The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impur
ities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.
This study develops a novel experimental method of deducing the profile of interaction induced between impurities in a trapped gas of ultracold Fermi/Bose atoms, which are often referred to as Fermi/Bose polarons. In this method, we consider a two-bo
dy Fermi/Bose polaron collision experiment in which impurities and atoms interact only weakly. Numerical simulations of the quantum dynamics reveal the possibility to obtain information regarding the non-local induced interaction between two polarons from a measured profile of the polaron wave packet at several snapshots. This is because the potential of the induced interaction is well balanced by the quantum potential whenever the WKB approximation for the relevant Schr{o}dinger equation is applicable.
We investigate how the presence of a localized impurity in a Bose-Einstein condensate of trapped cold atoms that interact with each other weakly and repulsively affects the profile of the condensed and excited components at zero temperature. By solvi
ng the Gross-Pitaevskii and Bogoliubov-de Gennes equations, we find that an impurity-boson contact attraction (repulsion) causes both components to change in spatial structure in such a way as to be enhanced (suppressed) around the impurity, while slightly declining (growing) in a far region from the impurity. Such behavior of the quantum depletion of the condensate can be understood by decomposing the impurity-induced change in the profile of the excited component with respect to the radial and azimuthal quantum number. A significant role of the centrifugal potential and the hole excitation level is thus clarified.
Observed well-developed $alpha$ cluster states in $^{16}$O, located above the four $alpha$ threshold, are investigated from the viewpoint of Bose-Einstein condensation of $alpha$ clusters by using a field-theoretical superfluid cluster model in which
the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV $0_7^+$ and 18.8 MeV $0_8^+$ states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with the spontaneous symmetry breaking of the global phase, which is caused by the Bose-Einstein condensation of the vacuum 15.1 MeV $0^+_6$ state with a dilute well-developed $alpha$ cluster structure just above the threshold. This gives evidence of the existence of the Bose-Einstein condensate of $alpha$ clusters in $^{16}$O. It is found that the emergence of the energy level structure with a well-developed $alpha$ cluster structure above the threshold is robust, almost independently of the condensation rate of $alpha$ clusters under significant condensation rate. The finding of the mechanism why the level structure that is similar to $^{12}$C emerges above the four $alpha$ threshold in $^{16}$O reinforces the concept of Bose-Einstein condensation of $alpha$ clusters in addition to $^{12}$C.
We investigate the real and imaginary chemical-potential dependence of pion and $rho$-meson screening masses in both the confinement and the deconfinement region by using two-flavor lattice QCD. The spatial meson correlators are calculated in the ima
ginary chemical potential region with lattice QCD simulations. We extract pion and $rho$-meson screening masses from the correlators. The obtained meson screening masses are extrapolated to the real chemical potential region by assuming some analytic function. In the real chemical potential region, the resulting pion and $rho$-meson screening masses monotonically increase as real chemical potential becomes large.
We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmet
ric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $mu-kappa$ plane as the number of states increases, where $mu$ $(kappa)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $mu$-dependence with respect to increasing the number of states.
We investigate QCD at large mu/T by using Z_3-symmetric SU(3) gauge theory, where mu is the quark-number chemical potential and T is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the t
wist angle theta as a parameter, and agrees with QCD when theta=0 and becomes symmetric when theta=2pi/3. For both QCD and the Z_3-symmetric SU(3) gauge theory, the phase diagram is drawn in mu--T plane with the Polyakov-loop extended Nambu--Jona-Lasinio model. In the Z_3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T lsim 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z_3 symmetry and then makes varphi finite. When mu gsim 300 MeV, the CSC phase is more stable than the perfectly confined phase at T lsim 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z_3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu lsim 300 MeV and T lsim 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of mu gsim 300 MeV and 100 lsim T lsim 200 MeV. The basic phase structure of Z_3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of varphi=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at theta=0 from those at theta=2pi/3.
We incorporate the effective restoration of $U(1)_{rm A}$ symmetry in the 2+1 flavor entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model by introducing a temperature-dependent strength $K(T)$ to the Kobayashi-Maskawa-t Hooft (KMT) d
eterminant interaction. $T$ dependence of $K(T)$ is well determined from pion and $a_0$-meson screening masses obtained by lattice QCD (LQCD) simulations with improved p4 staggered fermions. The strength is strongly suppressed in the vicinity of the pseudocritical temperature of chiral transition. The EPNJL model with the $K(T)$ well reproduces meson susceptibilities calculated by LQCD with domain-wall fermions. The model shows that the chiral transition is second order at the light-quark chiral-limit point where the light quark mass is zero and the strange quark mass is fixed at the physical value. This indicates that there exists a tricritical point. Hence the location is estimated.
We evaluate quark number densities at imaginary chemical potential by lattice QCD with clover-improved two-flavor Wilson fermion. The quark number densities are extrapolated to the small real chemical potential region by assuming some function forms.
The extrapolated quark number densities are consistent with those calculated at real chemical potential with the Taylor expansion method for the reweighting factors. In order to study the large real chemical potential region, we use the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the entanglement-PNJL model for the quark phase. The quantum hadrodynamics model is constructed to reproduce nuclear saturation properties, while the entanglement-PNJL model reproduces well lattice QCD data for the order parameters such as the Polyakov loop, the thermodynamic quantities and the screening masses. Then, we calculate the mass-radius relation of neutron stars and explore the hadron-quark phase transition with the two-phase model.
We determine the strength $G_{rm v}$ of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasinio (EPNJL) model from the results of recent lattice QCD simulations with two-flavor Wilson fermions. The quark-number
density is normalized by the Stefan-Boltzmann limit for small baryon chemical potential $mu$ and temperature $T$ higher than the pseudo-critical temperature $T_c$ of the deconfinement transition. The strength determined from the normalized quark-number density is $G_{rm v}=0.33 G_{rm s}$ for the strength $G_{rm s}$ of the scalar-type four-quark interaction. We explore the hadron-quark phase transition in the $mu$-$T$ plane, using the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the EPNJL model for the quark phase. When $G_{rm v}=0.33 G_{rm s}$, the critical baryon chemical potential of the transition at zero $T$ is $mu_c sim 1.6$ GeV that accounts for two solar mass measurements of neutron stars in the framework of the quark-hadron hybrid star model.
