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Physical review. B./Physical review. B

Exploring tunable non-Hermitian spin models based on dissipative bosonic atoms

Yu‐Yan Fang, Zuo-Yuan Zhang, Changyue Sun, Xinye Xu, Jin‐Ming Liu

Published Feb 28, 2025• 1 citation
Publisher

Abstract

We investigate the dynamical lattice behavior of ultracold bosonic atoms loaded into an optical lattice with two-body dissipation. In the Mott insulating limit, the resulting system can emulate a variety of spin-1/2 non-Hermitian Heisenberg models such as the non-Hermitian Ising, XX, and XXZ models. These different spin models are implemented by tuning the parameter spaces of the hopping amplitude, the loss rates of atoms, and on-site interaction of strength. Moreover, utilizing the improved non-Hermitian density-matrix renormalization group (NH-DMRG) algorithm, we present the correlation functions, Bell nonlocality $(\mathcal{B})$, and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and $\mathcal{B}$. Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.

DOI
10.1103/physrevb.111.054444

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We investigate the dynamical lattice behavior of ultracold bosonic atoms loaded into an optical lattice with two-body dissipation. In the Mott insulating limit, the resulting system can emulate a variety of spin-1/2 non-Hermitian Heisenberg models such as the non-Hermitian Ising, XX, and XXZ models. These different spin models are implemented by tuning the parameter spaces of the hopping amplitude, the loss rates of atoms, and on-site interaction of strength. Moreover, utilizing the improved non-Hermitian density-matrix renormalization group (NH-DMRG) algorithm, we present the correlation functions, Bell nonlocality (B)(\mathcal{B})(B), and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and B\mathcal{B}B. Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.
We investigated the behavior of non-Hermitian bosonic gases with Hubbard interactions in one-dimensional (1D) zigzag optical lattices through the calculation of dynamic response functions. Our findings showed the existence of a non-Hermitian quantum phase transition that is dependent on the pseudo-Hermitian symmetry. The system tends to exhibit a superfluid phase when subjected to weak dissipation. While under strong dissipation, the pseudo-Hermitian symmetry of the system is partially broken, leading to a transition toward a normal liquid phase. As the dissipation increases beyond the critical threshold, the pseudo-Hermitian symmetry is completely broken, resulting in a Mott-insulator phase. We propose an experimental setup using 1D zigzag optical lattices containing two-electron atoms to realize this system. In this paper, we emphasize the key role of non-Hermiticity in quantum phase transitions and offer a theoretical framework as well as experimental methods for understanding the behavior of dissipative quantum systems, implicating significant development of quantum devices and technologies.
We investigate the ground state and quantum dynamics of an interacting bosonic chain with nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, the ground state can support Mott insulators in systems with noninteger filling due to the competition between nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from their Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be nonconserved in the non-Hermitian quantum dynamics. To systematically identify the non-Hermitian conservation law, we establish a generic approach for constructing the conserved quantities in non-Hermitian many-body quantum systems with completely real spectra, and illustrate it concretely by the system under study. The direct experimental observation of Mott insulators in systems with noninteger filling and non-Hermitian conservation laws can be performed by ultracold atoms in optical lattices with the engineered nonreciprocal hopping.
We investigate the ground state and quantum dynamics of an interacting bosonic chain with the nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, the ground state can support Mott insulators at non-integer fillings due to the competition between the nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from its Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be non-conserved in the non-Hermitian quantum dynamics. To systematically identify the non-Hermitian conservation law, we establish a generic approach for constructing the conserved quantities in non-Hermitian many-body quantum systems with completely real spectrums, and illustrate it concretely by the system under study. The direct experimental observation of the non-integer-filling Mott insulators and non-Hermitian conservation laws can be performed by ultracold atoms in optical lattices with the engineered nonreciprocal hopping.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.
We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second-order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first-order processes versus the slower second-order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. F\"olling et al., Nature (London) 448, 1029 (2007); S. Trotzky et al., Science 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic ground states by adiabatic tuning of the superlattice parameters.
Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.