Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.
Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.
A mobile impurity particle immersed in a quantum degenerate gas leads to the formation of a quasiparticle, which can serve as a sensor for its environment. Here, we develop a unified wave function description of an impurity in a two-dimensional Bose-Hubbard model across the Mott-insulator to superfluid transition. Using a multi-mode variational ansatz based on the quantum Gutzwiller approach, we show that the impurity can form several kinds of polaronic and molecular states. In addition to their spectral properties, the wave function provides direct access to the microscopic structure of these states, and we demonstrate that strong correlations in the critical regime of the quantum phase transition give rise to several non-analytic features in the polaron properties. Increasing the impurity-boson interaction leads to transitions between polaron and molecular ground states, and the number of bosons in the impurity dressing cloud grows rapidly at the quantum critical point as the bath modes soften. We furthermore reveal qualitatively distinct non-equilibrium many-body dynamics after the injection of the impurity in the different phases of the Bose-Hubbard model. Our spectral, real space, and dynamical predictions describe complementary properties of polarons in a strongly correlated bosonic bath, which can be observed using current techniques with atoms in optical lattices.
We investigate the zero-temperature properties of a mobile impurity immersed in a bath of bosonic particles confined to a square lattice. We analyze the regimes of attractive and repulsive coupling between the impurity and the bath particles for different strengths of boson-boson interactions in the bath, using exact large-scale quantum Monte-Carlo simulations in the grand canonical ensemble. For weak coupling, the polaron mass ratio is found to decrease around the Mott insulator (MI) to superfluid (SF) transition of the bath, as predicted by recent theory, confirming the possible use of the impurity as a probe for the transition. For strong coupling in the MI regime, instead, the impurity is found to modify the bath density by binding to an extra bath particle or a hole, depending on the sign of the polaron-bath interactions. While the binding prevent the aforementioned use of the polaron mass ratio as an MI-SF transition probe, we show that it can be used instead as a probe of the binding itself. Our exact numerical results provide a benchmark for comparing lattice Bose polaron theories and are relevant for experiments with cold atoms trapped in optical lattices, where the presence of a confining harmonic potential can be modeled by a slowly varying local chemical potential.
We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors apply at a finite temperature, for both classical Berezinskii-Kosterlitz-Thouless transition and quantum phase transition from superfluid to Mott insulator. Our results represent the critical regime that should be observed in present experimental conditions.
The problem of mobile impurities in quantum baths is of fundamental importance in many-body physics. There has recently been significant progress regarding our understanding of this due to cold atom experiments, but so far it has mainly been concerned with cases where the bath has no or only weak interactions, or the impurity interacts weakly with the bath. Here, we address this gap by developing a new theoretical framework for exploring a mobile impurity interacting strongly with a highly correlated bath of bosons in the quantum critical regime of a Mott insulator (MI) to superfluid (SF) quantum phase transition. Our framework is based on a powerful quantum Gutzwiller (QGW) description of the bosonic bath combined with diagrammatic field theory for the impurity-bath interactions. By resumming a selected class of diagrams to infinite order, a rich picture emerges where the impurity is dressed by the fundamental modes of the bath, which change character from gapped particle-hole excitations in the MI to Higgs and gapless Goldstone modes in the SF. This gives rise to the existence of several quasiparticle (polaron) branches with properties reflecting the strongly correlated environment. In particular, one polaron branch exhibits a sharp cusp in its energy, while a new ground-state polaron emerges at the O(2) O ( 2 ) quantum phase transition point for integer filling, which reflects the nonanalytic behavior at the transition and the appearance of the Goldstone mode in the SF phase. Smooth versions of these features are inherited in the polaron spectrum away from integer filling due to the influence of Mott physics on the bosonic bath. We furthermore compare our diagrammatic results with quantum Monte Carlo calculations, obtaining excellent agreement. This accuracy is quite remarkable for such a highly non-trivial case of strong interactions between the impurity and bosons in a maximally correlated quantum critical regime, and it establishes the utility of our framework. Finally, our results show how impurities can be used as quantum sensors and highlight fundamental differences between experiments performed at a fixed particle number or a fixed chemical potential.
The Bose polaron has attracted theoretical and experimental interest because the mobile impurity is surrounded by a bath that undergoes a superfluid-to-normal phase transition. Although many theoretical works have studied this system in its ground state, only a few analyze its behavior at finite temperature. We have studied the effect of temperature on a Bose polaron system performing ab initio path integral Monte Carlo simulations. This method is able to approach the critical temperature without losing accuracy, in contrast with perturbative approximations. We have calculated the polaron energy for the repulsive and attractive branches and we have observed an asymmetric behavior between the two branches. When the potential is repulsive, the polaron energy decreases when the temperature increases, and contrariwise for the attractive branch. Our results for the effective mass and the dynamical structure factor of the polaron show unambiguously that its quasiparticle nature disappears close to the critical temperature, in agreement with recent experimental findings. Finally, we have also estimated the fraction of bosons in the condensate as well as the superfluid fraction, and we have concluded that the impurity hinders the condensation of the rest of bosons.
We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.