The class of two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be exactly mapped into two independent standard single-impurity spin-boson models where the role of the tunnelling parameter is played by the spin-spin coupling. The dynamics of the magnetization is analysed for different levels of (an)isotropy. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light.
We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a new, exactly solvable, three-level quantum dissipative system is derived as a generalisation of the standard spin-half spin-boson model. The new system has two environmental oscillator baths with ohmic coupling, and admits arbitrary detuning between the three levels. All tunnelling matrix elements are equal, up to one complex phase which is itself a function…
Using near-exact numerical simulations we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas which allows one to measure properties of the Bose gas non-destructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its red…
We study the correlation between an impurity and a small ensemble of bosonic particles in one dimension. Our study analyzes the one-body density matrix and calculates the corresponding von Neumann entanglement entropy as a function of the interaction strength between the impurity and the bosons when all particles have the same mass. We show that the entropy grows very fast for small and moderate interaction strength and then increases slowly toward the strongly interacting regime. Then we study the effect over the quantum correlations of a mass imbalance between the impurity and the bosons. In…
Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise non-interacting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, $α_c$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between $α_c=0.5$ and $α_c=1$ depending upon the spin separation and the strength of the transver…
Using the time-dependent density matrix renormalization group (TDMRG) we theoretically study the collision of a one-dimensional gas of interacting bosons with an impurity trapped in a shallow box potential. We study the dynamic response of both the impurity and the bosonic gas and find an approximate independence of the sign of the interaction (attractive or repulsive) between the impurity and the bosons. This sign-independence breaks down when the interaction energy is of the same order as the box potential depth, leading to resonant pair tunneling. Our predictions can be tested using contemp…
In this work, we put forward the theoretical foundation toward thermodynamics of quantum impurity systems measurable in experiments. The theoretical developments involve the identifications on two types of thermodynamic entanglement free--energy spectral functions for impurity systems that can be either fermionic or bosonic or combined. Consider further the thermodynamic limit in which the hybrid environments satisfy the Gaussian--Wick's theorem. We then relate the thermodynamic spectral functions to the local quantum impurity systems spectral densities that are often experimentally measurable…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some boson impurity models. They describe free bosons coupled to an impurity and include some of the most representative models in quantum optics. We also propose a family of wavefunctions to describe the bound states and verify that it accurately characterizes all parameter regimes by comparing its predictions with exact numerical calculations for a one-dimensio…
By means of a trial wave function, the multi-D$_1$ ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a two-impurity system embedded in a common Ohmic bath of bosons. Quantum criticality in both the impurity system and the Ohmic bosonic bath is investigated with relevant transition points and critical exponents determined accurately. With the linear grid of the Ohmic spectral density, our numerical calculations produce a much better description of the ground states with lower energie…
We investigate a temporal evolution of an impurity atom in a one-dimensional trapped Bose gas following a sudden change of the boson-impurity interaction strength. Our focus is on the effects of inhomogeneity due to the harmonic confinement. These effects can be described by an effective one-body model where both the mass and the spring constant are renormalized. This is in contrast to the classic renormalization, which addresses only the mass. We propose an effective single-particle Hamiltonian and apply the multilayer multiconfiguration time-dependent Hartree method for bosons to explore its…
We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization)…
We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the pr…
We unravel the correlated quantum quench dynamics of a single impurity immersed in a bosonic environment confined in an one-dimensional double-well potential. A particular emphasis is placed on the structure of the time-evolved many-body wave function by relying on a Schmidt decomposition whose coefficients directly quantify the number of configurations that are macroscopically populated. For a non-interacting bosonic bath and weak postquench impurity-bath interactions, we observe the dynamical formation of a two-fold fragmented many-body state which is related to intra-band excitation process…
Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum $p_0$. We examine the infinite-time value of the momentum of the impurity, $p_\infty$, as a function of $p_0$. A lower bound on $|p_\infty(p_0)|$ is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of an impurity in a one-dimensional gas of nonintera…
We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we …
We report on the experimental doping of a $^{87}$Rubidium (Rb) Bose-Einstein condensate (BEC) with individual neutral $^{133}$Cesium (Cs) atoms. We discuss the experimental tools and procedures to facilitate Cs-Rb interaction. First, we use degenerate Raman side-band cooling of the impurities to enhance the immersion efficiency for the impurity in the quantum gas. We identify the immersed fraction of Cs impurities from the thermalization of Cs atoms upon impinging on a BEC, where elastic collisions lead to a localization of Cs atoms in the Rb cloud. Second, further enhancement of the immersion…
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov a…
We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless tran…
The challenge of understanding the dynamics of a mobile impurity in an interacting quantum many-body medium comes from the necessity of including entanglement between the impurity and excited states of the environment in a wide range of energy scales. In this paper, we investigate the motion of a finite mass impurity injected into a three-dimensional quantum Bose fluid as it starts shedding Bogoliubov excitations. We uncover a transition in the dynamics as the impurity's velocity crosses a critical value which depends on the strength of the interaction between the impurity and bosons as well a…
A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）
We study finite size scaling for the magnetic observables of an impurity residing at the endpoint of an open quantum Ising chain in a transverse magnetic field, realized by locally rescaling the magnetic field by a factor $μ\neq 1$. In the homogeneous chain limit at $μ= 1$, we find the expected finite size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit, $μ= 0$, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. For this case…
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi one dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are…
We develop an efficient variational approach to studying dynamics of a localized quantum spin coupled to a bath of mobile spinful bosons. We use parity symmetry to decouple the impurity spin from the environment via a canonical transformation and reduce the problem to a model of the interacting bosonic bath. We describe coherent time evolution of the latter using bosonic Gaussian states as a variational ansatz. We provide full analytical expressions for equations describing variational time evolution that can be applied to study in- and out-of-equilibrium phenomena in a wide class of quantum i…
We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induce…
We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since Feynman. Indeed, it underlies several numerical methods for solving impurity problems, as well as many approaches to more general quantum many-body problems, such as the dynamical mean field theory. The sparsity pattern is easily motivated by a formal perturbative expansion using Feynman diagrams. However, to the extent of our knowledge, a rigoro…
We study the dynamics of a two-level impurity embedded in a two-dimensional Bose-Hubbard model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular, we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the Bose-Hubbard environment and its non-Gaussian statistic…
The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interaction and that an impurity and a boson have a zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presen…
We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.
The behavior of an ideal $D$-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrarily to an old standing folklore, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\neq 0$ for $D=1,2,3$ if there is a point-like impurity at the bottom of the vessel containing the gas.
The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.
One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding many-particle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes/vortices to it and thereby convert…
