We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of non-thermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.
Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons
我们证明了准二维偶极玻色-爱因斯坦凝聚体（BEC）孤子与谐波陷阱沿垂直于极化方向$z$的$x$方向的排斥接触相互作用的强、稳定、可移动的激发态.这样的孤子可以在y-z平面内自由运动。一个丰富的各种各样的这样的激励被认为是：一个量子的激励沿（i）y轴或（ii）z轴或（ii）两者的运动。本文还讨论了在实验室中利用相位印记技术制备这些激发孤子态的方案。我们还考虑了准二维偶极BEC孤立子的激发态，其中偶极相互作用的符号被旋转定向场反转。在这种符号变化的情况下，孤子在$z$方向上的谐波陷阱的作用下在x-y平面内自由运动。在中等速度下，两个这样的孤子的迎头碰撞被发现是准弹性的，几乎没有变形。研究结果表明，在三个和两个空间维度采用现实的相互作用参数的偶极$^{164}$ Dy BEC的数值模拟。
We explore the energy dynamics of a two dimensional (2D) harmonically trapped Bose-Einstein condensate inside a box potential, excited by a moving red-detuned laser potential (RDLP). For an RDLP velocity $v$ less than a critical value $v_c$, energy oscillations are observed to begin simultaneously with the motion of the RDLP. For $v > v_c$, these oscillations are delayed through a transient in the energy. At the end of the delay time $t_{ons}$, the energy oscillations are regenerated again, and $t_{ons}$ is found to depend on $v$ through universal relations for two cases: one for an RDLP depth…
Excited-state quantum phase transitions (ESQPTs) extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for ESQPTs poses however a major challenge. We introduce spinor Bose-Einstein condensates as a versatile platform for studies of ESQPTs. Based on the mean-field dynamics, we define a topological order parameter that distinguishes between excited-state phases, and discuss how to interferometrically access the order parameter in current experiments. Our work opens the way for the expe…
A few-body properties of spinless Bose particles interacting via the contact three-body potential in geometries with fractional dimensions $1<d<2$ are considered. In the four-body sector at three-body resonance we predict the existence of infinite tower of the Efimov bound states, and a similar behavior is found in the five-body problem. It is shown that a ratio of the high-energy levels in these two sectors is a universal constant. The consequences of emergence of the Efimov physics on the many-body behavior are briefly discussed.
In this paper, we studied a dilute quasi two-dimensional dipolar Bose-condensed with two- and three-body contact, and Coulomb interactions using the Hartree-Fock-Bogoliubov-Popov approximation. We analyze numerically the effects of three-body contact, and Coulomb interactions on the energy spectrum, the quantum and thermal noncondensate fraction of the system. We show that increasing the three-body contact and Coulomb interactions leads to the appearance of rotonization and condensate instability at stronger dipole-dipole interaction. Also we find that the temperature dependence of the thermal…
We propose and demonstrate the appearance of an effective attractive three-body interaction in coherently-driven two-component Bose Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. Importantly, its strength can be controlled with the Rabi-coupling strength and it does not come with additional losses. In the experiment, the three-body interactions are adjusted to play a predominant role in the equation of state of a cigar-shaped trapped condensate. This is confirmed though two striking obser…
We study the equilibrium properties of self-bound droplets in two-dimensional Bose mixtures employing the time-dependent Hartree-Fock-Bogoliubov theory. This theory allows one to understand both the many-body and temperature effects beyond the Lee-Huang-Yang description. We calculate higher-order corrections to the excitations, the sound velocity, and the energy of the droplet. Our results for the ground-state energy are compared with the diffusion Monte Carlo data and good agreement is found. The behavior of the depletion and anomalous density of the droplet is also discussed. At finite tempe…
The spin squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis counter-twisting mechanism, accelerating the spin squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measu…
We investigate the nonlocal Gross-Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose-Einstein condensates (BECs). It is found that the dipolar BECs exhibit stability not only for the usual combination of attractive binary and repulsive three-body interactions, but also for the case when these terms have opposite signs. The trapless stability of the dipolar BECs may be further enhanced by time-periodic modulation of the three-body in…
We investigate numerically the momentum density and phase maps $-$in coordinate and momentum space$-$ of a two dimensional Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential. The BEC is confined in a harmonic trap cutoff by hard walls. The system and excitation scheme are as in our previous work (Roger R. Sakhel {\it et al.} to appear in J. Low Temp. Phys. (2013)); but with twice the number of particles and interaction strength. We solve the time-dependent Gross-Pitaevskii equation numerically using the split-step Crank-Nicolson method in real time. It is demonstrat…
Excited-state quantum phase transitions depend on and reveal the structure of the whole spectrum of many-body systems. While they are theoretically well understood, finding suitable signatures and detect them in actual experiments remains challenging. For instance, in spinor gases, excited-state phases have been identified and characterized through a topological order parameter that is challenging to measure in experiments. Here, we propose the Raman-dressed spin-orbit coupled gas as a novel platform to explore excited-state quantum phase transitions. In a weakly-coupled regime, the dressed sy…
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here, we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low…
Three-body exclusion principle, duality mapping, and exact ground state of a harmonically trapped, ultracold Bose gas with three-body hard-core interactions in one dimension
In an atomic Bose-Einstein condensate quenched to the unitary regime, we predict the sequential formation of a significant fraction of condensed pairs and triples. At short-distances, we demonstrate the two-body and Efimovian character of the condensed pairs and triples, respectively. As the system evolves, the size of the condensed pairs and triples becomes comparable to the interparticle distance, such that many-body effects become significant. The structure of the condensed triples depends on the relative size of Efimov states to density scales. Unexpectedly, we find universal condensed tri…
We explore the energy dynamics of a two dimensional (2D) trapped Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential (RDLP). The trap is a combination of a power-law (PL) potential cutoff by a hard-wall box potential (HWBP). It is found that by a restricted measurment of the energy within the boundaries of the HWBP, the energy demonstrates oscillations indicative of solitons. It is then demonstrated, that the geometry of the PL potential influences the lifetime of these oscillations, i.e., the lifetime of the ensuing solitons inside the HWBP. We argue that the energy…
Identifying dynamical signatures of excited state quantum phase transitions (ESQPTs) in experimentally realizable quantum many-body systems is helpful for understanding the dynamical effects of ESQPTs. In such systems, the highly controllable spinor Bose-Einstein condensates (BECs) offer an exceptional platform to study ESQPTs. In this work, we investigate the dynamical characteristics of the ESQPT in spin-$1$ BEC by means of the Loschmidt echo spectrum. The Loschmidt echo spectrum is an extension of the well-known Loschmidt echo and definded as the overlaps between the evolved state and the e…
