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arXiv:2307.02298 · Physical Review A

Effects of atom losses on a one-dimensional lattice gas of hard-core bosons

François Riggio, Lorenzo Rosso, Dragi Karevski, Jérôme Dubail

Published Feb 6, 2024• 15 citations
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Abstract

Atom losses occur naturally during cold atoms experiments. Since this phenomenon is unavoidable, it is important to understand its effect on the remaining atoms. Here we investigate a toy model: a lattice gas of hard-core bosons subject to $K$-body losses (where $K=1,2,3,\ensuremath{\cdots},$ is the number of atoms lost in each loss event) on $K$ neighboring sites. In particular, we investigate the effect of losses on the rapidity distribution $\ensuremath{\rho}(k)$ of the atoms. Under the assumption that losses are weak enough so that the system relaxes between two loss events, we are able to determine the loss functional $F[\ensuremath{\rho}](k)$ encoding the loss process for $K$-body losses. We derive closed expressions for the cases of one- and two-body losses and show their effects on the evolution of the total number of particles. Then we add a harmonic trapping potential and study the evolution of the position-dependent rapidity distribution of this system by solving numerically the evolution equation for one-, two-, and three-body losses.

DOI
10.1103/physreva.109.023311

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Atom losses occur naturally during cold atoms experiments. Since this phenomenon is unavoidable, it is important to understand its effect on the remaining atoms. Here we investigate a toy model: a lattice gas of hard-core bosons subject to KKK-body losses (where K=1,2,3,\ensuremath⋯,K=1,2,3,\ensuremath{\cdots},K=1,2,3,\ensuremath⋯, is the number of atoms lost in each loss event) on KKK neighboring sites. In particular, we investigate the effect of losses on the rapidity distribution \ensuremathρ(k)\ensuremath{\rho}(k)\ensuremathρ(k) of the atoms. Under the assumption that losses are weak enough so that the system relaxes between two loss events, we are able to determine the loss functional F[\ensuremathρ](k)F[\ensuremath{\rho}](k)F[\ensuremathρ](k) encoding the loss process for KKK-body losses. We derive closed expressions for the cases of one- and two-body losses and show their effects on the evolution of the total number of particles. Then we add a harmonic trapping potential and study the evolution of the position-dependent rapidity distribution of this system by solving numerically the evolution equation for one-, two-, and three-body losses.
We theoretically investigate the effect of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K K -body losses ( K=1,2,3,\dots K = 1 , 2 , 3 , … ) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion – where the gas behaves like an ideal Bose gas – and hard-core repulsion – where the gas is mapped to a non-interacting Fermi gas –, we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.
We present a theoretical investigation of a lattice Tonks–Girardeau gas that is created by inelastic, instead of elastic interactions. An analytical calculation shows that in the limit of strong two-body losses, the dynamics of the system is effectively that of a hard-core boson gas. We also derive an analytic expression for the effective loss rate. We find good agreement between these analytical results and results from a rigorous numerical calculation. The hard-core character of the particles is visible both in a reduced effective loss rate and in the momentum distribution of the gas.
We explore the dynamics of hard-core lattice bosons in the presence of strong nonlocal particle loss. The evolution occurs on two distinct time scales, first a rapid strongly correlated decay into a highly degenerate Zeno state subspace, followed by a slow almost coherent evolution. We analytically solve the fast initial dynamics of the system, where we specifically focus on an initial Mott insulator state, and perform an analysis of the particle arrangements in the Zeno subspace. We investigate the secondary slow relaxation process that follows and find an intricate regime where the competition between dissipation and coherence results in various types of interacting particle complexes. We classify them and analyze their spectral properties in the presence and absence of nearest-neighbor interactions. Under certain circumstances the dispersion relations of the complexes feature flat bands, which are a result of an effective spin-orbit coupling.
Experimental control over ultracold quantum gases has made it possible to investigate low-dimensional systems of both bosonic and fermionic atoms. In closed one-dimensional systems there are many similarities in the dynamics of local quantities for spinless fermions and strongly interacting ``hard-core'' bosons, which on a lattice can be formalized via a Jordan-Wigner transformation. In this study, we analyze the similarities and differences for spinless fermions and hard-core bosons on a lattice in the presence of particle loss. The removal of a single fermion causes differences in local quantities compared with the bosonic case because of the different particle exchange symmetry in the two cases. We identify deterministic and probabilistic signatures of these dynamics in terms of local particle density, which could be measured in ongoing experiments with quantum gas microscopes.
We observe the dissipative dynamics of a dense, strongly interacting gas of bosonic atom pairs in an optical lattice, controlling the strength of the two-body interactions over a wide parameter regime. We study how three-body losses contribute to the lattice dynamics, addressing a number of open questions related to the effects of strong dissipation in a many-body system, including the relationship to the continuous quantum Zeno effect. We observe rapid break-up of bound pairs for weak interactions, and for stronger interactions we see doublon decay rates that are asymmetric when changing from attractive and repulsive interactions and which strongly depend on the interactions and on-site loss rates. By comparing our experimental data with a theoretical analysis of few-body dynamics, we show that these features originate from a nontrivial combination of dissipative dynamics described by a lattice model beyond a standard Bose-Hubbard Hamiltonian, and the modification of three-atom dynamics on a single site, which is generated alongside strong three-body loss. Our results open new possibilities for investigating bosonic atoms with strong three-body loss features and allow for the better understanding of the parameter regimes that are required to realize strong effective three-body interactions.
The one-dimensional δ-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra-cold atoms in one-dimensional traps. Even though the model is integrable, integrability breaking effects are always present in the real-world experiments. In this work we consider the integrability breaking due to atomic loss, which is the most relevant effect in the experiments. We set up a framework for the exact computation of the losses of the canonical charges of the model, and compute an exact result for the energy loss due to the local K-body processes, valid for arbitrary K. Our result takes the form of multiple integrals, which are explicitly factorized in the experimentally relevant cases of K=1,2,3.