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Register a new userNon-hermitian approach to decaying ultracold bosonic systems
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A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.
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We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.
We present a general scheme for constructing robust excitations (soliton-like) in non-integrable multicomponent systems. By robust, we mean localised excitations that propagate with almost constant velocity and which interact cleanly with little to no radiation. We achieve this via a reduction of these complex systems to more familiar effective chiral field-theories using perturbation techniques and the Fredholm alternative. As a specific platform, we consider the generalised multicomponent Nonlinear Schr{o}dinger Equations (MNLS) with arbitrary interaction coefficients. This non-integrable system reduces to uncoupled Korteweg-de Vries (KdV) equations, one for each sound speed of the system. This reduction then enables us to exploit the multi-soliton solutions of the KdV equation which in turn leads to the construction of soliton-like profiles for the original non-integrable system. We demonstrate that this powerful technique leads to the coherent evolution of excitations with minimal radiative loss in arbitrary non-integrable systems. These constructed coherent objects for non-integrable systems bear remarkably close resemblance to true solitons of integrable models. Although we use the ubiquitous MNLS system as a platform, our findings are a major step forward towards constructing excitations in generic continuum non-integrable systems.
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 impurity problems. In the accompanying paper [Y. Ashida {it et al.}, Phys. Rev. Lett. 123, 183001 (2019)], we present a concrete application of this general formalism to the analysis of the Rydberg Central Spin Model, in which the spin-1/2 Rydberg impurity undergoes spin-changing collisions in a dense cloud of two-component ultracold bosons. To illustrate new features arising from orbital motion of the bath atoms, we compare our results to the Monte Carlo study of the model with spatially localized bosons in the bath, in which random positions of the atoms give rise to random couplings of the standard central spin model.
The Bernard-LeClair (BL) symmetry classes generalize the ten-fold way classes in the absence of Hermiticity. Within the BL scheme, time-reversal and particle-hole come in two flavors, and pseudo-Hermiticity generalizes Hermiticity. We propose that these symmetries are relevant for the topological classification of non-Hermitian single-particle Hamiltonians and Hermitian bosonic Bogoliubov-de Gennes (BdG) models. We show that the spectrum of any Hermitian bosonic BdG Hamiltonian is found by solving for the eigenvalues of a non-Hermitian matrix which belongs to one of the BL classes. We therefore suggest that bosonic BdG Hamiltonians inherit the topological properties of a non-Hermitian symmetry class and explore the consequences by studying symmetry-protected edge instabilities in a simple 1D system.
We introduce non-Hermitian generalizations of Majorana zero modes (MZMs) which appear in the topological phase of a weakly dissipative Kitaev chain coupled to a Markovian bath. Notably, the presence of MZMs ensures that the steady state in the absence of decoherence events is two-fold degenerate. Within a stochastic wavefunction approach, the effective Hamiltonian governing the coherent, non-unitary dynamics retains BDI classification of the closed limit, but belongs to one of four non-Hermitian flavors of the ten-fold way. We argue for the stability of MZMs due to a generalization of particle-hole symmetry, and uncover the resulting topological phase diagram. Qualitative features of our study generalize to two-dimensional chiral superconductors. The dissipative superconducting chain can be mapped to an Ising model in a complex transverse field, and we discuss potential signatures of the degeneracy.
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