We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.
We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.
We investigate the influence of a Bose–Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation (QME) for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the QME reproduces the exact evolution of the qubits. We characterize the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and super-decoherence is observable for realistic experimental parameters. Furthermore, the BEC phonons mediate an attractive interaction between the impurities, which has an important impact on their spatial distribution. If the lattice atoms are allowed to move, there occurs a sharp transition with the impurities aggregating in a macroscopic cluster at experimentally achievable temperatures. We also investigate the impact of the BEC on the transport properties of the impurity atoms and show that a crossover from coherent to diffusive behaviour occurs with increasing interaction strength.
We investigate the influence of a Bose-Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the quantum master equation reproduces the exact evolution of the qubits. We characterise the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and superdecoherence is observable for realistic experimental parameters. Furthermore, the BEC phonons mediate an attractive interaction between the impurities, which has an important impact on their spatial distribution. If the lattice atoms are allowed to move, there occurs a sharp transition with the impurities aggregating in a macroscopic cluster at experimentally achievable temperatures. We also investigate the impact of the BEC on the transport properties of the impurity atoms and show that a crossover from coherent to diffusive behaviour occurs with increasing interaction strength. PACS numbers: 03.75.-b, 03.67.-a, 03.65.Yz, 36.40.-cDynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates2 1.
We investigate the dynamics of quantum information flow in one and two impurity qubits trapped in a double-well potential and interacting with a one-dimensional ultracold Bose-Bose mixture reservoir. For a single qubit immersed in a binary Bose mixture, we show that the system maintains coherence over finite timescales and exhibits non-Markovian dynamics, particularly in the upper branch of the environment. We explore the transition from Markovian to non-Markovian dephasing through the Ohmicity of the spectral density functions, which are significantly influenced by interspecies interactions. In the case of two spatially separated qubits coupled to the Bose-Bose mixture reservoir, we demonstrate that collective decoherence affects the system dynamics, leading to prolonged coherence survival in both branches of the mixture. The intricate evolution of the decoherence factors is reflected in the density spectral functions and their Ohmicity characteristics. We find that the decoherence functions and spectra oscillate with increasing distance between the qubits, modifying the information flow dynamics. Additionally, we conduct a thorough investigation of the entanglement dynamics between the two qubits induced by the binary Bose mixture reservoir in both branches, underscoring the critical role of interspecies interactions.
The counterflow dynamics of two correlated impurities in a double well coupled to a one-dimensional bosonic medium is explored. We determine the ground-state phase diagram of the system according to the impurity-medium entanglement and the impurities' two-body correlations. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinement of the medium. Accordingly the impurities' dynamical response, triggered by suddenly ramping down the central potential barrier, is affected by the medium's trapping geometry. In particular, for a box-confined medium, repulsive impurity-medium couplings lead, due to attractive induced interactions, to the localization of the impurities around the trap center. In contrast, for a harmonically trapped medium the impurities perform a periodic collision and expansion dynamics further interpreted in terms of a two-body effective model. Our findings elucidate the correlation aspects of the collisional physics of impurities which should be accessible in recent cold-atom experiments.
We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator B_{xσ} for an atom at the site x with a two-component (pseudo-) spin σ(=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon described by a CP^1 field (Schwinger boson) z_{xσ} and a holon described by a hard-core-boson field ϕ_x as B_{xσ}=ϕ^†_x z_{xσ}. ϕ_x is then expressed by a pseudo-spin, which is, in turn, represented by another CP^1 (pseudo) spinon w_{xη} as ϕ_x = w_{x2}^†w_{x1}. We then have a double-CP^1 representation of the model by z_{xσ} and w_{xη}. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. They should be compared with the possible experimental results of a recently studied boson-boson mixture like ^87Rb and ^41K in an optical lattice.
Quantum dynamics of impurities in a bath of bosons is a long-standing problem in solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms have focused on this problem, studying atomic impurities immersed in an atomic Bose–Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano−Feshbach resonance technique. Here, we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity consisting of a few 41 K atoms and a BEC of 87 Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the inter-species interaction strength (regardless of its sign), we find that the impurity, which starts from outside the BEC, simply causes the BEC cloud to oscillate back and forth, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC, and strongly changes its amplitude of oscillation. In the strong interaction regime, if the inter-species interaction is attractive, a local maximum (bright soliton) in the BEC density occurs where the impurity is trapped; if, instead, the inter-species interaction is repulsive, the impurity is not able to enter the BEC cloud and the reflection coefficient is close to one. However, if the initial displacement of the impurity is increased, the impurity is able to penetrate the cloud, leading to the appearance of a moving hole (dark soliton) in the BEC.