two-body clusters bound purely by many-body effects, scaling continuously with the atomic density. As the unitary Bose gas forms, three-body Efimov clusters are first localized and then sequentially absorbed into the embedded atom-molecule scattering continuum of the surrounding depletion. These results highlight the interplay of quantum depletion and evolving scaling laws in the formation of the unitary Bose gas.
We study the impact of three-body physics in quenched unitary Bose gases, focusing on the role of the Efimov effect. Using a local density model, we solve the three-body problem and determine three-body decay rates at unitarity, finding density-dependent, log-periodic Efimov oscillations, violating the expected continuous scale invariance in the system. We find that the breakdown of continuous scale invariance, due to Efimov physics, manifests also in the earliest stages of evolution after the interaction quench to unitarity, where we find the growth of a substantial population of Efimov states for densities in which the interparticle distance is comparable to the size of an Efimov state. This agrees with the early-time dynamical growth of three-body correlations at unitarity [Colussi et al., Phys. Rev. Lett. 120, 100401 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.100401]. By varying the sweep rate away from unitarity, we also find a departure from the usual Landau-Zener analysis for state transfer when the system is allowed to evolve at unitarity and develop correlations.
We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.
We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.
We study the growth of few-body correlations in an ultracold Bose gas quenched to unitarity. This is encoded in the dynamics of the two- and three-body contacts. By connecting many-body correlations dynamics with few-body models, we map out signatures of the Efimov effect. For the thermal resonantly interacting Bose gas where the contact dynamics have been measured experimentally, we find that atom-bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales. NWO Grant 680-47-623, NSF Grant PHY-1607204, and NASA.
We study the quench of a degenerate ultracold Bose gas to the unitary regime, where interactions are as strong as allowed by quantum mechanics. We lay the foundation of a cumulant theory able to simultaneously capture the three-body Efimov effect and ergodic evolution. After an initial period of rapid quantum depletion, a universal prethermal stage is established, characterized by a kinetic temperature and an emergent Bogoliubov dispersion law, while the microscopic degrees of freedom remain far from equilibrium. Integrability is then broken by higher-order interaction terms in the many-body Hamiltonian, leading to a momentum-dependent departure from power law to decaying exponential behavior of the occupation numbers at large momentum. We also find signatures of the Efimov effect in the many-body dynamics and make a precise identification between the observed beating phenomenon and the binding energy of an Efimov trimer. Throughout the paper, our predictions for a uniform gas are quantitatively compared with experimental results for quenched unitary Bose gases in uniform potentials.